MCAT PHYSICS EQUATIONS Flashcards
Scalar
Physical quantity with only magnitude and no direction
Vector
Physical quantity with magnitude and direction
Speed
Distance/Time (Scalar)
Velocity
Displacement/Time (Vector)
Acceleration
Change in velocity/Time (Vector)
Distance
Measured by number of steps a person takes (Scalar)
Displacement
The NET distance (vector)
Air resistance
factors affecting it include speed, surface area and shape
x=
x0+v0t+1/2at^2
v=
v0+at
v^2=
v0^2+2ax
vavg=
1/2(v+v0)
Inertia
the tendency of an object to remain in its present state of motion
Mass
Measure of an object’s inertia
Weight
gravitational force an object feels while near a much larger body. W=mg
Gravitational Force
mass x gravity
Newton’s First Law
An object in a state of rest or in a state of motion will remain in that state unless acted upon by a net force.
Newton’s Second Law
For an object with a constant mass m, the second law states that the force F is the product of an object’s mass and its acceleration F=ma
Newton’s Third Law
For every action there is an equal and opposite reaction
Newton’s Law of Universal Gravitation
F=Gm1m2/r^2 r=distance between the centers of the two objects G=gravitational constant (6.7x10^-11 Nm^2/kg^2) Final answer should be in N
What is a Newton equal to?
N=1kg m/s^2
Net Force (Inclined Planes)
The sum of the gravitational and normal forces gsinø=a=usually less than g Fnet=mgsinø
Normal Force (Inclined Planes)
Always perpendicular to the surface that applies it. Fnormal=mgcosø
Centripetal Acceleration
For the velocity of an object, the magnitude it constant, the direction is continuously changing. Always points TOWARDS the center of the circle. a centripetal =v^2/ r
Centripetal Force
The NET force that accompanies centripetal acceleration. Always points TOWARDS the center of the circle. Whenever centripetal force exists there is some other force responsible for it. Fcentripetal=mv^2/r
Normal Force
is always perpendicular to the contact surface
Frictional Force
is always parallel to the contact surface
Static Friction
Force opposing motion when two contiguous surfaces are NOT moving relative to each other.
Fn or N is equal to mass x gravity
Kinetic Friction
Force existing once the two surfaces are sliding relative to each other.
Tension
A force acting through a flexible object with no mass such as a string or rope.
Tension requires and equal force on both ends of the rope but Tension is only equal to one of the forces.
Hooke’s Law
Describes the Force applied by most objects AGAINST A DEFORMING FORCE.
Applied to springs, F is the tension of the spring, and F can be mg
F=-kdeltax
k is a spring constant that must be given
Static Equilibrium
Constant Velocity at zero
Dynamic equilibrium
Constant velocity Not at zero
System in equilibrium
Fupward=Fdownward
Fleft=Fright
Systems not in equilibrium
Write equations as if systems were in equilibrium
Decide which side experiences less force and add ma to the side.
Example: Fupward +ma =F downward
and solve for acceleration
Torque=
Force x Lever Arm
Tclockwise= T counterclockwise
Hold system motionless at arbitrary point of rotation and determine direction of forces.
Set clockwise and counterclockwise torques equal to each other and solve.
Kinetic Energy
Energy of Motion
K.E.=1/2mv^2
Potential Energy
Energy of Position
Gravitational P.E. =mgh
Elastic Potential Energy=1/2kdeltax^2
k=spring constant
The universe is an isolated system so…
the energy of the universe remains constant
Work
Transfer of energy via a force (measured in Joules )
Work= F d cosø
Work=(Force)(Displacement)
Heat
Transfer of energy by natural flow from a warmer body to a cooler body
F=dcosø
Work=
Frictional forces change
Internal energy and mechanical energy
If NO friction and NO heat then work equals?
W=change in K.E. + change in P.E.
If there is friction and heat then what is work?
W= change in K.E.+ change in P.E. + change in internal energy
Energy
Energy=Work +Internal
Power
P=Change in Energy/ time
P=(Force) (Velocity)(cosø)
Rate of energy transfer
Watt=Joule/Sec
Momentum
Momentum is always conserved in an isolated system.
Momentum= Mass x Velocity
Elastic Collisions
Mechanical energy is conserved. No energy is dissipated to internal energy
P.E. initial + K.E. intial= P.E final + K.E. final
Inelastic Collisions
Colliding objects lose some of their energy mechanical energy to internal energy.
Momentum intial= Momentum Final
Impulse
Impulse= Change in momentum
Impulse=Favg x change in time
delta mv=
Favg x change in time
Machines
Work is constant
Force is decreased
Displacement is increased
Work=Force x Displacement
Rest Mass energy
E=mc^2
c=300,000,000= 3x10^8 m/s
Half life
length of time necessary for 1/2 of a substance to decay
Alpha Decay
Creation of Helium nucleus from 2 protons and 2 neutrons
Original Element: Mass-4 and Atomic Number-2
Beta Decay
Creation of an electron and a proton from a neutron.
Original Element- same mass and PLUS one atomic number
“Bumping it up”
Positron Emission
Creation of a positron and a neutron from a proton.
Original element: Same mass and minus one atomic number
Electron Capture
Creation of a neutron from captured electron and proton
Original element: same mass and minus one atomic number
Gamma Decay
ORIGINAL ATOM DOES NOT CHANGE
Gamma rays are emitted from matter-antimatter/ electron-positron collisions
Energy is released in gamma rays
Solids
Molecules bond strongly and vibrate in a fixed position.
Fluids
Liquids and gases- molecules bond weakly and rotate, spin and move past each other.
Density
Density= Mass/Volume
kg/m^3
Specific Gravity
S.G.= Density of substance/ Density of Water
Density of Water
1000 kg/m^3
1g/cm^3
Pressure
Pressure= Force/Area
SI Units is Pascals
Fluid at rest Pressure=
Pressure= Density x g x depth of fluid
Atmospheric pressure=101,000 Pascals
Gauge Pressure
Measure of Pressure compared to local atmospheric pressure.
(relative difference only)
Pascal’s Principle
Pressure applied anywhere to an enclosed incompressible fluid will be distributed undiminished throughout the fluid.
Hydraulic Lift
Work Stays the same
Pressure is constant
Force applied changes as area changes
Archimede’s Principle
Buoyant force is an upward force, acting on a submerged object and is equal to the weight of the fluid that is displaced by the submerged object.
Buoyant force equation
F buoyancy= (Density of the fluid)(Volume)(g)
volume is volume of water that was displaced
Submerged Object
displaces an amount of fluid equal to its OWN volume
Floating object
Displaces an amount of water equal to its own weight.
% Submerged=
Density of floating object/ Density of Fluid
Random Translational Motion
Contributes to fluid pressure
Uniform Translational Motion
Contributes to overall fluid motion
Ideal Fluid
No viscosity
Uniform density (incompressible)
Experiences steady flow (constant flow rate)
Volume Flow Rate=
=(area x velocity)
Bernoulli’s Equation
K= Pressure + Density(gh) + 1/2 (density)(v^2)
Surface Tension
Intensity of the intermolecular forces per unit length
Intermolecular forces
Pull inward to minimize surface area by creating a more spherical shape.
Between molecules
Capillary Action
Stronger forces between liquid and medium molecules-(liquid rises) capillary action
Stronger forces between liquid molecules-liquid doesn’t rise
Solids
Stress=
F/A
N/m^2 to distinguish from pressure
Strain=
Change of dimension/ original dimension
Modulus of elasticity
Stress/strain
Young’s Modulus
Stretching and Compressing tensile strength
Shear’s modulus
Shear stress
Bulk Modulus
Compression and expansion of whole volume
Waves
Transfer of energy and momentum from one point to another
Mechanical waves
Require some sort of medium to travel through.
Transverse: medium is displaced perpendicular to the wave
Longitudinal: medium is displaced parallel to the wave’s direction
wave velocity
Velocity=frequency x wavelength
Period of a wave
Period=1/frequency
Frequency of a wave
Wave frequency is the number of waves that pass a fixed point in a given amount of time. The SI unit for wave frequency is the hertz (Hz), where 1 hertz equals 1 wave passing a fixed point in 1 second. A higher-frequency wave has more energy than a lower-frequency wave with the same amplitude
Amplitude
Maximum displacement from zero
Wave velocity is dictated by the medium
- Medium’s resistance to change in shape
- Medium’s resistance to change in motion
For Gas the velocity increases with
temperature
Wave Power is the
rate at which a wave transfers energy
Intensity of a wave increases with
Square of amplitude and square of all frequencies
For decibels
10x intensity is
100x intensity is
1000x intensity is
+10 decibels
+20 decibels
+30 decibels
Phase
Relates to its wavelength, frequency, and place and time of origin.
One wavelength is 360 degrees / 1/2 wavelength is 180 degrees
Constructive Interference
When the sum of the displacements results in a greater displacement. Add amplitudes.
Destructive Interference
When the sum of displacements results in a small displacement. Subtract amplitudes
Beat Frequency
fbeat= |f1-f2|
When a wave transfers from one medium to the next:
Frequency remains the same
wavelength changes
First Harmonic
Only two nodes.
Wall to wall is 1/2 wavelengths
Second Harmonic
Wall to wall is 1 wavelength
3 nodes
The period of a pendulum is
independent of its mass
The pendulum period formula, T, is fairly simple: T = (L / g)1/2, where g is the acceleration due to gravity and L is the length of the string attached to the bob
Doppler Effect
Change of f/ f source =v/c
Change of wavelength/ wavelength source=v/c
c=3×10^8 ms-¹
If source and Observer are getting closer…
Wavelength decreases
frequency increases
pitch increases
If source and observer are getting farther apart…
Wavelength increases
frequency decreases
pitch decreases
Charge is measured in
Coulombs (C)
Universal Law of Conservation of Charge
The universe has no net charge
Opposite charges attract
Like charges repel
Coulomb’s Law
F=kq1q2/r^2
Newtons
k=9x10^9 Nm^2/C^2
r= distance between two charges
An electric field points from
Positive to negative
Electric field is E
N/C or V/m
Force on a charge in an electric field (E)
F=Eq
Potential energy of a charge in an electric field
P.E.=Eqd
d=displacement (net distance moved)
P.E.=kq1q2/r Joules (J)
Voltage
Potential for work by an electric field in moving any charge
V=Energy x Displacement Volts or J/C
Current is measured in
AMPS (A) or C/s or (I)
Resistance is measured in
Ohms
Ohms Law
V=IR
Voltage=Electric current/ Resistance
Kirchoff’s First Rule
The amount of current flowing into any node must be the same amount that flows out
Kirchoff’s second rule
The voltage around any path in a circuit must SUM to ZERO
EMF (Electromotive force) is
Not a force, just another word for voltage
Capacitor
Used to temporarily store energy in a circuit
Capacitance=Charge/Volt
C=Q/V
Dielectric Constant (K)
Substance between the two capacitor plates
Must be an insulator
Resistors in a series
Requiv=R1+R2+R3…
Resistors in parallel
1/Requiv=(1/R1)+(1/R2)+(1/R3)…
Capacitors in a series
1/Cequiv=(1/C1)+(1/C2)+(1/C3)…
Capacitors in Parallel
Cequiv= C1+C2+C3…
Power=
P=IV
P=I^2R
P=V^2/R
Alternating Current
Typical rms in US homes is 120 V corresponding to a 170 volt max
Vmax=Squareroot (2Vrms)
Imax=Squareroot (2Irms)
Magnetic fields (B) are measured in
Teslas (T)
Lines of force in a magnetic field point from
North Pole to South Pole
Changing electric field creates
a magnetic field
Stationary charge does nothing but a moving charge creates
a magnetic field
Current is moving charge ergo current creates
a magnetic field
Force on a charge moving through a magnetic field
F=qvBsinø
Force is perpendicular to both velocity and magnetic field
For a long straight wire magnetic field varies with
r (radius)
Right Hand Rule (long straight wire)
Thumb in direction of the current
Grab the wire
Direction of the fingers wrapping around wire is direction of magnetic field.
Right hand rule charge moving through a magnetic field
Thumb in direction of Moving charge
Fingers in direction of the Magnetic field
Palm points in the direction of the Force
An electromagnetic wave is the traveling oscillation of
an electric and magnetic field
Visible Light
Visible Light Equations
c=f(wavelength)
f=c/wavelength
wavelength=c/f
c=3x10^8 m/s
Index of Refraction
n=c/v
ø incidence=ø reflection
Snells law
n1sinø1=n2sinø2
The path that light travels is the
shortest path possible in terms of time
Remember, mediums
slow down light
When light crosses into a new medium,
frequency remains the same, wavelength changes
Energy of a single photon
E=hf
h=plancks constant=6.63x10^-34 j=Js
f=frequency of photon
Total internal reflection at critical angle of
90 degrees
Diffraction
another wave bending phenomenon.
When a wave moves through a small opening it bends around corners of the small opening
Small hole and long wavelengths means
MORE bending
Mirrors reflect and lenses
refract
Virtual image
Does not actually exist outside mind of observer.
Real Images
Exist separately from the observer
Concave mirror/ diverging lense
Observer ) )(
Convex mirror/ converging lense
Observer ( ()
ThiCker
Center
Converges
Light
Focal Point
Light is reflected by concave mirrors/ refracted by converging lenses to focus on a single point
Focal Length
fmirror=1/2 r
Power measured in Diopters
P=1/f
Magnification
m= -di/do= hi/ho
Thin lense equation
P=1/f= 1/do+1/di
System for Mirrors and Lenses
- Draw the mirror/ lense and an eye on the side of the observer
- On the eye side write positive/ Real/ Inverted
a. EYE am Positive that Real is Inverted
b. Images and focal points on this side will always be positive, real and inverted - front and back
For mirrors the eye is in front of the mirror
For lenses the eye is behind the lense
Objects are POSITIVE when they are IN FRONT of a mirror or lens
Front -Eye- Object -Focal Point -Concave Mirror=
+real inverted image
Front- Eye-Object-Convex Mirror-Focal Point =
-virtual upright image
Back-Eye-Focal Point-Converging Lens-Object=
+real inverted
Back- Eye- Diverging Lens-Focal Point- Object =
-virtual upright image
