Physics Flashcards
Centripetal Force (F)
= m (v^2 / r)
Points radially inward
Centripetal Acceleration (a)
= v^2 / r
SI Units
Meter, Kilogram, Second, Ampere, Mole, Kelvin and Candela
Vector
Have magnitude and direction
Is displacement vector or scalar?
Vector
Is velocity vector or scalar?
Vector
Is acceleration vector or scalar?
Vector
Is force vector or scalar?
Vector
Scalar
Have magnitude but no direction or dimension
Is speed vector or scalar?
Scalar
Are coefficients of friction vector or scalar?
Scalar
Dot product
Multiplying 2 vectors and resulting in a scalar quantity
= |A| |B| cos (theta)
Cross product
Multiplying 2 vectors and resulting in a vector quantity
= |A| |B| sin (theta)
Static friction (fs)
= 0 < fs < fk
Exists between 2 objects that are not in motion relative to one another
Can take on many values depending on the magnitude of an applied force
Kinetic friction (fk)
= us N
Exists between 2 objects that are in motion relative to one another
A constant value
Coefficient of friction
Depends on the 2 materials in contact
Which is greater: the coefficient of static friction or the coefficient of kinetic friction?
The coefficient of static friction
Newton’s first law (the law of inertia)
F = m a = 0
An object will remain at rest or move with constant velocity if there is no net force acting on it
Newton’s second law
F = m a
Any acceleration is the result of the sum of the forces acting on an object
Newton’s third law
Any 2 objects interacting with one another experience equal and opposite forces as a result of their interaction
Is free fall linear, projectile or circular motion?
Linear
Linear motion
Motion in which the velocity and acceleration are parallel or antiparallel
Projectile motion
Contains x and y components
The only force acting on the object is gravity
Inclined planes
Two dimensional motion
Dimensions are parallel and perpendicular to the surface of the plane
What are the dimensions of circular motion?
Has radial and tangential dimensions
Uniform circular motion
The only force is the centripetal force
No work is done
Potential energy is constant
In which direction does instantaneous velocity point?
Always points tangentially
Translational equilibrium
Occurs in the absence of any new forces acting on an object
The object has constant velocity and/or rotational equilibrium
Rotational equilibrium
Occurs in the absence of any new torques acting on an object
The object has constant angular velocity
Component vectors
x = v cos (theta) y = v sin (theta)
Velocity (v)
= x / t
Universal gravitation equation (F)
= (G m1 m2) / r^2
Acceleration (a)
= v / t
Kinematics (no displacement)
v = vo + (a t)
Kinematics (no final velocity)
x = (vo t) + [(a t^2) / 2]
Kinematics (no time)
v^2 = vo^2 + (2 a x)
Kinematics (no acceleration)
x = v t
Components of gravity on an inclined place
Fg, parallel = m g sin (theta)
Fg, perpendicular = m g cos (theta)
Torque (T)
= r F sin (theta)
Examples of potential energy
Gravitational, electrical, elastic, chemical
Gravitational potential energy (U)
= m g h
Conservative forces
The mechanical energy of the system remains constant
The path the object takes does not matter
Nonconservative forces
The mechanical energy of the system decreases (energy is dissipated)
The path the object takes matters (more energy is dissipated with a longer path)
Is gravity a conservative or nonconservative force?
Conservative
Are electrostatic forces conservative or nonconservative forces?
Conservative
Are elastic forces conservative or nonconservative forces?
Conservative
Is friction a conservative or nonconservative force?
Nonconservative
Is air resistance a conservative or nonconservative force?
Nonconservative
Is viscous drag a conservative or nonconservative force?
Nonconservative
Work (W)
= F d cos (theta)
= P delta V
= delta K
= delta U = q delta V
The dot product of the force and displacement vectors
W = F d cos (theta)
mechanical work
The area under a pressure-volume curve
W = P delta V
isobaric gas-piston system
The work-energy theorem
W = delta K
As the length of an inclined plane increases, what happens to the force required to move an object the same displacement?
As the length of an inclined plane increases, the amount of force necessary to perform the same amount of work (moving the object the same displacement) decreases.
As the effort decreases in a pulley system, what happens to the effort distance to maintain the same work output?
As the effort (required force) decreases in a pulley system, the effort distance increases to generate the same amount of work
What accounts for the difference between work input and work output in a system that operates at less than 100% efficiency?
The decrease in work output is due to nonconservative or external forces that generate or dissipate energy
What does it mean for a device to provide mechanical advantage?
When a device provides mechanical advantage, it decreases the input force required to generate a particular output force. Generally, this is accomplished at the expense of increased distance over which the force must act.
Total mechanical energy
= U + K
The sum of a system’s kinetic and potential energies
What happens if only conservative forces are acting on an object?
The total mechanical energy is conserved
Kinetic energy (K)
= 1/2 m v^2
Elastic potential energy (U)
= 1/2 k x^2
Conservation of mechanical energy (delta E)
= delta U + delta K = 0
Work done by nonconservative forces (W)
= delta E = delta U + delta K
Power (P)
= W / t = delta E / t
Mechanical advantage
= F out / F in
Efficiency
= W out / W in
= [(load) (load distance)] / [(effort) (effort distance)]
Why is there no work done in uniform circular motion?
The displacement vector and force vector are always perpendicular to one another; therefore, no work is done.
Why is potential energy constant in uniform circular motion?
The potential energy does not depend on the position of the object around the circle.
The zeroth law of thermodynamics
When two objects are both in thermal equilibrium with a third object, they are in thermal equilibrium with one another
No heat is flowing
Closed system
Transfers energy
Does not transfer matter
Isolated system
Does not transfer energy or matter
Open system
Transfers both energy and matter
State function
Variables independent of the path taken to achieve a particular equilibrium and are properties of a given system at equilibrium
They may be dependent on one another
Process function
Define the path (or how the system got to its state) through variables
Is heat a process or state function?
Process
Is work a process or state function?
Process
Is pressure a process or state function?
State
Is density a process or state function?
State
Is temperature a process or state function?
State
Is volume a process or state function?
State
Is enthalpy a process or state function?
State
Is internal energy a process or state function?
State
Is Gibbs free energy a process or state function?
State
Is entropy a process or state function?
State
The first law of thermodynamics (conservation of energy)
U = Q - W
In a closed system, the internal energy of a system is equal to the heat put into the system minus the work done by the system
Conduction
Heat exchange by direct molecular interactions
Convection
Heat exchange by fluid movement
Radiation
Heat exchange by electromagnetic waves
Does not depend on matter
What is entropy on a macroscopic level?
The tendency towards disorder
What is entropy statistically?
The measure of the spontaneous dispersal of energy at a specific temperature, increasing the number of available micro states for a given molecule
What is a system’s entropy’s relationship with the system’s surrounding for any thermodynamic process?
The entropy of the system and its surroundings will never decrease; it will always either remain zero or increase.
Specific heat
Heat required to bring the liquid to its boiling point
The amount of energy necessary to raise one gram of substance by one degree Celsius or one kelvin
The specific heat of water
= 1 cal / (g K)
Heat of transformation
During phase change, heat energy causes changes in the particles’ potential energy and energy distribution (entropy), but not kinetic energy
There is no change in temperature
Isothermal processes
The temperature is constant, and the change in internal energy is therefore 0
Adiabatic processes
No heat is exchanged (Q = 0)
Isobaric processes
Pressure is held constant
Isovolumetric (isochoric) processes
The volume is held constant and the work done by or on the system is 0
The second law of thermodynamics
delta S universe = delta S system + delta S surroundings > 0
In a closed system, energy will spontaneously and irreversibly go from being localized to being spread out (dispersed)
Entropy
A measure of how much energy has spread out or how spread out energy has become
Natural process
Irreversible process
Can only be reversible under highly controlled conditions
Fahrenheit (F)
= 9/5 C + 32
Kelvin (K)
= C + 273
Thermal expansion equation (delta L)
= alpha L delta T
Volume expansion equation (delta V)
= beta V delta T
Heat gained or lost (with temperature change) (q)
= m c delta T
Heat gained or lost (phase change) (q)
= m L
Entropy and heat (delta S)
= Q / T
Why does the internal energy increase in an adiabatic compression process?
Q = 0 Compression = work is done on the gas (not by the gas) Therefore, work done by the gas < 0 U = Q - W U = 0 - (- W) U = + W
Heat of fusion
Heat required to melt a solid
Heat of vaporization
Heat required to boil a liquid
How does gauge pressure (P gauge) relate to the pressure exerted by a column of fluid?
Gauge pressure = pressure exerted by a column of fluid + the ambient pressure above the fluid - atmospheric pressure
= P absolute (hydrostatic) - P atmospheric = (Po + p g z) - P atmospheric
Weight of a volume of fluid (Fg)
= density * volume * acceleration due to gravity
= p V g
SI unit for pressure
Pascals (Pa)
Is density a scalar quantity?
Yes
When does gauge pressure = fluid pressure?
When the only pressure above the fluid column is atmospheric pressure
Pressure units
mmHg, torr, atm and Pa
Cohesion
Molecules attaching to one another in a fluid
Give rise to surface tension
Adhesion
Molecules attaching to the container surface containing a fluid
What would the meniscus of a liquid that experiences equal cohesive and adhesive forces look like?
There would be no meniscus and the liquid surface would be flat
A block is fully submerged 3 inches below the surface of a fluid, but is not experiencing any acceleration. What can be said about displaced volume of fluid and the buoyant force?
Displaced volume = volume of the block
Buoyant force = weight of block = weight of fluid displaced
The block and the fluid in which it is immersed must have the same density
To determine the volume of an object by fluid displacement, must the object have a specific gravity greater than 1?
No
A fluid with a low specific gravity can be used instead of water to determine volumes of objects that would otherwise float in water
To which side of a hydraulic lift would the operator usually apply a force: the side with the larger cross-sectional area, to the side with the smaller cross-sectional area?
Smaller cross-sectional area. Because the pressure is the same on both sides of the lift, a smaller force can be applied on the smaller surface area to generate the desired pressure
Dynamic pressure
= 1/2 p v^2
Pressure associated with flow
(like kinetic energy)
Static pressure
Pressure associated with position
like potential energy
Pitot tube
A device that measures static pressure during flow to calculate speed
Viscosity
How thick a fluid is (i.e. the resistance of a fluid to flow)
A measure of the fluid’s internal friction
Laminar flow
Flow in which there are no eddies and in which streamlines roughly parallel each other
Turbulence
The presence of back flow or current eddies
How do the following concepts relate to one another: Venturi effect, Bernoulli’s equation and continuity equation?
Venturi’s effect results from combining Bernoulli’s equation and the continuity equation
What variables does flow rate depend on?
Radius of the tube, pressure gradient, viscosity and length of the tube
What does the continuity equation describe?
The relationship of flow and cross-sectional area in a tube
What does Bernoulli’s equation describe?
The relationship between height, pressure and flow
What does the Venturi effect describe?
The direct relationship between cross-sectional area and pressure
Can the continuity equation be applied to human circulation?
No, due to the presence of pulses, the elasticity of the vessels and the nature of the pressure gradient
Poiseuille’s law can be used for isolated segments
During exhalation, how does the total resistance of the encountered airways change as air leaves the alveoli to escape the nose and mouth?
Total resistance increases as the air exits the body despite the increase in the diameter of the airways. This is because there are fewer airways in parallel with each other.
How does flow in the venae cavae relate to flow in the main pulmonary artery?
In theory, there should be equal flow in the venae cavae and the main pulmonary trunk. In reality, the flow in the venae cavae is actually slightly less than that in the pulmonary trunk because some of the blood entering the right side of the heart is actually from cardiac (coronary) circulation, not systemic circulation.
Density (p)
= m / V
Specific gravity (SG)
= p / (1 g/cm^3)
Pressure (P)
= F / A
Absolute (hydrostatic) pressure (P)
= Po + p g z
= Pressure at the surface of the fluid (usually atmospheric pressure) + pressure due to the fluid itself
The sum of all the pressures at a certain point within a fluid
Pascal’s principle
P = F1 / A1 = F2 / A2 F2 = (F1 A2) / A1
Pressure applied to an incompressible fluid will be distributed undiminished throughout the entire volume of the fluid
Buoyant force (F buoyant)
= p fluid V fluid displaced g = p fluid V submerged g
Poiseuille’s law
Q = (pi r^4 delta P) / (8 nu L)
Q = flow rate r = radius of tube P = pressure nu = fluid viscosity L = length of tube
Determines the rate of laminar flow
Critical speed (vc)
= (Nr nu) / (p D)
Nr = Reynold's number nu = fluid viscosity p = fluid density D = diameter of tube = 2 r, r = radius of tube
Continuity equation (Q)
= v1 A1 = v2 A2
Similar to conservation of mass
Bernoulli’s equation
P1 + 1/2 p v1^2 + p g h1 = P2 + 1/2 p v2^2 + p g h2
(Similar to conservation of energy)
States that the sum of static pressure and dynamic pressure will be constant between any two points in a closed system
Can fluids exert perpendicular forces?
Yes
Can fluids exert shear forces?
No
Is pressure a scalar or vector quantity?
Scalar
In which direction does a gas exert pressure on a container?
Perpendicular direction
Hydraulic machines
Operate based on the application of Pascal’s principle to generate mechanical advantage
Archimedes’ principle
Governs the buoyant force
When an object is placed in a fluid, the fluid generates a buoyant force against the object that is equal to the weight of the fluid displaced by the object
In which direction does the buoyant force point?
Opposite to the direction of gravity
What happens if the maximum buoyant force is larger than the force of gravity on the object?
The object will float (only works if the object is less dense than the fluid)
What happens if the maximum buoyant force is smaller than the force of gravity on the object?
The object will sink (only works if the object is more dense than the fluid)
Viscous drag
Nonconservative force generated by viscosity
When will there be an inverse relationship between pressure and speed (Venturi effect)?
Horizontal flow
When will there be a direct relationship between cross-sectional area and pressure exerted on the walls of the tube (Venturi effect)?
In a closed system
Venturi effect
In horizontal flow, there will be an inverse relationship between pressure and speed
In a closed system, there will be a direct relationship between cross-sectional area and the pressure exerted on the walls of the tube
Is the circulatory system open, closed or isolated?
Closed
Does the circulatory system have constant flow?
No
What happens to resistance as the cross-sectional area increases?
Decreases
What motivates arterial circulation?
The heart
Does venous circulation have higher or lower volume than arterial circulation?
3 times higher
What motivates venous circulation?
Skeletal musculature and expansion of heart
What creates the pressure gradient for the respiratory and circulatory systems?
Inspiration and expiration
What is the air speed in alveoli?
Zero
Why is the speed of blood in the aorta much higher than the speed of blood through a capillary bed?
The cross-sectional area of all the capillaries added together is much greater than the cross-sectional area of the aorta
How does Bernoulli’s equation explain the upward force that permits planes to fly?
The speed of airflow is greater over the curved top of the wing, resulting in less pressure on the top of the wing and the production of a new upward force on the wind, in turn resulting in flight
When placed one meter apart from each other, which will experience a greater acceleration: one coulomb of electrons or one coulomb of protons?
Electrons will experience the greater acceleration because they are subject to the same force as the protons, but have a significantly smaller mass
Is blood a conductor or an insulator?
Conductor
Is hair a conductor or an insulator?
Insulator
Is copper a conductor or an insulator?
Conductor
Is glass a conductor or an insulator?
Insulator
Is iron a conductor or an insulator?
Conductor
Is sulfuric acid a conductor or an insulator?
Conductor
Is distilled water a conductor or an insulator?
Insulator
What is the electric field midway between two negative charges in isolation?
The electric field would be zero because the two charges are the same. In this cases, the fields exerted by each charge at the midpoint will cancel out and there will be no electric field.
What direction does a negative electrostatic force point?
Towards the source charge (because we use the perspective of a small positive test charge)
What direction does a positive electrostatic force point?
Away from the source charge (because we use the perspective of a small positive test charge)
How do distance and charge relate to electrostatic force?
Electrostatic force is directly related to the charge and related to distance by an inverse square relationship
How do distance and charge relate to electric field?
Electric field is unrelated to test charge but is still related to distance by an inverse square relationship
What creates the electric field: test charge or source charge?
Source charge
How does a change in electrical potential energy from -4 J to -7 J reflect on the stability of a system?
The system has become more stable
The relationship between electrical potential energy and Coulomb’s law
Electric potential energy is Coulomb’s law multiplied by distance
The relationship between gravitational potential energy and the universal law of gravitation
Gravitational potential energy is the universal law of gravitation multiplies by distance
How does electrical potential energy change between two particles as the distance between them increases?
If both particles have the same charge, the electric potential energy decreases and distance increases. If the two particles have opposite charges, then the electrical potential energy increases as distance increases.
Electrical potential
The ratio of a charge’s electrical potential energy to the magnitude of the charge itself
Voltage (potential difference)
A measure of the change in electrical potential between two points, which provides an indication of the tendency towards movement of a test charge in one direction or the other
How will a charge that is placed at a point of zero electrical potential move relative to a source charge?
A charge will move in such a way to minimize its potential energy. Placing a charge at a point of zero electrical potential does not indicate that there is zero potential difference, so the charge may or may not move (and if it moves, it may move towards or away from the source depending on the sign of the source charge and the test charge).
Are the units of electrical potential energy, electrical potential, potential difference (voltage) different?
Yes, electrical potential energy is in joules, while electrical potential and potential difference (voltage) are in volts
Equipotential lines
The sets of points within space at which the potential difference between any two points is zero (i.e. they have the same electric potential). This is best visualized as concentric spheres surrounding a source charge.
Electric dipole
The separation of charge within a molecule such that there is a permanent or temporary region of equal and opposite charges at a particular distance
What is the voltage between two points on an equipotential line? Will this voltage cause a charge to move along the line?
There is no voltage between two points on an equipotential line, so there will be no acceleration along the line. However, there is a potential difference between different sets of equipotential lines, which can cause particles to move and accelerate.
Why is the electrical potential at points along the perpendicular bisector of a dipole 0?
The perpendicular bisector of an electric dipole is an equipotential plane that is perpendicular to the axis of the dipole. As such, the equation V = [(k q d) / r^2] cos (theta) is necessarily equal to 0 because cos 90 = 0
What is the behavior of an electric dipole when exposed to an external electric field?
A dipole will rotate within an external field such that its dipole moment aligns with the field (angle between dipole and field is 0 degrees)
What are the requirements to have a nonzero electric field?
Charge
What are the requirements to have a nonzero magnetic field?
Moving charge
What are the requirements to have a nonzero magnetic force?
External field acting on a charge moving in any direction except parallel or antiparallel to the external field
Which would experience a larger magnetic field: an object placed five meters to the left of a current carrying wire, or an object placed at the center of a circle with a radius of five meters?
The magnetic field created by the current-carrying wires is B = (uo I) / (2 pi r)
The magnetic field created by the loop of wire is B = (uo I) / (2 r)
The magnetic field at the center of the loop must be larger because the denominator in that equation does not include pi
Cross product right hand rule
Index in the direction of velocity
Palm in the direction of magnetic field
Thumb in the direction of force
What is the direction of force if velocity points up the page, magnetic field points to the left and the particle is an electron?
Into the page
What is the direction of force if velocity points into the page, magnetic field points out of the page and the particle is a proton?
None, sin 180 = 0
What is the direction of force if velocity points to the right, magnetic field points into the page and the particle is a Proton?
Up the page
What is the direction of force if velocity points out of the page, magnetic field points to the left and the particle is an electron?
Up the page
What is the direction of force if velocity points down the page, magnetic field points to the right and the particle is a neutron?
None, q = 0
Coulomb’s law
Fe = (k q1 q2) / r^2
Give the magnitude of the electrostatic force vector between two charges
Electric field (E)
= Fe / q = (k Q) / r^2
The ratio of the force that is exerted on a test charge to the magnitude of that charge
Electric potential energy (U)
= (k Q q) / r
The amount of work required to bring the test charge from infinitely far away to a given position in the vicinity of a source charge
Electric potential (from electrical potential energy) (V)
= U / q
Electric potential (from source charge) (V)
= (k Q) / r
Voltage equation (delta V)
= Vb - Va = Wab / q
Electrical potential near a dipole (V)
= [(k q d) / r^2] cos (theta)
Dipole moment (p)
= q d
Electric field on the perpendicular bisector of a dipole (E)
= [1 / (4 pi epsilon o)] (p / r^3)
Torque on a dipole in an electric field (T)
= p E sin (theta)
Magnetic field from a straight wire (B)
= (uo I) / (2 pi r)
Magnetic field from a loop of wire (B)
= (uo I) / (2 r)
Magnetic force on a moving point charge (Fb)
= q v B sin (theta)
Magnetic force on a current-carrying wire (Fb)
= I L B sin (theta)
SI unit for charge
Coulomb
Charge on a proton and an electron
1.60e-19 C
Conductor
Allow the free and uniform passage of electrons when charged
Insulators
Resist movement of charge and will have localized areas of charge that do not distribute over the surface of the material
Where does the electrostatic force vector point?
Along the line connecting the centers of the two charges
Does every charge generate an electric field?
Yes
Can the electric field exert forces on other charges?
Yes
Field lines
Represent electric field vectors
Radiate outward from positive source charges
Radiate inward towards negative source charges
In which direction does a positive test charge move?
In the direction of field lines
In which direction does a negative test charge move?
In the opposite direction of field lines
How does the electrical potential energy of a system increase?
When two unlike charges move away from each other or when two like charges move towards each other
How does the electrical potential energy of a system decrease?
When two unlike charges move towards each other or when two like charges move further apart
Do different points in the space of an electric field surrounding a source charge have different electrical potential values?
Yes
Is voltage path dependent?
No
Is voltage a state or process function?
State
In which direction do positive test charges move?
High potential to low potential
In which direction do negative test charges move>
Low potential to high potential
In which direction to equipotential lines point?
Perpendicular to electric field lines
Is work done when a charge is moved from one equipotential line to another?
Yes, but it is independent of the pathway taken between the lines
Is work done when a charge moves from one point to another on the same equipotential line?
No
How is an electric dipole generated?
Two charges of opposite signs are separated by a fixed distance d
Will a dipole experience a net torque in an external electric field?
Yes, until it is aligned with the field
How are magnetic fields created?
Magnets and moving charges
SI unit for magnetic field
Tesla
Diamagnetic materials
Do not possess unpaired electrons and are slightly repelled by a magnet
Paramagnetic materials
Possess unpaired electrons and become weakly magnetic in an external magnetic field
Ferromagnetic materials
Possess unpaired electrons and become strongly magnetic in an external magnetic field
In which direction do field lines in magnets point?
From the North Pole to the South Pole
Magnetic fields in current-carrying wires
Concentric circles surrounding the wire
When do point charges undergo uniform circular motion?
In uniform magnetic fields, wherein the centripetal force is the magnetic force acing on the point charge
Lorentz force
The sum of the electrostatic and magnetic forces acting on a body
Magnetic field right hand rule
Thumb tangent to circle in direction of charge motion
Curled fingers in direction of magnetic field
A dipole is placed in an electric field and is allowed to come to equilibrium. Why does the dipole experience no rotational or linear movement when the direction of the electric field is suddenly reversed?
Torque is a function of both force applied and the angle at which it is applied. A dipole placed in an electric field will experience a torque until it comes to rest oriented within the field, at which point the angle between the plane of the dipole and the electric field is 0 degrees. Once this point if reached, inverting the electric field has no impact on the dipole because it will now have an angle of 180 degrees, the sine of which is still 0. Note, however, that is is an unstable setup; any deviation in the dipole from its rest position will immediately result in torque on the dipole and force it to realign with the new field.
Current
The movement of positive charge through a conductive material over time from the high-potential end to the low-potential end
Voltage
A potential difference between two points
Electromotive force (emf)
The potential difference of the voltage source for a circuit, usually a battery
Conductivity
The reciprocal of resistance and is a measure of permissiveness to current flow
In a circuit, are the number of electrons entering a point and leaving that point the same?
Yes
Is the sum of voltage sources in a circuit always equal to the sum of voltage drops in that circuit?
No
Current unit
Amperes = C / s
Amperes
= C / s
Voltage unit
Volts = J / C
Volts
= J / C
Electromotive force (emf) unit
Volts = J / C
Conductivity unit
Siemens (S)
Kirchhoff’s junction rule
The number of electrons (currents) entering a point and leaving that same point are the same
I into junction = I leaving junction
How does adding a resistor in series affect the total resistance of a circuit that has resistors in series?
Increase total resistance
How does adding a resistor in parallel affect the total resistance of a circuit that has resistors in series?
Decrease total resistance
What four physical quantities determine the resistance of resistor?
Resistivity, length, cross-sectional area and temperature
How does power relate to current, voltage and resistance?
P = I V = I^2 R = V^2 / R
Will the internal resistance of a battery lower the amount of current it can provide?
Yes
The internal resistance will lower the available voltage for the circuit. Lowering the available voltage will also lower current for any given resistance.
How does removing a resistor in series affect the total resistance of a circuit that has resistors in series?
Decrease total resistance
How does adding a resistor in series affect the total resistance of a circuit that has resistors in series?
Increase total resistance
Assuming the plates are attached by a conductive material, how does a capacitor behave after the voltage source has been removed from a circuit?
The capacitor discharges, proving a current in the opposite direction of the initial current
How does a dielectric material impact capacitance?
Increase capacitance
How does a dielectric material impact voltage?
Decrease voltage if the capacitor is isolated when the dielectric is introduced
Constant voltage if the capacitor is in a circuit when the dielectric is introduced because it is dictated by the voltage source
How does a dielectric material impact charge?
If the capacitor is isolated, the stored charge will remain constant because there is no additional source of charge
If the capacitor is in a circuit, the stored charge will increase
How does adding a capacitor in series affect the total capacitance of a circuit that has capacitors in series?
Decrease total capacitance
How does removing a capacitor in series affect the total capacitance of a circuit that has capacitors in series?
Increase total capacitance
How does adding a capacitor in parallel affect the total capacitance of a circuit that has capacitors in series?
Increase total capacitance
How does removing a capacitor in parallel affect the total capacitance of a circuit that has capacitors in series?
Decrease total capacitance
What physical qualities contribute to the capacitance of a capacitor?
Surface area, distance and dielectric constant
What does an ammeter measure?
Current
Where is an ammeter placed?
In series with the point of interest
What is the ideal resistance for an accurate ammeter reading?
0
What does a voltmeter measure?
Voltage drop (potential difference)
Where is a voltmeter placed?
Parallel with circuit element of interest
What is the ideal resistance for an accurate voltmeter reading?
Infinit amount
What does an ohmmeter measure?
Resistance
Where is an ohmmeter placed?
Two points in series with circuit element of interest
Inserted around a resistive element to measure resistance
Self-powered
What is the ideal resistance for an accurate voltmeter reading?
0
Should a voltmeter and an ammeter be placed in the same circuit?
They can be
Voltmeters and ammeters are designed to have minimum impact on a circuit, thus they can be used together
Current (I)
= Q / delta t
Kirchhoff’s loop rule
V source = V drop
In a closed loop, the sum of voltage sources is always equal to the sum of voltage drops
Resistance (R)
= (p L) / A
The opposition to the movement of electrons through a material
Ohm’s law
V = I R
For a given resistance, the magnitude of the current through a resistor is proportional to the voltage drop across the resistor
Voltage and cell emf (V)
= E cell - (I r internal)
Electric power (P)
= IV = I^2 R = V^2 / R
Voltage drop across circuit elements (series)
V total = V1 + V2 + …
Equivalent resistance (series)
R total = R1 + R2 + …
Voltage drop across circuit elements (parallel)
V total = V1 = V2 = …
Equivalent resistance (parallel)
1 / R total = (1 / R1) + (1 / R2) + …
Capacitance (C)
= Q / V
Capacitance based on parallel plate geometry
C = epsilon o (A / d)
In parallel plate capacitors, capacitance is determined by the area of the places and the distance between the plates
Electric field in a capacitor (E)
= V / d
Potential energy of a capacitor (U)
= 1/2 CV^2
Capacitance with a dielectric material (C’)
= k C
Equivalent capacitance (series)
1 / C total = (1 / C1) + (1 / C2) + …
Equivalent capacitance (parallel)
C total = C1 + C2 + …
Can current flow in non-conductive materials?
No
Current only flows in conductive materials
Metallic conduction
Relies on uniform movement of free electrons in metallic bonds
Electrolytic conduction
Relies on the ion concentration of a solution
Insulators
Materials that do not conduct current
Kirchhoff’s laws
Explain conservation of charge and energy
Resistor
Conductive martial with a moderate amount of resistance that slow down electrons without stopping them
Across each resistor in a circuit, a certain amount of power is dissipated, which is dependent on the current through the resistor and the voltage drop across the resistor
Capacitor
Has the ability to store and discharge electrical potential energy
Dielectric materials
Insulators placed between the plates of a capacitor that increase capacitance by a factor equal to the material’s dielectric constant, k
Wave speed
The rate at which a wave transmits the energy or matter it is carrying
The product of frequency and wavelength
Frequency
A measure of how often a waveform passes a given point in space
Measured in Hz
Angular frequency
The same as frequency: a measure of how often a wave form passes a given point in space
Measured in radians per second
Period
The time necessary to complete a wave cycle
Equilibrium position
The point with zero displacement in an oscillating system
Amplitude
The maximal displacement of a wave from the equilibrium position
Traveling wave
Have nodes and antinodes that move with wave propagation
Have continuously shifting maximum and minimum displacement
Standing wave
Have defined nodes and antinodes that do not move with wave propagation
What happens if two waves that are perfectly in phase collide?
The amplitude of the resulting wave is equal to the sum of the amplitudes of the interfering waves
Are sound waves transverse or longitudinal waves?
Longitudinal waves
How does applying a force at the natural frequency of a system change the system?
The object will resonate because the force frequency equals the natural (resonant) frequency. The amplitude of the oscillation will increase.
What happens if two waves that are perfectly out of phase collide?
The amplitude of the resulting wave is the difference of the amplitudes of the interfering waves
How is sound produced and transmitted?
Sound is produced by mechanical vibrations, generated by solid objects and fluids
Sound is propagated as longitudinal waves in matter
To which property of a sound wave does amplitude correspond?
Volume (sound level) = intensity
To which property of a sound wave does frequency correspond?
Pitch
If two objects are traveling towards each other, how does the apparent frequency differ from the original frequency?
It is larger
If two objects are traveling away from each other, how does the apparent frequency differ from the original frequency?
It is smaller
If one objects is following another, how does the apparent frequency differ from the original frequency?
It could be higher, lower or equal to the original frequency depending on the relative speeds of the detector and the source
Can sound propagate in a vacuum?
No
What phenomenon can be detected or treated using ultrasound?
Prenatal screening, diagnose gallstones, breast and thyroid masses, and blood clots, needle guidance in biopsy, dental cleaning, treating deep tissue injuries, kidney stones, small tumors, cataracts, etc.
Wavelength of a pipe open in both ends (i.e. open pipe) (lambda)
= 2 L / n
Wavelength of a pipe open in one end (i.e. closed pipe) (lambda)
= 4 L / n
Wavelength of a pipe closed on both ends (i.e. string) (lambda)
= 2L / n
Wave speed equation (v)
= frequency * wavelength = f * lambda
Period equation (T)
= 1 / frequency = 1 / f
Angular frequency (omega)
= 2 pi frequency = (2 pi) / period
= 2 pi f = (2 pi) / T
Speed of sound equation (v)
= square root (B / rho)
Doppler effect (f’)
= f [(v +/- vd) / (v -/+ vs)]
Intensity (I)
= P / A = Power / Area
Sound level (beta)
= 10 log (I / Io)
Change in sound level (beta f)
= beta i + 10 log (If / Ii)
Frequency of a standing wave in strings and open pipes (f)
= n v / 2 L
Frequency of a standing wave in closed pipes (f)
= n v / 4 L
Transverse waves
Have oscillations of wave particles perpendicular to the direction of wave propagation
Longitudinal waves
Have oscillations of wave particles parallel to the direction of wave propagation
Displacement in a wave
Refers to how far a point is from the equilibrium position, expressed as a vector quantity
Amplitude in a wave
The magnitude of its maximal displacement
Crest
The maximum point of a wave (point of most positive displacement)
Trough
The minimum point of wave (point of most negative displacement)
Wavelength in a wave
The distance between two crests or two troughs
Constructive interference
Occurs when waves are exactly in phase with each other
The amplitude of the resultant wave is equal to the sum of the amplitudes of the two interfering waves
Destructive interference
Occurs when waves are exactly out of phase with each other
The amplitude of the resultant wave is equal to the difference in amplitude between the two interfering waves
Partially constructive and partially destructive interference
Occur when two waves are not quite perfectly in or out of phase with each other
The displacement of the resultant wave is equal to the sum of the displacements of the two interfering waves
How are standing waves produced?
By constructive and destructive interference of two waves of the same frequency traveling in opposite directions in the same space
Antinodes
Points of maximum oscillation
Nodes
Points where there is no oscillation
Resonance
The increase in amplitude that occurs when a periodic force is applied at the natural (resonant) frequency of an object
Damping (attenuation)
A decrease in amplitude (and therefore intensity) over distance and energy is lost due to applied or nonconservative forces
Where does sound propagate the fastest?
In solids
Where does sound propagate the slowest?
In gases
What happens to the speed of sound as the medium’s density increases?
Decreases
Doppler effect
A shift in perceived frequency of a sound compared to the actual frequency of the emitted sound when the source of the sound and its detector are moving relative to one another
How do shock waves (sonic booms) form?
When the source is moving at or above the speed of sound
In what kind of pipe is the length of the pipe equal to some multiple of half-wavelengths?
Strings (pipes closed at both ends) and open pipes (pipes open at both ends)
In what kind of pipe is the length of the pipe equal to some odd multiple of quarter-wavelengths?
Closed pipes (pipes closed at only one end)
How do ultrasound machines calculate distance?
Based on the travel time of the reflected sound
When do shock waves have the greatest impact?
When the source is traveling at exactly the speed of sound
Surface area of a sphere
= 4 pi r^2
Log 100
= 2
Order the types of electromagnetic radiation from highest energy to lowest energy
Gamma-rays > x-rays > ultraviolet > visible light > infrared > microwaves > radio
What properties of light follow the same trend as energy?
Frequency : as energy increases so does frequency
Are light waves longitudinal or transverse waves?
Transverse
Why are light waves transverse?
Because the direction of propagation is perpendicular to the direction of oscillation
What are the boundaries of the visible spectrum?
400 nm - 700 nm
How does the range of the visible spectrum compare to the range of the full electromagnetic spectrum?
It is very small since the entire electromagnetic spectrum ranges from 0 to 10^9 m
What properties of light follow the opposite tend as energy?
Wavelength : as energy increases, wavelength decreases
o is positive in a mirror
Object is in front of the mirror
i is positive in a mirror
Image is in front of the mirror (real image)
r is positive in a mirror
Mirror is concave (converging)
f is positive in a mirror
Mirror is concave (converging)
m is positive in a mirror
Image is upright (erect)
o is negative in a mirror
Object is behind the mirror
i is negative in a mirror
Image is behind the mirror (virtual image)
r is negative in a mirror
Mirror is convex (diverging)
f is negative in a mirror
Mirror is convex (diverging)
m is negative in a mirror
Image is inverted
o is positive in a lens
Object is on the same side of lens as light source
i is positive in a lens
Image is on opposite side of lens from light source (real image)
r is positive in a lens
Lens is convex (converging)
f is positive in a lens
Lens is convex (converging)
m is positive in a lens
Image is upright (erect)
o is negative in a lens
Object is on opposite side of lens from light source
i is negative in a lens
Image is on same side of lens as light source
r is negative in a lens
Lens is concave (diverging)
f is negative in a lens
Lens is concave (diverging)
m is negative in a lens
Image is inverted
Real image in mirrors
Image that is in front of the mirror
Concave mirror
Converging mirror
Virtual image in mirrors
Image that is behind the mirror
Convex mirror
Diverging mirror
Real image in lenses
Image is on the opposite side of the lens from the light source
Convex lens
Converging lens
Virtual image in lenses
Image is on the same side of the lens as the light source
Concave lens
Diverging
Is the incident angle always measured with respect to the normal?
Yes
Describe the bending of light when moving from a medium with low refractive index to one with high refractive index
The light will bend towards the normal
Describe the bending of light when moving from a medium with high refractive index to one with low refractive index
The light will bend away from the normal
Dispersion
The tendency for different wavelengths of light to experience different degrees of refraction in a medium, leading to separation of light into the visible spectrum (a rainbow)
Involves the breaking up go polychromatic light into its component wavelengths, because the degree of refraction depends on the wavelength
Aberration
Whether spherical or chromatic, is the alteration or distortion of an image as a result of an imperfection in the optical system
What are the two mathematical relationships between image distance and object distance?
1 / f = 1 / o + 1 / i
m = - i / o
What happens if the incident angle is larger than the critical angle?
Total internal reflection will occur
How does the diffraction patter for a single slit differ from a slit with a thin lens?
Diffraction through a single slit does not create characteristic fringes when projected on a screen, although the light does spread out. When a lens is introduced into the system, the additional refraction of light causes constructive and destructive interference, creating fringes.
What wave phenomenon do diffraction fringes result from?
Constructive and destructive interference between light rays
How does double-slit diffraction and interference differ from single-slit diffraction?
The image formed during double0slit diffraction contains fringes because light rays constructively and destructively interfere. A single slit forms an image of a wide band of light, spread out from its original beam.
Are the maxima in diffraction patterns always equidistant between two minima?
Yes
Maxima and minima alternate in a diffraction pattern. A maximum is equidistant between two minima, and a minimum is equidistant between two maxima.
Plane-polarized light
Contains light waves with parallel electric field vectors
Circularly polarized light
Selects for a given amplitude and has a continuously rotating electric field direction
All the light rays have electric fields with equal intensity
How does the application of a policed filter impact the wavelength of light passing through the filter?
Plane polarization has no effect on the wavelength, or frequency, or speed of light. Polarization does affect the amount of light passing through medium and light intensity
Speed of light from frequency and wavelength (c)
= f * lambda
Law of reflection
Theta 1 = theta 2
Optics equation
1 / f = 1 / o + 1 / i = 2 / r
Magnification (m)
= - i / o
Index of refraction (n)
= c / v
Snell’s law
n1 sin (theta 1) = n2 sin (theta 2)
Critical angle (theta c)
= sin^-1 (n2 / n1)
Lensmaker’s equation
1 / f = (n - 1) (1 / r1 - 1 / r2)
Power (P)
= 1 / f
Focal length of multiple lens system
1 / f = 1 / f1 + 1 / f2 + …
Power of multiple lens system
P = P1 + P2 + …
Magnification of multiple lens system
m = m1 * m2 * …
Positions of dark fringes in slit-lens setup
alpha sin (theta) = n * lambda
Positions of dark fringes in double-slit setup
d sin (theta) = (n + 0.5) * lambda
Are electromagnetic waves transverse or longitudinal waves?
Transverse
Electromagnetic waves
Transverse waves that consist of an oscillating electric field and an oscillating magnetic field, perpendicular to one another and to the direction of wave propagation
Electromagnetic spectrum
The range of frequencies and wavelengths found in electromagnetic waves
Violet wavelength
400 nm
Red wavelength
700 nm
Reflection
The rebounding of incident light waves at the boundary of a medium
Law of reflection
The incident angle will equal the angle of reflection, as measured from the normal
Spherical mirrors
Have centers and radii of curvature as well as focal points
What kind of images do concave (converging) mirrors produce?
Real and inverted OR virtual and upright, depending on the placement of the object relative to the focal point
What kind of images do convex (diverging) mirrors produce?
Virtual and upright images
What kind of images do plane mirrors produce?
Virtual and upright images behind the mirror (these images are the same size as the objects)
Plane mirrors
Have infinite radii or curvature
Refraction
The bending of light as it passes from one medium to another
What changes the speed of light?
Index of refraction
What causes refraction?
The change in the speed of light as it passes from one medium into another
What does the amount of refraction depend on?
Wavelength
What causes dispersion of light through a prism?
The fact that the amount of refraction depends on the wavelength of the light involved
Snell’s law (the law of refraction)
There is an inverse relationship between the index of refraction and sine of the angle of refraction (measured from the normal)
Total internal reflection
Occurs when light cannot be refracted out of a medium and is instead reflected back inside the medium. This happens when light moves from a medium with a higher index of refraction to a medium with a lower index of refraction with a high incident angle
Critical angle
The minimum incident angle at which total internal reflection occurs
Where is the focal point in a thin symmetrical lens?
On both sides of the lens
What kind of images do convex (converging) lenses produce?
Real and inverted OR virtual and upright
What kind of images do concave (diverging) lenses produce?
Virtual and upright images
When is it important to use the lenasmaker’s equation?
When working with lenses of non-negligible thickness
Diffraction
The bending and spreading out of light waves as they pass through a narrow slit
It may produce a large central light fringe surrounded by alternating light and dark fringes with the addition of a lens
Does interference support the wave theory of light?
Yes
Young’s double-slit experiment
Shows the constructive and destructive interference of waves that occur as light passes through parallel slits, resulting in minima (dark fringes) and maxima (bright fringes) of intensity
How is plane-polarized light created?
By passing unpolarized light through a polarizer
How is circularly polarized light created?
By exposing unpolarized light to special pigments or filters
Where to plane mirrors project the images?
As far away as the object is
In concave mirror, if the object is placed at the center of the mirror’s curvature, what is the object distance?
2f
What changes as light rays travel from one medium to another?
The wavelength and speed
What remains constant as light rays travel from one medium to another?
The frequency and period
A source of light passes through three plane polarizers. The first two polarizers are in the same direction, while the third is rotated 90 degrees with respect to the second polarizer. What happens to the light at the third polarizer?
It will not pass through the third polarizer because all the light rays will be oriented in the direction dictated by the first and second polarizers.
What does the degree of refraction depend on?
Wavelength
Polarization
The alignment of the electric field component of light waves
Where is a real image projected in a convex lens system?
Farther than the focal point
Where is a virtual image projected in a convex lens system?
Closer than the focal point (i.e. between the lens and the focal point)
For a single mirror or lens system, is the real image inverted or erect?
Inverted
For a single mirror or lens system, is the virtual image inverted or erect?
Erect
Sin (45 degrees)
= 0.707 = square root of 2 / 2
What happens to the light passing through a narrow opening if the opening narrows?
The light waves spread even more
What happens to the light passing through a narrow opening and a lens if the opening narrows?
The central maximum (the brightest and most central fringe) becomes wider
What happens to the light passing through a narrow opening if a lens is introduced?
A pattern consisting of alternating bright and dark fringes can be observed
How does the work function relate to the energy necessary to emit an electron from a metal?
The work function describes the minimum amount of energy necessary to emit an electron. Any additional energy from a photon will be converted to excess kinetic energy during the photoelectric effect
What does the threshold frequency depend upon?
The chemical composition of a material (that is, the identity of the metal)
What electrical phenomenon results from the application of the photoelectric effect?
The accumulation of moving electrons creates a current during the photoelectric effect
What determines the absorption spectrum of a single atom?
The energy differences between ground-state electrons and higher-level electron orbits determine the frequencies of light a particular material absorbs (its absorption spectrum)
Can small changes in chemical structure (e.g. protonation, deprotonation, change in oxidation state, change in bond order) impact light absorption and emission patterns?
Yes
During which electronic transitions is photon emission most common?
When electrons transition from a higher-energy state to a lower-energy state
What causes fluorescence?
Energy transition
Fluorescence
A special stepwise photon emission in which an excited electron returns to the ground state through one or more intermediate excited states
Each step has less energy than the absorbed light and is within the visible range of the electromagnetic spectrum
When can materials release photons of light in the visible range?
When the energy transition is smaller than the initial energy absorbed
Strong nuclear force
One of the four primary forces
Provides the adhesive force between the nucleons (protons and neutrons) within the nucleus
Mass defect
The apparent loss of mass when nucleons come together, as some of the mass is converted into energy during nuclear fusion
The difference between the mass of the unbounded nucleons and the mass of the bonded nucleons within the nucleus
Binding energy
Energy holding nucleons together
What are the four fundamental forces of nature?
Gravitational force, electrostatic force, stone nuclear forces and weak nuclear forces
How does the mass defect relate to the binding energy?
There is a transformation of nuclear matter to energy with a resultant loss of matter
E = m c^2
Do both nuclear fission and nuclear fusion release energy?
Yes
What is the size of reactant particles in nuclear fission?
Large (actinides and lanthanides)
What is the size of reactant particles in nuclear fusion?
Small (H and He)
What is the change in nuclear mass during a reaction with nuclear fission?
Decrease
What is the change in nuclear mass during a reaction with nuclear fusion?
Increase
What kind of particle does alpha decay emit?
He (2, 4)
What kind of particle does beta-negative decay emit?
1 electron (in the products) and antineutrino
What kind of particle does beta-positive decay emit?
1 positron (in the products) and neutrino
What kind of particle does gamma decay emit?
Neutron, gamma ray
What kind of particle does electron capture emit?
1 electron absorbed from the inner shell (in the reactants)
delta Z of alpha decay
-2
delta Z of beta-negative decay
+1
delta Z of beta-positive decay
-1
delta Z of gamma decay
0
delta Z of electron capture
-1
delta A of alpha decay
-4
delta A of beta-netative decay
0
delta A of beta-positive decay
0
delta A of gamma decay
0
delta A of electron capture
0
How many half-lives are necessary for the complete decay of a radioactive sample?
Because the amount remaining is cut in half after each half-life, the portion remaining will never quite reach zero. This is mostly a theoretical consideration; “all” of a sample is considered to have decayed after 7 to 8 half-lives.
Which type of nuclear decay could be detected in an atomic absorption spectrum?
Because gamma radiation produces electromagnetic radiation (rather than nuclear fragments), it can be detected on an atomic absorption spectrum
Energy of a photon of light (E)
= h f
Maximum kinetic energy of an electron in the photoelectric effect (K max)
= h f - W
Work function (W)
= h fT
Mas defect and energy (E)
= m c^2
Nuclear decay (general form)
A. A’
X —>. Y + emitted decay particle
Z. Z’
Alpha decay
A. A - 4. 4
X —>. Y + alpha
Z. Z - 2. 2
Beta-negative decay
A. A
X —>. Y + beta-
Z. Z + 1
Beta-positive decay (positron emission)
A. A
X —>. Y + beta+
Z. Z - 1
Gamma decay
A. A
X* —>. X + gamma
Z. Z
Electron capture
A. A
X + e- —>. Y
Z. Z - 1
Rate of nuclear decay
delta n / delta t = - lambda n
Exponential decay (n)
= no e^(- lambda t)
Decay constant (lambda)
= ln 2 / T1/2 = 0.693 / T1/2
ln 2
= 0.693
Photoelectric effect
The ejection of an electron from the surface of a metal in response to light
Occurs when a photon of sufficiently high energy stakes an atom with a sufficiently low work function
Threshold frequency
The minimum light frequency necessary to eject an electron from a given metal
Work function
The minimum energy necessary to eject an electron from a given metal
What does the value of the work function depend on>
The metal used
Planck’s constant (h)
= 6.626e-34 m^2 kg / s
What happens to the kinetic energy the ejected electron can posses if the energy of the incident photon above the work function increases?
Increases
Current
Created by the ejected electrons
What is the magnitude of current proportional to?
The intensity of the incident beam of light
Bohr model of the atom
Electron energy levels are stable and discrete, corresponding to specific orbits
An electron can jump from a lower-energy to a higher-energy orbit by absorbing a photon of light of the same frequency as the energy difference between the orbitals
When an electron falls from a higher-energy to a lower-energy orbit, it emits a photon of light of the same frequency as the energy difference between the orbits
How may the absorption spectra be impacted?
By small changes in molecular structure
Nuclear binding energy
The amount of energy that is released when nucleons bind together
Nucleons
Protons and electrons
How is the atom’s nucleus stabilized?
With more binding energy per nucleon release
Do unbounded constituents have more or less energy than bonded constituents?
More
Do unbounded constituents have more or less energy than bonded constituents?
More
Fusion
Occurs when small nuclei combine into larger nuclei
Fission
Occurs when a large nucleus splits into smaller nuclei
Radioactive decay
The loss of small particles from the nucleus
Alpha decay
The emission of an alpha particle, which is a helium nucleus
Beta-negative decay
The decay of a neutron into a proton, with emission of an electron and an antineutrino
Beta-positive decay (positron emission)
The decay of a proton into a neutron, with emission of a positron and a neutrino
Gamma decay
The emission of a gamma ray, which converts a high energy nucleus into a more stable nucleus
Electron capture
The absorption of an electron from the inner shell that combines with a proton in the nucleus to form a neutron
Half-life
The amount of time required for half of a sample of radioactive nuclei to decay
Exponential decay
The rate at which radioactive nuclei decay is proportional to the number of nuclei that remain
Does ultraviolet light have higher or lower frequency than visible light?
Higher
Does ultraviolet light have higher or lower wavelength than visible light?
Lower
Does ultraviolet light have higher or lower energy than visible light?
Higher
How is the number of incident photons affected with respect to intensity?
It increases as the intensity increases (provided that the frequency of the light remains above the threshold)
How is the number of electrons ejected affected with respect to the number of incident photons?
It increases as the number of incident photons increases (provided that the frequency of the light remains above the threshold)
How is current affected with respect to the number of electrons ejected?
It increases as the number of electrons ejected increases (provided that the frequency of the light remains above the threshold)
The frequency of light will determine the kinetic energy of the ejected electrons under what conditions?
Only when the frequency of light is above the threshold frequency
The intensity of the light will determine the number of electrons ejected per time (the current) under what conditions?
Only when the frequency of light is above the threshold frequency
Mass defect calculation
= the mass of each of the protons and neutrons in the unbound state added together minus the mass of the formed (bound) nucleus
Binding energy (E)
= m c^2
A graph of an exponential decay process is created. The y-axis is the natural logarithm of the ratio of the number of intact nuclei at a given time to the number of intact nuclei at time t=0. The x-axis is time. What does the slope of such a graph represent?
- lambda
The expression:
n = no e^(-lambda t)
is equivalent to:
n / no = e^(-lambda t)
Taking the natural logarithm of both sides, we get:
ln (n / no) = -lambda t
From this expression, plotting ln (n / no) v. t will give a straight line with a slope of - lambda
When rounding two numbers containing decimals, in which direction should each number go for multiplication?
Adjust the two decimals in opposite directions : if one number is rounded up, the other number should be rounded down
When rounding two numbers containing decimals, in which direction should each number go for division?
Adjust the two decimals in the same direction : if one number is rounded up, the other number should also be rounded up
Simplify: (a + b)^2
a^2 + 2ab + b^2
Simplify: (a^2 + 2a^2) / 5a^3
3a^2 / 5a^3 = 3 / 5a
Simplify: log a (a)
1
Simplify: log (a^3) - log (a)
log (a^3 / a) = log (a^2) = 2 log a
Estimate: square root (392)
Answer is between: square root (361) and square root (400)
Answer is between 19 and 20
= square root (4) * square root (49) * square root (2)
= 2 * 7 * 1.4
= 14 * 1.4
= 19.6 (actual 19.8)
Estimate: log (7,426,135,420)
= log (7.4e9)
= 9 + 0.74
= 9.74 (actual 9.87)
During vector addition, how is the angle of the resultant calculated?
The value of a trigonometric function calculated from the dimensions of the resultant vector is used in the inverse tangent function to calculate the resultant vector angle
How is sine calculated given the dimensions of a right triangle?
Opposite / Hypotenuse
How is cosine calculated given the dimensions of a right triangle?
Adjacent / Hypotenuse
How is tangent calculated given the dimensions of a right triangle?
Opposite / Adjacent
Is it only the angles in right triangles that have characteristic values of the trigonometric functions?
No
While calculating the values or sine, cosine and tangent is more complicated in a triangle that does not contain a right angle, all possible angles do still have characteristic trigonometric values
How can angles be calculated?
With inverse trigonometric ratios
What does it mean for two variables to have a direct relationship?
As one variable increases, so does the other
As one variable decreases, so does the other
What does it mean for two variables to have an inverse relationship?
As one variable increases, the other decreases
As one variable decreases, the other increases
Substitution
- Solve one equation for one variable in terms of the other
2. Substitute this expression into the other equation
Setting equations equal
(A modified version of substitution)
Solve both equations for the same variable and set them equal to each other
Elimination
- Multiply or divide one (or both) equations so that the coefficient in front of one of the variables is the same in both equations
- Add or subtract the equations to eliminate one of the variables
x^0
= 1
x^a * x^b
= x^(a+b)
x^a / x^b
= x^(a-b)
(x^a)^b
= x^(ab)
(x/y)^a
= x^a / y^a
x^-a
= 1 / x^a
x^(a/b)
= b square root (x^a)
square root 2
= 1.4
square root 3
= 1.7
log a (1)
= 0
log a (a)
= 1
log (a x b)
= log a + log b
log (a / b)
= log a - log b
log (a^b)
= b log (a)
log (1 / a)
= - log (a)
log (x)
= ln (x) / 2.303
log (n x 10^m)
= m + 0.n
sin (theta)
= opposite / hypotenuse = a / c
= cos (90 - theta)
cos (theta)
= adjacent / hypotenuse = b / c
tan (theta)
= opposite / adjacent = a / b
Fahrenheit (F)
= 9/5 C + 32
Kelvin (K)
= C + 273
In measurements, is the last digit considered a significant figure?
No
Significant figures in addition
The answer must have the same number of decimal places as the number with the fewest number of decimal places
Significant figures in subtraction
The answer must have the same number of decimal places as the number with the fewest number of decimal places
Significant figures in multiplication
The answer must have the same number of significant figures as the number with the fewest number of significant figures
Significant figures in division
The answer must have the same number of significant figures as the number with the fewest number of significant figures
What is the inverse of exponents?
Logarithms
What is the base of natural logarithms?
e
What is the base of common logarithms?
10
2^3 = 8 in log form
log base 2 of 8 = 3
pH equation
= pKa + log ([A-] / [HA])
log (1)
= 0
How can the value of a natural logarithm be converted to the value of a common logarithm?
The normal logarithm is divided by a constant
|sin (theta) x cos (theta)|
|sin (theta)| + |cos (theta)|
sin (theta) / cos (theta)
= tan (theta)
tan (90)
= undefined
What forces are acting on an object in uniform circular motion?
Centripetal force
Errors or biases during publication of results are most likely to affect which stages of the scientific method?
Errors during publication of current studies adversely affect the quality of future experimentation by providing an incomplete or flawed research base. Without accurate resources, subsequent hypotheses are likely to be flawed.
An experiment with an improperly tared (zeroed) mass balance would suffer from what type of error?
Inaccuracy error
What is the purpose of a control during experiments?
Controls in experiments help to establish causality by demonstrating that the outcome does not occur in the absence of an intervention
What characteristics of experimental research would be reduced in the absence of a control?
Controls are used to keep the manipulations of different systems as similar as possible, or as a known standard against which to judge an experimental manipulation. WiWithout controls, it is far more difficult to establish causality.
Can a researcher who fails to demonstrate temporality still provide evidence for a causal relationship by satisfying the rest of Hill’s criteria?
No
Temporality is the only necessary criterion from Hill’s criteria. If temporality is not satisfied, the relationship cannot be said to be causal. The addition of other criteria increases the probability of a causal relationship, assuming that temporality has not been invalidated.
Observational research
Does not involve manipulation of the subject’s environment
Experimental research
Involves manipulation of the subject’s environment
Bias
A systematic (unidirectional) error that occurs during the selection of subjects or the measurement and collection of data
Confounding
An error that occurs during data analysis, in which an association is erroneously drawn between two variables because of a shared connection to a third variable
Which is more conclusive: observational or experimental research?
Experimental research
Which is more subjective: observational or experimental research?Less conclusive and more subjective than experimental research
Observational research
Autonomy in medical ethics
The right of an individual to make decisions on his or her own behalf and to have those decisions be respected
Respect for persons in research ethics
Requires honesty, confidentiality, informed consent, and freedom from coercion
During study design, a company wishing to market a drug to severe diabetics proposes to enroll only mild diabetics. Which principle of research ethics is the company violating? Are there any research concerns in this proposed study besides ethics?
The company is violating the principle of justice by choosing participants that are not part of the target population. The company is also introducing selection bias.
Coercive influence
The subject loses autonomy to make the decision to participate
Monetary compensation
Does not impact the decision to participate
What are some populations that must receive special consideration for coercion?
Children, pregnant women and prisoners
Internal validity
The tendency of the same experiment to produce the same results when repeated, and provides support for causality
The identification of causality in a study between the independent and dependent variables
External validity (i.e. generalizability)
The ability to take the information generated during research and apply it to a larger group
Why might small samples provide insufficient information about a population?
Small samples are subject to more random variation than large samples and is more susceptible to being affected by outliers
What qualities must a study have to provide justification for an intervention?
A study must have not statistical significant and clinical significance to provide justification for an intervention. A study without statistical significance may be the result of random chance, whereas one without clinical significance will not impact patients
Scientific method
A series of eight steps for the generation of new knowledge
- Generate a testable question
- Gather data and resources
- Form a hypothesis
- Collect new data
- Analyze the data
- Interpret the data and existing hypothesis
- Publish and verify results
FINER method
Assess the value of a research question on the basis of whether or not it is:
Feasible Interesting Novel Ethical Relevant
Controls
Used to correct for any influences of an intervention that are not part of the model
Types of controls
Positive or negative controls
Positive controls
Ensure that a change in the dependent variable occurs when expected
Negative controls
Ensure that no change in the dependent variable occurs when none is expected
Types of errors in measurement
Accuracy (validity) and precision (reliability)
Accuracy (validity)
The quality of approximating the true value
Precision (reliability)
The quality of being consistent in approximations
What kind of research is one consisting of human subjects?
Observational
Cohort studies
Record exposures throughout time and then assess the rate of a certain outcome
Cross-sectional studies
Assess both exposure and outcome at the same point in time
Case-control studies
Assess outcome status and then assess for exposure history
What is causality in observational studies supported by?
Hill’s criteria
Hill’s criteria
- Temporality
- Strength
- Dose-response relationships
- Consistency
- Plausibility
- Consideration of alternative explanations
- Experiments
- Specificity
- Coherence
Forms of error
Bias, confounding or random error
Bias
Systematic and results from a problem during data collection
Selection bias
The sample differs from the population
What is the most common bias in human subjects research?
Selection bias
Detection bias
Arises from education professionals using their knowledge in an inconsistent way by searching for an outcome disproportionately in certain populations
Hawthorn effect
Results from changes in behavior - by the subject, experimenter or both - that occur as a result of the knowledge that the subject is being observed
Confounding
An error in data analysis that results from a common connection of both the dependent and independent caiciables to a third variable
Medical ethics
Refers to the four principles of:
Beneficence
Nonmaleficence
Respect for patient autonomy
Justice
How were research ethics established?
By the Belmont Report
Research ethics
Respect for persons
Justice
Beneficence
Respect for persons in research ethics
Autonomy, informed consent and confidentiality
Justice in research ethics
Which study questions are with pursuing and which subjects to use
Beneficence in research ethics
Do the most food with the least harm
Do not perform an intervention without equipoise
Equipoise
A lack of knowledge about which arm of the research study is better for the subject
Populations
All of the individuals who share a set of characteristics
Parameters
Population data
Samples
A subset of a population that are used to estimate population data
Statistics
Sample data
How is an intervention supported?
By statistical and clinical significance
Statistical significance
The low likelihood of the experimental findings being due to chance
Clinical significance
The usefulness or importance of experimental findings to patient care or patient outcomes
What would establish a class causal link: an observational study or an experiment?
Experiment
What happens when data is off in a systematic way (reads at a value that is not a true value)?
Bias (lack of validity or accuracy)
Does unreliable data suffer from random or systemic error?
Random
Does confounding arise from errors in data analysis or data collection?
Data analysis
Does invalid data lead to bias or confounding?
Bias
What types of data sets are best analyzed using the mean as a measure of central tendency?
A data set with relatively normal distributing (not one that has outliers)
Is the mean of a sample considered a parameter?
No; the mean of a sample is a statistic; the mean of a population is a parameter
How do the mean, median and mode compare for a right-skewed distribution?
The mean of a right (positively) skewed distribution is to the right of the median, which is to the right of the mode
Can data that do not follow a normal distribution be analyzed with measures of central tendency and measures of distribution?
Any distribution can be mathematically or procedurally transformed to follow a normal distribution by virtue of the central limit theory. Regardless, a distribution that is not normal may still be analyzed with these measures.
What is the difference between normal or skewed distributions, and bimodal distributions?
Bimodal distributions have two peaks whereas normal or skewed distributions have only one.
How to determine outliers from the interquartile range?
Outliers are data points more than 1.5 x IQR below Q1 or above Q3
How to determine outliers from the standard deviation?
Outliers are data points more than 3 standard deviations above or below the mean
How do range and standard deviation generally relate to one another mathematically?
Where the data is not available, the range can be approximated as four times the standard deviation
Why would the average difference from the mean be an inappropriate measure of distribution?
The average distance from the mean will always be zero. This is why, in calculations of standard deviation, we always square the distance from the mean and then take the square root at the end - it forces all of the values to be positive numbers, which will not cancel out to zero.
Assume the likelihood of having a male child is equal to the likelihood of having a female child. In a series of ten live births, the probability of having at least one boy is equal to:
The probability of having all girls is (0.5)^10
The probability of having at least one boy is:
1 - (0.5)^10 => 99.90%
Independence
A condition of events wherein the outcome of one event has no effect on the outcome of the other
Mutual exclusivity
A condition wherein two outcomes cannot occur simultaneously
Exhaustiveness
There are no other possible outcomes
Hypothesis tests
Used to validated or invalidate a claim that two populations are different, or that one population differs from a given parameter
We calculate a p-value and compare it to a chosen significance level (alpha) to conclude if an observed difference between two populations (or between a population and the parameter) is significant or not
Use a known distribution to determine whether a hypothesis of no difference (the null hypothesis) can be rejected
Confidence intervals
Used to determine a potential range of values for the true mean of a population
A range of values about a sample mean that are used to estimate the population mean (A wider interval is associated with a higher confidence level, 95% is common)
If the p-value is greater than alpha in a given statistical test, what is the outcome of the test?
We fail to reject the null hypothesis
How is the p-value calculated during a hypothesis test?
After the test statistic is calculated, a computer program or table is consulted to determine the p-value of the statistic
Is power the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true for the population?
Yes
What type of data relationship is least likely to require transformation into a semilog or log-log plot?
Linear relationships
Pros of a pie chart
Easily constructed
Useful for categorical data with a small number of categories
Pros of a bar graph
Multiple organization strategies
Good for large categorical data sets
Pros of a box plot
Information-dense
Can be useful for comparison
Pros of a map
Provide relevant and integrated geographic and demographic information
Pros of a graph
Provide information about relationships
Useful for estimation
Pros of a table
Categorical data can be presented without comparison
Does not require estimation for calculations
Cons of a pie chart
Easily overwhelmed with multiple categories
Difficult to estimate values with circles
Cons of a bar graph
Axes are often misleading because of sizable breaks
Cons of a box plot
May not highlight outliers or mean value of a data set
Only useful for numerical data
Cons of a map
May only be used to represent at most two variables coherently
Cons of a graph
Axis labels and logarithmic scales require careful interpretation
Cons of a table
Disorganized or unrelated data may be presented together
Exponential curve
Has a steep component
Has horizontal symptoms and become flat on one side
Parabolic curve
Has a steep component
Is symmetrical and has steep components on both sides of a center point
Is statistical significance a sufficient criteria to enact policy change?
No : There must be practical (clinical) as well as statistical significance for a conclusion to be useful
Are two variables that are causally related also correlated with each other?
Yes
Median position
= (n + 1) / 2
Interquartile range (IQR)
= Q3 - Q1
Standard deviation
= square root ([{x1 - mean}^2 + {x2 - mean}^2 + …] / [n - 1])
Probability of two independent events co-occurring
P(A ∩ B) = P(A and B) = P(A) x P(B)
Probability of at least one event occurring
P(A U B) = P(A or B) = P(A) + P(B) - P(A and B)
Measures of central tendency
Provide a single value representation for the middle of a group of data
Arithmetic mean (average)
Measure of central tendency that equally weighs all values
It is most affected by outliers
Median
The value that lies in the middle of the data set
Fifty percent of data points are above and below the median
Mode
The data point that appears most often; there may be multiple (or zero) modes in a data set
How are distributions classified?
By measures of central tendency and measures of distribution
Normal distribution
Symmetrical
The mean, median and mode are all the same
68% of data points occur within one standard deviation of the mean
95% of data points occur within two standard deviations of the mean
99% of data points occur within three standard deviation s of the mean
Standard distribution
A normal distribution with a mean of zero and a standard deviation of one
Used for calculations
68% of data points occur within one standard deviation of the mean
95% of data points occur within two standard deviations of the mean
99% of data points occur within three standard deviation s of the mean
Skewed distribution
Has differences in its mean, median and mode
What is the direction of a skew?
The direction of the tail of the distribution
Bimodal distribution
Has multiple peans, although not necessarily multiple modes
Range
The difference between the largest and smallest values in a data set
Interquartile range
The difference between the value of the third quartile and first quartile
Used to determine outliers
Standard deviation
A measure of variability about the mean
Used to determine outliers
Outliers
May be a result of true population variability, measurement error or a non-normal distribution
When are procedures for handling outliers formulated?
Before the beginning of a study
Does the probability of an independent event change based on the outcome of another event?
No
Does the probability of a dependent event change based on the outcome of another event?
Yes
Mutually exclusive outcomes
Outcomes that cannot occur simultaneously
Null hypothesis
A hypothesis of no difference
How is a finding determined to be statistically significant?
By the comparison of a p-value to the selected significance level (alpha)
Common significance level (alpha)
0.05
Pie chart (circle chart)
Used to compare categorical data
Bar chart
Used to compare categorical data
Histogram
Used to compare numerical data
Box plot (box-and-whisker plot)
Used to compare numerical data
Maps
Used to compare up to two demographic indicators
How can linear, semilog and log-log plots be distinguished?
By their axes
Which plot is easiest when trying to find the slope?
Linear
Tables
May contain related or unrelated categorical data
How are correlation and causation linked?
By Hill’s criteria
In a sample of hospital patients, the mean age is found to be significantly lower than the median. What is the shape of the distribution?
Skewed to the left : The mean is to the left of the median, which implies that the tail of the distribution is on the left side
A hypothesis test was correctly conducted and the experimenter failed to reject the null hypothesis. What must be true?
The p-value was greater than alpha and a type I error did not occur :: Type I error occurs when the null hypothesis is incorrectly rejected :: If we failed to reject the null hypothesis, then the p-value must be greater than the significance level
A 95% confidence interval will fall within what distance from the mean?
+/- 2 standard deviations
Which measure of distribution is most useful for determining probabilities?
Standard deviation because it is the most closely linked to the mean of a distribution and can be used to calculate p-values, which are probabilities (specifically, p-values are the probability that an observed difference between two populations is due to chance)
What does low power in a study mean?
If a study has low power, it is more difficult to get results that are statistically significant.
What corresponds to the probability of a type I error?
Significance level (alpha)
Type I error (alpha)
The probability of mistakenly rejecting the null hypothesis
We set the type I error level by selecting a significance level (alpha)
Power (1 - beta)
Correctly rejecting the null hypothesis
Confidence
Correctly failing to reject the null hypothesis
Type II error (beta)
Mistakenly not rejecting the null hypothesis
