Physics and SMRM Flashcards
Estimating fractions
If numerator is larger- create compound fraction
If denominator is larger- use high-low method (chance denominator to one digit higher or lower to find easier fraction)
Raising a number in scientific notation to a power
The number is put to that power, the power is multiplied by the second power
(3 x 10^4)^2 = 9 x 10^8
Sin theta
Cos theta
Tan theta
Sin: Opposite / hypotenuse
Cos: adjacent / hypotenuse
Tan: opposite / adjacent
Sin0 Sin30 Sin45 Sin60 Sin90
Sin0 = 0 Sin30 = 1/2 or 0.5 Sin45 = (square root 2)/2 or 0.7 Sin60 = (square root 3)/2 or 0.9 Sin90 = 1
Cos0 Cos30 Cos45 Cos60 Cos90
Cos0 = 1 Cos30 = (square root 3)/2 or 0.9 Cos45 = (square root 2)/2 or 0.7 Cos60 = 1/2 or 0.5 Cos90 = 0
Decimal equivalent of square root of 2
Decimal equivalent of square root of 3
Of 2: 1.4
Of 3: 1.7
Circle circumference
2(pi)r
pi x diameter
Sphere volume
4/3(pi)(r^3)
Surface area of a sphere
4(pi)(r^2)
Area of a circle
(Pi)(r^2)
How many radians are in 1 circle
6 radians in one circle
Thus, if something rotates 12rad/s it makes 2 revolutions/s
When are graphic relationships linear
If both variables contain the exact same math applied to them (both cubed, both square roots, etc)
Specific real area bias
Non representative sample
Self selection bias
Participants choose level or involvement
Berkson’s Fallacy
Selection of participants from hospitals- less healthy than norm
Finding probability of multiple events happening together
Finding the probability of either events happening, but not together
AND = MULTIPLY probabilities
OR = ADD probabilities
Estimating percent increases and decreases using fractions
Percent increases: 1 + fraction representation of the increase
Percent decrease: 1 - fraction representation of the increase
take this fraction and multiply to value being altered
Convert 1 electron volt (eV) to joules (J)
1 eV = 1.6x10^-19 J
How do you multiply vectors to obtain a scalar?
use dot product
A•B=|A||B|costheta
How do you multiply vectors to obtain a third vector?
Use cross product
A x B = |A||B|sintheta
Assign direction via right hand rule
What is the difference between displacement and distance?
Displacement measures net change in position- has magnitude and direction (vector)
Distance is a scalar
What is the equation measuring gravitational force?
Fg = Gm1m2
———
r^2
G = 6.67 x 10^-11
What is a Newton in SI Units?
N = (kg•m)
———
s^2
What is the universal gravitational constant?
G = 6.67x10^-11
True or false: kinetic friction has a constant value
TRUE: kinetic friction is constant, static friction can change
What are the 3 kinematic equations?
1: v = v0 + at
2: x = v0t + 1/2(at^2)
3: v^2 = v0^2 + 2ax
Which kinematic equation could you use given initial velocity and time, looking for acceleration?
v = v0 + at
1st kinematic equation
You are given final velocity, displacement, and acceleration. Which Kinematic equation should you use to find initial velocity?
v^2 = v0^2 + 2ax
3rd kinematic equation
Given displacement, 0 v0, and acceleration, how would you find time?
x = v0t + 1/2(at^2)
2nd kinematic equation
Given initial and final velocity and displacement, how would you find time?
First use kinematic equation 3:
v^2 = v0^2 + 2ax
This gives acceleration
Then use kinematic equation 1:
v = v0 + at
This gives time
When is terminal velocity achieved?
Terminal velocity = when drag force equals weight in magnitude
Object falls at constant velocity
What is the equation that describes the force of circular motion?
Fc = mv^2
——
r
Centripetal force
What is the equation for torque?
T(torque) = r x F = rFsintheta
Find the change of velocity for a 1000kg Rocket going 100m/s with a 20kN force acting on it in the direction of its motion for 8 seconds.
Acceleration is the change of velocity over the change of time
F = ma
F = m (delta V/ delta T)
Delta V = F(deltaT) / m
(20kN)(8) / 1000kG …. 160 m/s
V = (square root) (2gh)
Can be used to find initial or final velocity - how is that?
When ignoring air resistance, initial and final vertical velocities are the same for any projectile due to symmetry of motion
What is the terminal velocity of an objecting falling in a vacuum?
Objects in vacuums do not attain terminal velocity because there is no air resistance - continually accelerate
For two objects A and B, A=2B in mass. What is the ratio of the forces between them, and the ratio of acceleration between them?
This is an action- reaction pair, so the forces are the same (hint- forces BETWEEN them)
F = ma And force is the same so if A=2B in mass then acceleration of A is half of B
How do you find acceleration down an inclined plane?
a = (g)sin(theta)
You hang a 4kg mass on a spring and it stretches 1m. What is the spring constant?
First find force- F=mg so the force is 40N
F = k(delta)x
This is Hooke’s law for springs
So 40 = k (1m) —> k = 40N/m
True or false: a ball moving with twice the kinetic energy can compress a spring twice as far
True or false: a ball moving with 3x velocity can compress spring 3x far
First: FALSE. Kinetic energy is transformed to PE, so KE=(1/2)kx^2
KE is related to square or x, so 4x KE needed to compress spring 2x far
Second: TRUE. Writing KE=PE as
(1/2)mv^2 = (1/2)kx^2
Shows that v and x are both squared, so increase is linear
If a ball is floating 3/4 submerged in liquid with density of 2g/cm^3, what is the density of the ball?
Ball is 3/4 submerged so it has 3/4 density of liquid, so 1.5g/cm^3
Convert 1 atm to mmHg, Torr, and Pa
1 atm = 760mmHg = 760 Torr = 1x10^5 Pa
How do you do find specific gravity?
Specific gravity = density (object)
———————
Density (water)
What is the equation for gravitational potential energy?
PE = mgh
h is height
What is absolute pressure?
Absolute pressure = atmospheric pressure + gauge pressure
How does surface area affect buoyancy force?
It doesn’t ! There is no variable for surface area in the equation for buoyancy force, however how much the object is submerged matters.
B = pVg where p = density of fluid, V is volume of displaced fluid, g = gravity
An 80kg object falls from 2000m height with no air resistance. In how many seconds would it reach the ground?
X = v0t + 1/2at^2
Initial velocity is 0
X = 1/2at^2
20 seconds
What does the area under the curve of a velocity vs time graph represent?
Displacement
Why do you use sin(theta) when measure angles from the vertical?
Because sin(theta) is opposite from the theta angle in the triangle
When asked for final velocity, given drop height, you should use what equation?
V = square root
To calculate time spent in the air for projectiles, use:
t(air) = 2V/g
For round trip times, V is vertical component of initial velocity only
Will air resistance increase or decrease with increased velocity?
Increased velocity=increased air resistance
What is the formula for the force of gravity?
F = Gmm/r^2
G = 6.67x10^-11 or ~7x10^-11
What equation is used to find gravitational potential energy?
PE = mgh (near earth)
For fluid: PE = pgh (p is fluid density)
PE = -Gmm/r^2 (in space)
How do you find the force of friction?
F = uFn
Or
F = u(mgcostheta)
What equation represents Hooke’s law?
F = kx
How is elastic potential energy calculated?
PE = 1/2kx^2
Likely to be used in conservation of energy problems
To find the period of simple harmonic motion for a mass on a spring, use this equation
T = 2pisquare root
What is the equation for buoyant force?
Fb = pvg
p is density of fluid, v is volume of fluid displaced
Buoyant force = weight of displaced fluid
What is apparent weight?
Apparent weight = actual weight - buoyant force
What is the fluid pressure formula?
P = pgh
p is density of fluid, h is depth
Equation for flow rate
Q = AV
Bernoulli’s equation
K = P + pgh + 1/2pv^2
h is height, not depth here
K is always constant- energy transferred from one form to another
How to find capacitance of parallel plate capacitor?
C = e0A/d
e0 is constant, A is area, d is plate separation
Which wavelength contains photons with more energy, 400nm or 700nm?
v = frequency x wavelength
V = speed of light = constant
Larger wavelength = smaller frequency
E=hf —> higher frequency = more energy
Shorter waves have higher energy
What affects speed of light?
Speed of light is a function of the medium in which it travels
As arteries narrow, how are velocity and pressure effected?
Narrower arteries —> lower pressure, higher velocity
Q = AV
What is the thin lens equation?
1/di + 1/do = 1/f
di is image distance
do is object distance
f is focal length
If the object distance is greater than the focal length, what kind of image is created by a converging lens?
Positive image is created by converging lens as long as object distance is greater than focal length
You’re shot from a cannon with an initial velocity of 40m/s at 30 degrees above horizontal. Ignoring air resistance, what maximum height will you reach, and how long will you be in the air?
Vertical velocity determines time in air:
(40m/s)(sin30)=(40)(0.5)= 20m/s vertical velocity
Gravity is -10m/s, so 2 seconds in air to reach 0 vertical velocity
Average vertical velocity is 10m/s
(10m/s)(2s)= 20m max height
Projectile motion is symmetrical—> 4 seconds total in air, 20m max height
A barometer is filled with mercury and allowed to equilibrate at atmospheric pressure. The mercury inside is 50cm above the surface. What is the approximate atmospheric pressure? SG of mercury = 14
P = pgh (p is density of fluid)
SG of 14 means mercury is 14x as dense as water—> 14,000kg/m^3
P = (14,000)(10)(0.5m) = 70,000 Pascals
A plastic barge floats on a lake with 5,000kg cinder blocks inside, and becomes 1/4 submerged in the water. What is the volume of the barge?
D = m/v
Density of water = 1,000kg/m^3
1,000 = 5,000 / v V = 5m^3
This is only 1/4 of the volume of the barge, so the total volume is 20m^3
A water tank is partially full; the water line is 45m up. A spigot at the base is opened. What is the velocity of the water leaving?
V = square root
V = square root = 30m/s
A pipe has volume flow rate of 100m^3/s. What is the flow rate when the radius of the pipe is tripled?
flow rate: Q = AV
Area of a circle = (pi)r^2
So:
Q = (pi)r^2V
Tripling radius increases flow rate by factor of 9–> new flow rate is 900m/s
How do you find capacitance of a parallel plate capacitor?
C = e0A/d
e0 is constant, A is area, d is plate separation
Which wavelength contains photons with more energy, 400nm or 700nm?
V = (f)(wavelength)
V = c (speed of light) = constant
Larger wavelength = small frequency
E = hf
High frequency = high energy
—>
Short waves = higher energy (400>700)
Speed of light wave is a function of…
The medium in which it travels
What is the thin lens equation?
(1/d,image) + (1/d,object) = 1/f
F = focal length
What image does a converging lens create, assuming the object distance is greater than the focal length?
Positive image
PRI and NVU:
Positive images are Real and Inverted
Negative images are Virtual and Upright
You clean a 275kg barbell (good for you!), then hold it 2.4m overhead. How much work did you do lifting the bar, and how much to hold it overhead?
W = Fdcos(theta) W = (mg)(d)(cos0) W = (275x10)(2.4)(1) W = 6468J
0 work to hold it overhead- no displacement
A 2000kg car accelerates 0 to 30m/s in 6s- what average power is needed to achieve this acceleration?
W = deltaKE W = (1/2)(m)(vf^2 - vi^2) W = (1/2)(2000)(900-0)
P = W/t P = (900,000)/6s P = 150,000W (150kW)
A 40kg block falls off a 5m table. At 2m, what is its total mechanical energy?
U = mgh U = (40)(10)(5) U = 2,000J
Conservation of energy says mechanical energy is constant as it falls
During uniform circular motion, which of the following is necessary true?
- no work is done
- centripetal force does work
- velocity does work
- potential energy depends on position around the circle
No work is done always true
Displacement vector is always perpendicular to the force vector
PE is constant in uniform circular motion
What is Planck’s constant?
6.6x10^-34 m^2kg/s
What secondary structural motif stabilizes protein chains in silkworm structural proteins?
Beta sheets
Pressure is the ratio of what?
Force per unit area (F/A)
What is absolute (hydrostatic) pressure?
What’s its equation?
Total pressure exerted on an object submerged in fluid
P = P0 + pgh
P0 = ambient pressure (at surface)
What is gauge pressure?
Amount of pressure in a closed space above and beyond atmospheric pressure
Pgauge = P - Patm
What equation represents Pascals principle?
P = F1/A1 = F2/A2
In a closed system
When force is multiplied by displacement, what do you get?
Work
W = Fd = P(delta)V
Applying Pascals principle, how does area affect force?
Larger area = larger force
But force will be exerted through a smaller distance
On the other hand, exerting a small force over a small area through a large distance will generate a much larger force over a large area through a smaller distance
Explain how Bernoulli’s equation says the total pressure is static + dynamic fluid pressure?
P + pgh = static pressure
1/2pv^2 = dynamic pressure
Bernoulli’s:
P = P + pgh + 1/2pv^2
Explain how fluids help planes fly given that wing tops are curved
Air streaming over top of wing must travel farther than air passing below, so it passes faster
Air below is slower and therefore exerts more force on the wing than air above
Explain how parallel resistor circuits are similar to blood circulation?
Away from heart vessels increase resistance until capillaries. Total resistance decreases though because of increased number of vessels in parallel
Does (-) or (+) pressure move air into lungs?
Negative
Object A and B are submerged 1 m in liquid with specific gravity of 0.8, and density of B is 1/3 that of A. If object A has a gauge pressure of 3 atm, what is the gauge pressure of object B?
3 atm
Submerged at same depth, so same gauge pressure (object density doesn’t matter)
An anchor weighing 833N is suspended in seawater by a chain. If density of anchor is 7800kg/m3 and seawater is 1025kg/m3, which of these is likely the tension in the chain? 100N 724N 833N 957N
T = Fg - Fb Fb = pvg
Recognize that tension must be slightly less than anchor weight because of buoyancy, so only logical answer is 724N
The actual math is too long here
According to Bernoulli’s equation, at equal height, speed and pressure of a fluid are related in this way: (also know as Venturi effect)
Inversely
What is the fundamental unit of charge in coulombs?
1.6x10^-19 C
Coulomb’s law quantifies the magnitude of the electrostatic force between 2 charges. What is the formula?
Fe = kq1q2
———
r^2
k = 9x10^9
What is the formula for the magnitude of an electric field?
E = (kQ) = Fe
—— ——
r^2 q
Q is source charge, q is test charge
By convention, the direction of the electric field vector is the direction that a (positive/negative) would move in the presence of the source charge
Positive
If a source charge is positive, then the test charge (in an electric field) will experience (repulsive/ attractive) force
Repulsive
By convention the direction of the electric field charge is given as direction that positive charge would move
Positive charges have electric field vectors that radiate…
Outward (away from positive)
By convention the direction of the electric field charge is given as direction that positive charge would move
What is the equation for electric potential energy? What does it represent?
U = kQq
———
r
Work necessary to move a test charge from infinity to a point in space in an electric field surrounding a source charge (which creates the electric field)
For two unlike charges, how does moving closer together affect electric potential energy?
More stable closer together
Negative potential energy becomes more negative
Decrease in energy represents increase in stability
For two like charges, how does moving farther apart affect electric potential energy?
More stable farther apart
Positive potential energy will decrease (become smaller positive number)
What is electric potential a ratio of?
Magnitude of charges electric potential energy (work done to move a test charge from infinity to a point) to magnitude of the charge itself, measured in volts
V = U / q V = (kQ)/r
Positive charges spontaneously move in a direction that ____ electric potential?
Decrease electric potential—> negative voltage
Potential energy decreases—> more stable
Negative charges spontaneously move in a direction that ____ electric potential?
Increase electric potential—> positive voltage
Decrease electric potential energy—> more stable
What is the equation for a dipole moment?
p = qd
Product of charge and distance
What is the voltage between 2 points on an equipotential line?
No voltage
What is the electric potential at points along the perpendicular bisector of a dipole? Explain
V = (kqd)/r^2 (costheta)
Costheta = 90 = 0 along perpendicular bisector
0 electric potential
What is the magnetic field for an infinitely long and straight current carrying wire?
B = u0I
——
2(pi)r
Magnitude at any perpendicular distance
What is the magnitude of the magnetic field for a circular loop of current carrying wire?
B = u0I
——
2r
Magnitude at center of circular loop
What is the formula for magnetic force?
Fb = qvBsin(theta)
v is velocity because a magnetic is created by a moving charge
If a charge moves parallel or antiparallel to a magnetic field vector, will it experience a magnetic force?
No
For a straight wire, what is the magnitude of a force created by an external magnetic field?
Fb = ILBsin(theta)
I = current L = length of wire B = magnitude of magnetic field
A 2m wire has a current of 5A toward the top of the page and through a 30 gauss uniform magnetic field directed into the page. What is the magnitude and direction of the magnetic force on the wire?
Fb = ILBsin(theta)
1 Tesla = 10^4 gauss
Fb = (5)(2)(3x10^-4)(sin90) Fb = 3x10^-2 N
Right hand rule- thumb points up the page (direction of L), fingers point into the page (direction of B)—> current of flow is positive so Fb is in the direction of your palm—> to the left
What are the minimum requires to have a nonzero:
Electric field
Magnetic field
Magnetic force
Electric field- charge
Magnetic field- moving charge
Magnetic force- external electric field acting on a moving charge (except parallel/antiparallel)
Use the right hand rule to determine the direction of the magnetic force given:
Electron, velocity up the page, B pointed left
Into the page
Use the right hand rule to determine the direction of the magnetic force given:
Proton, velocity right, B pointed into the page
Up the page
Use the right hand rule to determine the direction of the magnetic force given:
Electron, velocity out of the page, B pointed left
Up the page
The direction of an electric field is defined by:
Direction of force that would be exerted on a positive charge
An electron is accelerated over distance (d) by electric potential (V). The electric potential is then increased by 4x and the electron travels distance (d) again. The electron speed at the end of the second trial will be larger by the first by a factor of:
Electric potential (V) is proportional to work (W), so energy increases 4x
E = 1/2mv^2
So speed increases 2x to give an energy increase of 4x
A 9V battery is used to move a 2 C charge. How much work is done by the battery?
V = deltaU/ q = W/ q
9 = W / 2
W = 18 J
A dipole in an electric field experienced torque until…
It comes to rest oriented with the direction of the electric field
If one sphere has 2x the radius of another, how do their volumes compare?
In volume of sphere, radius is cubed
2x2x2 = 8x more volume
15kg toy rocket falls at constant velocity of 20m/s. A small amount of fuel pushes rocket downward with 30N. What is force of air resistance?
Constant velocity - no net force
(15x10)+30 = 180N
20kg hangs 3m from fulcrum- what should mass be on other end 5m from fulcrum to balance?
T = Frsin(theta)
(20)(10)(3) = (x)(10)(5)
X = 12kg
120kg rocket accelerates to Earth at 8m/s^2. Ah! The engine adds 200N force. Oh good, a parachute slows the descent! What’s the air resistance?
F = ma = (120)(8) = 960N
960N = Fair - Frocket - Fg 960 = Fair - 200 - (120x10) Fair = 440N
What are the two formulas for gravitational potential energy?
PE = mgh PE = -(GMm)/r
What are the 3 formulas for electric potential energy?
PE = (kQq)/r
PE = Eqd
PE = qV
What are the 3 formulas for capacitor potential energy?
PE = 1/2QV
PE = 1/2CV^2
PE = (1/2Q^2) / C
How much work is done when a 1,000kg car going 40m/s slows to a stop?
W = change in energy KE = 1/2mv^2
KE = (1/2)(1000)(40)^2 W = KEfinal - KEinitial W = 0 - (8x10^5J) W = -8x10^5 J Work is negative because it is in the opposite direction of displacement (car is slowing down)
How much work is done to compress a spring 0.5m (k = 10N/m)?
Work = change in energy PEelastic = 1/2kx^2 W = (1/2)(10)(0.5)^2 W = 1.25 J
You need to lift a heavy Christmas present onto the table to wrap it. It’s 50kg, and the table is 2m high! How much work does this require? If you build a ramp 2m high and 8m long, how much force will you need? How much work?
Work is that needed to overcome gravitational potential energy and will be the same with or without machine. W = mgh = (50)(10)(2) = 1000J
With machine, F = (mgh)/d where d is length of ramp
F = 1000/8m = 125N
Merry Christmas!
A very small parallel plate capacitor connected to a battery is charged until it bears a max charge of 8x10^-19C. A change in the dielectric causes the charge on the plates to decrease. Which of the following could be a new charge? 1.9x10^-19C 4.8x10^-19C 4x10^-19C 7.9x10^-19C
4.8x10^-19C
Nano capacitor (very small)
Charge is quantized as 1.6x10^-19C per electron
Charge never decreases or increases by a number that is not a multiple of 1.6x10^-19C
Answer: 4.8x10^-19C (only one that is a multiple)
MCAT hint: when looking at questions about electric fields, r is used for distance for ____ and d is used for distance for ____
r - point charges
d - constant/uniform electric fields (between parallel plate capacitors)
When comparing electric field equations to gravity, what is voltage (electric potential) equivalent to?
What is charge equivalent to?
Voltage/electric potential equivalent to gh (gravitational potential)
q = m (mass)
For gravity near earth, F=mg. Knowing the relationship between gravity and electric field equations, derive the equation for the force of a constant electric field
F = mg
m equivalent to q
F = qE
For real gravity, F = GMm/r^2. Knowing the relationship between gravity and electric field equations, derive the equation for the force of a point charge electric field.
F = GMm/r^2
F = KQq/r^2 (coulombs law)
How do the equations for the electric field compare for constant electric fields and point charge electric fields?
Constant: E = F/q
(Compare to strength of gravity near earth g=F/m)
Point charge: E = Kq/r^2
(Compare to strength of real gravity g=Gm/r^2)
For gravity near earth, PE=mgh. Knowing the relationship between gravity and electric field equations, derive the equation for PE of constant electric field.
PE = mgh
m equivalent to q, g equivalent to E, h equivalent to d
PE = qEd
For real gravity, PE=-GMm/r. Knowing the relationship between gravity and electric field equations, derive the equation for PE of point charge electric field.
PE = -GMm/r
m is equivalent to q
PE = KQq/r
What is the voltage of a point charge electric field (equation)?
V = Kq/r
Using the phrase “potential energy”, describe what voltage is
Potential energy per unit charge
V = PE/q
What is the equation for force of a magnetic field?
F = qvBsin(theta)
What is the resistance of a conductor with resistivity of 2, length of 4, and cross sectional area of 2?
R = pL/A where p is resistivity
R = (2)(4)/(2) = 4
True or false: if voltage increases ans current remains constant, resistance will increase
FALSE: resistance is permanent quality of resistor itself
Ohm’s law: V =IR
What two equations do you need to solve any question about capacitance?
C = Q/V where C is capacitance
PE stored by capacitor: U=1/2CV^2
What is a dielectric and how does it relate to capacitance?
Dielectric- substance between 2 capacitor plates
Increase dielectric strength increases capacitance
How does increasing plate area affect capacitance? What about increasing distance between the plates?
Plate area- increases C, more room to store electrons
Plate distance- decreases C, by increases voltage for a given charge on the plates, following: C=Q/V
What terminal does the longer line on a battery represent?
Positive
Memory trick:
A longer line could be cut in half to make the two lines of a plus sign
The shorter line is only long enough to make a minus sign (negative terminal)
Essentially, batteries do what?
Create separation of charge
What is the total resistance for resistors in parallel?
1/Rtotal = 1/R1 + 1/R2 …
What is the total capacitance for capacitors in series?
1/Ctotal = 1/C1 + 1/C2 …
If you wire 2 12V batteries with a 50Ah (capacity, amp-hours) together in series, you basically get ____. If they are wired in parallel, you basically get____.
Series- equivalent of one 24V battery with a 50Ah capacity
Parallel- equivalent of one 12V battery with 100Ah
Battery in series- current and capacity remain same
Battery in parallel- voltage remains the same
What two formulas do you need to solve problems about electrical power?
P = IV
V = IR
At a concert, sound rises from 20 to 60 decibels. How has the intensity of sound changed?
60-20= 40 decibels, or 4 factors of 10
Sound intensity increases by 10,000X
What’s the formula for wave speed?
V = wavelength x frequency
Wave speed determined by medium
Frequency never changes when a wave moves from medium to medium
Wavelength will change
What is the relative velocity when the observer is traveling east 5m/s and the source is traveling east 2m/s?
3m/s
What is the relative velocity when the observer is traveling east 5m/s and the source is traveling west 2m/s?
7m/s
Going towards each other- additive
How do harmonic frequencies relate to the fundamental frequency?
Frequency of any harmonic is equal to n*fundamental frequency
Each harmonic has one more node and anti node
How many wavelengths are in the first and second harmonic? Third?
1st- half a wavelength
2nd- one wavelength
Third- 1.5 wavelengths
A pipe open at both ends will always resonate at a (shorter/longer) wavelength for same harmonic than a pipe of same length open at one end and closed at the other
Shorter wavelength
How can you combine formula for energy of proton with formula for wave speed?
E = hf c = f x wavelength
E = hc/wavelength
What is snells law equation (about refraction)?
n1sin(theta)1 = n2sin(theta)2
For total internal reflection to occur, light must pass from Higher—> lower Or Lower—> higher Index medium?
Higher index medium to lower index medium
Slower to faster medium
All waves reflected back to denser medium
Wire A has a 5A current headed towards point P.
Wire B has a 3A current headed away from point P.
Using Kirchoff’s junction rule, what must be the magnitude and direction of wire C, the third wire meeting at the junction of point P?
Junction rule:
I(into junction) = I(out of junction)
Wire C flows away from point P at 2A
What are the 3 equations for power of an electric circuit?
What is Ohm’s law?
P = IV = I^2R = (V^2)/R
Ohm’s law: V = IR
For resistors in series, which of these are additive?
Voltage
Current
Resistance
Voltage and resistance
Current is same at every point
As electrons flow through each resistor energy is dissipated-> voltage drop at each resistor
Since V = IR resistance is also additive
Is voltage drop the same at each resistor for parallel or series resistors?
Parallel
All pathways originate from common point and end at common point within circuit (think of river that splits into multiple streams before coming back together)
Explain why equivalent resistance of resistors in parallel is calculated as
1/R = 1/R1 + 1/R2 …
Resistance of each pathway differs depending on varying currents (based on what path electrons “choose”- some will be more “crowded” than others)
Giving more conduction paths reduced equivalent resistance (like more lanes for a highway)
Voltage drop is the same at each branch, so magnitude of current will be inversely proportional to resistance (Ohms law: V = IR)
What is step one for approaching circuit problem?
Find the total circuit values- voltage (given usually as battery), resistance (add for series, add 1/R for parallel), current (must find total resistance first, then use V = IR)
For which- in series or parallel- is capacitance calculated as
1/C = 1/C1 + 1/C2 ….
Series- capacitors must share the voltage drop in the loop and therefore cannot store as much charge
Simply additive for parallel
What did that Boyle guy say about pressure and volume?
Absolute pressure and volume of a given mass of confined gas are inversely proportional
P1V1 = P2V2
Just like if y’a got a big Boyle on ur face, the more volume in there the bigger it’ll become (gross)
At constant pressure, volume of a given mass of ideal gas increase/decreases by same factor of temp. Who said this, and what equation represents this statement?
Charles law
V1/T1 = V2/T2
What does Avogadro’s law say? (Think about his number…)
Under same pressure and temp, equal volumes of gas have same number or molecules
The pressure of a given mass of gas varies (indirectly/ directly) with absolute temp when volume is constant. And who said it first?
Varies directly
P1/T1 = P2/T2
Gay Lussac law
When you’re running, where does the force come from that moves you forward?
Work done ON an object (you, moving you forward) must be a force ON the object (you, so force cannot come from you)
The GROUND does work on YOU
You need to know how far someone travelled during their initial acceleration- what can you use?
Distance = average velocity x time
Convert 1 cm^3 to meters
1 cm^3 = 1^-6 m^3
What does Newton’s 2nd law describe?
Any net or unbalanced force on a mass will cause it to accelerate
Doesn’t describe objects with force on them but not net force so no acceleration
How can you use average force to find work?
W = Favg x distance
Compare Hooke’s law for force of spring to the potential energy of a spring?
Hooke’s law: F=kx
PE=1/2kx^2
How does angle and length of lever arm affect torque?
Perpendicular angle and longer lever arm increase torque
Where does v=[square root]2gh come from?
1/2mv^2 = mgh KE = PE
At what height that you fall from will you reach the ground going 5m/s?
v=[square root]2gh
5=square root(10)(h)
Simplify as (5^2)/(2x10)=h=1.25m
How is intensity related to amplitude And frequency?
Intensity directly proportional to both amplitude squared and frequency squared
What is the Doppler equation?
fo = f [c +/- vo]
————
[c +/- vs]
Where fo is observed frequency
Vo is observer velocity
Vs is source velocity
c is speed of sound
+/- depends on whether observed frequency should be bigger or smaller
How do you find the wavelength for harmonics of pipe with matching ends (both closed/open)? What about for half open, half closed?
Matching ends:
L=n(wavelength)/2
Mixed ends: L=n(wavelength)/4
Where n is the harmonic, L is length of string or pipe
How does the second and third harmonic frequency compare to the fundamental frequency?
n * fundamental frequency
How do wavelengths compare for first, second, and third harmonic?
First- 2L
Second- L
Third- 2/3L
Where L is length of string or pipe
First- length = 1/2 of wavelength
Second- length = 1 wavelength
Third- length = 3/2 of a wavelength (a little longer then a wavelength, can fit 1.5 wavelengths along its length, so one wavelength is only 2/3 of the length)
How to find index of refraction? (snell’s law)
n = c\v
What equation can you use to find the distance between slits in Young’s experiment?
X = (wavelength)L/d
X is distance between fringes
d is distance between slits
L is distance between double slits and screen (length)
For all waves, velocity can be found by this equation
V = square root
————————-
Inertia/density
How does temperate and density affect velocity of waves in gas?
For gas, v=[square root]T
Which is always NVU? For the other, under which circumstance can NVU occur?
- concave mirrors/ converging lens
- convex mirrors/ diverging lens
Concave mirrors/ converging lens are usually PRI, only NVU if object is within focal point
Convex mirrors/ diverging lens are ALWAYS NVU
What are the 3 rules when using the thin lens equation?
- Object distance (do) is ALWAYS positive
- Frequency is (+) for concave/converging, (-) for convex/diverging
- Image distance (di) js (+) if image is on opposite side of object, (-) if image is on same side of object
What type of lens is magnifying glass and what type of image is made?
Magnifying glasses are converging lenses, but have NVU images because the object is closer than the focal point
How do you find magnification? What does +/- magnification mean?
M = -(di)/do = hi/ho
Where hi is image height, ho is object height
Remember the negative sign in front of image distance!
\+M = upright image -M = inverted image
Describe the force of friction of rolling tires
Friction opposes sliding. Tires want to slide in opposite direction of travel (they are rolling CCW), so frictional force on car’s tires is in direction of travel
Sin60
0.9
A problem asks you to find “average force”. What do u do?
Think about work!
W= Favg x distance
Alternatively, v0^2=2ax then find force using F=ma
You’re trying to lift a set of weights with a rope that hangs over the rig. The weights sum up to 200kg. How’s that going for you pal?
For a pulley system to work, there must be more ropes pulling up on weight than those being pulled
Good luck pal
Divide 750 by 500
1.5
How does increasing gravity affect the force of kinetic friction?
Fk = ukFn where Fn is normal force
Normal force opposes gravity
So increasing gravity will increase kinetic friction
You’re pulling a 5x5 box across the floor. Richie is pulling a 10x10 box across the floor. Which is the ratio of kinetic friction between the boxes?
1:1
Area of contact has no effect
Fk=ukFn
No area in that formula
What are two equations that relate the force of the electric field to charge and voltage, respectively
E = F/q = V/d
A uniform electric field is decreased 3/4 in strength. How will this affect the potential energy between of the electric field?
PE of constant E =
PE = qEd
PE directly proportional to E, so E will decrease 3/4
What is the power of a conductor with a current of 6A and voltage of 7?
P=IV
P= (6)(7)= 42W
To decrease resistance in your household wires, should the wires be made longer or shorter?
Decreased length = decreased resistance
True or false: reducing voltage increases capacitance
TRUE
True or false: you can add together the PE of all capacitors in a system to get the total capacitance of the system
TRUE
PE=1/2CV^2 for each, add them all up
How does increasing voltage by 1/2 and decrease current by 2 affect resistance?
It don’t
Resistance is characteristic of material, doesn’t change with voltage or current
R=pL/A where p is density, L is length, A is area
Which has less energy, red or blue light?
Red- has longer wavelength
For a single lens system:
- All object distances are ___
- All images and focal points on the same side of the lens/mirror as observer are ___
- All images and focal points on the opposite side of the lens/mirror as observer are ___
- Negative/virtual images are always___
For a single lens system:
- All object distances are POSITIVE
- All images and focal points on the same side of the lens/mirror as observer are POSITIVE
- All images and focal points on the opposite side of the lens/mirror as observer are NEGATIVE
- Negative/virtual images are always UPRIGHT
Object on the front side of a converging lens beyond focal length is ____ and ____ image
Real and upside down
What kind of lens is a magnifying glass
Converging lens
Forms image on opposite side of the glass from the eye
NVU because object is within focal length
How does relaxing the ciliary muscles affect focal distance
Relax ciliary muscles increases focal distance of eyes lens
How does minimal focal length of eye change with age?
Increases
How do ciliary muscles work to affect the lens
Ciliary muscles work against ligaments that flatten lens- allow lens to be more spherical
This decreases focal length and increases power. Closer object requires more powerful lens (powerful lenses have short focal lengths)
True or false: nodes and antibodies only exist in standing waves
TRUE
Standing waves transfer no energy
How does amplitude influence frequency?
It doesn’t
How does temperature affect wave speed in a gas?
Lower temp = lower wave speed
Which of these will increase wave speed for a wave on a string?
- increasing modulus of elasticity
- increasing mass per unit length
Increasing modulus of elasticity
V = sqrt
Along the same lines, increasing bulk modulus of medium increases wave speed for sound wave (modulus on top of fraction)
When apparent frequency increases due to Doppler effect, white light undergoes what color shift?
Blue- higher frequency/ energy
Red shift for decreased apparent frequency
What is the wavelength of the third harmonic?
2/3L
L=3/2wavelength
How would increasing the wavelength in Young’s experiment affect the number of light and dark bands, respectively?
Both would decrease- bigger wavelength allows for less interference from two waves (if wavelength was much bigger than screen, you would only see one band of interference)
Destructive interference occurs when two waves are…
180 degrees or pi radians out of phase
What has to be the same for all harmonics?
Velocity- determined by medium
Period and wavelength decreases with increasing harmonics, frequency increases
Which are slower, sound or radio waves?
Sound- longer frequency
Nodes are points of 0 ___
Displacement
The distance between any 2 adjacent nodes in a wave is…
1/2 wavelength
What doesn’t change as waves pass between mediums?
Frequency never changes between mediums
Velocity decreases as light goes from low index to high index material
Larger line on a battery end is the ___ terminal, shorter line is the ___ terminal
Long = + Short = -
What do batteries do in circuits functionally?
Create a potential difference
5kg mass accélérâtes down 60* plane at 5m/s^2. Find force of friction
Fnet = 5x5 = 25N
Fg = 5x10xsin60
Sin60= 0.9
50 x 0.9 = 45
25 = 45 - Ff
Force of friction = 20N
You need to move 100kg box to 2m high table, but your max force you can give is 200N. How long does your ramp need to be to make this work?
F = mgh = 100x10x2 = 2000N
Framp= (mgh)/d
You’re capable of 200N
200N = 2000N/d
d= 10m
A 20C particle is dropped into parallel plate capacitor and experiences 250N. The distance between the plates is 2m. What’s the voltage?
Parallel plate capacitor = constant electric field
Econstant = F/q = V/d
250/20 = 12.5
12.5 = V/2m
V = 25V
Two small parallel plate capacitors are connected by conducting wire. Both are connected to circuit with resistor and battery. Voltage across each is 20V, capacitance of each is 10C/V. What’s total potential energy?
PE of capacitor in constant electric field = 1/2CV^2
1/2(10)(20)^2 = 2000kJ
There’s 2, and it’s additive, so 4,000kJ total for the system
Closer objects require (more/less) powerful lenses
More
A guitar string is 2m long. What’s the wavelength of the first and second harmonic?
First- 2L = 4m
Second - L = 2m
Ukulele string is 0.3m. If velocity is 10m/s, whats the frequency of the third harmonic?
Third harmonic has 3 nodes, so wavelength is 2/3 length of the string—> you can fit 1.5 (3/2) wavelengths on the string.
L = 3/2wavelength, so wavelength=2/3L
V=frequency x wavelength
10 = f x (2/3)(0.3) = 50Hz
Which has longer frequency, sound or radio waves?
Sound- slower
For a pipe closed at both ends, what is the distance between the first and fourth nodes?
Distance between any 2 nodes is 1/2 wavelength, so distance between 1 and 3 is 1 wavelength, and distance between 1 and 4 is 1.5 or 3/2 wavelength
An electromagnetic wave in air encounters medium with n = 1.5. Which is the same in both mediums? Velocity Frequency Wavelength Intensity
Frequency never changes between mediums
Put these in correct order of auditory pathway: vestibulocochlear nerve, pinna, tympanic membrane, cochlea, ossicle
Pinna -> tympanic membrane -> ossicles -> cochlea -> vestibulocochlear nerve
What kind of waves are sound waves
Longitudinal
Sound particles pushed forward, sent backwards (compression and rarefaction/decompression)
Mechanical disturbance of particles along sound waves direction or propagation
How to find angular frequency
w = 2(pi)f = (2pi)/T
For simple harmonic motion in springs and pendula
How many degrees are waves when completely out of phase (0 amplitude)
180*
Half a wavelength (one wavelength is 360*)
Red light shift occurs due to
Observed frequency decrease (red light is lower frequency end of visible spectrum)
Relationship between intensity and distance from source
Intensity inversely proportional to square of distance from source
Because I=P/A and surface area of sphere is A=4(pi)r^2
For double bonds, which is E and Z
Z is “zis” aka cis
E is trans
Relate capacitance to charge and voltage
C = Q/V
Another way to think:
V = CQ
V is the potential energy, which is determined by ability to store charge (C) and magnitude of charge (Q)
How to solve pKa = -logKa (mathematically)
If n = log(a/b), how do you find a/b?
-log(1x10^n) = n
n = log(a/b) —> a/b = 1x10^n
What is the unit for pressure in PV=nRT
Atm
1 atm = 760 torr
If gas is collected over solution, how do you solve for pressure of gas with PV=nRT
Must subtract vapor pressure from total pressure to get pressure of gas
PV=nRT
if V is decreased 33%, what happens to P
down 33% means V x 2/3
Flip fraction
P goes up 3/2
How does doubling distance from a sound source affect intensity
2x distance = intensity decrease by 4x
Tripling distance decreases intensity by 9x, etc (squared math)
Sound source located 1m from microphone is 80dB. Measured 3m away, what is intensity
Triple distance = intensity down 9x
9x is close to 10x decrease, so basically intensity decreases by factor or 10
80dB-10dB = 70dB
Area of circle
(Pi)r^2
GPa is how many pascals
10^9 Pascals
Light travels from the air to a medium with an index of refraction of 3. Does the light slow down or speed up?
Lowest index of refraction = fastest light travel
From air to index of 3, light slows down
What kind of lens will correct hyperopia?
Hyperopia = farsighted, light is focused behind retina (rather then on retina)
Aka; light is not concerning quickly enough.
Can be fixed with converging (convex) lens
Myopia (nearsighted, YOU) corrected with diverging (concave) lens- light is converging too soon, need to spread out rays
Your head is 5kg, with center of mass 2cm in front of spine. Your trap inserts 1cm behind spine. How much downward force does your trap create to maintain equilibrium?
Basically a fulcrum question
(5kg)(10m/s2)(0.02m)=(F)(0.01m)
F = 100N
dispersion
higher frequency light bends more than lower frequency light
You run around a track at a constant 7mph (trying to catch Maeg). Is there a net force?
YES- if you are changing direction then there must be acceleration, so you WILL have a net force
micro in scientific notation
10^-6
Object with -8m/s^2 acceleration and initial velocity of 24m/s travels until it reaches 0m/s- how far did it go? explain two ways to solve
vf^2 = v0^2 + 2ax 0 = (24)^2 + 2(-8)x ----> x = 36m
average velocity is 12m/s, would take 3s to get to 0m/s with -8m/s^2
3s x 12m/s = 36m
inertia
object’s resistance to change in velocity
quantified as mass
wavelength below 400nm is __
wavelength above 700nm is __
below 400nm is ultraviolet
above 700nm is infrared
total internal reflection occurs when
angle is greater than critical angle (n2 > n1)
all light is reflected (none transmits) so there is no angle of refraction
for a reflection from a plane surface (like a mirror), incident angle is always…
equal to angel of reflection
light has frequency of 4.7x10^14Hz. If electron wave absorbs 20% of the photons that strike its surface, how much energy is absorbed per 1,000 photons?
Planck’s constant = 6.6x10^-34 J*s
20% of 1000 is 200 photons
E = (200)(6.6x10-34)(4.7x10^14)
E = 6.23x10^-17J
DIVERGING lens makes light ___
CONVERGING lens makes light ___
DIVERGING makes light DIVERGE (spread)
CONVERGING makes light CONVERGE (come together)
two parallel wires with opposing current will have magnitude of force that is:
zero
makes them attract
makes them repel
repel- following right hand rule, magnetic fields will cause force in opposite directions that cause repulsion
1m board hangs from rope 0.2m from its left end. directly at left end is 30kg mass. if board is motionless and horizontal, what is mass of board?
fulcrum question
assume center of mass to be where the weight of board will pull… 1/2=0.5. 0.5-0.2 = 0.3m from fulcrum
(0.2)(30)=(0.3)x
x= 20kg
500kg mass slides across floor from tension of 1,000N. If coefficient of kinetic friction is 0.05, what is acceleration of object?
Fk = ukFn = (0.05)(500)(10) = 250N
Fnet = ma
1000 - 250 = 500a
a = 1.5m/s
a calculator is powered by two small electrodes separated 2cm, with potential difference of 10V. If current is 1x10^-4A, how much power is required to run the calculator? What is the strength of the electric field?
P=IV
P= (1x10^-4)(10)= 1x10^-3 or 1mW
E=V/d=F/q
E=10/(2x10^-2)= 500N/C
ray of light passes from air to medium with n=1.5. which decreases/ increases: angle of refraction and velocity
both decrease
waves SLOW DOWN when they hit denser medium
T/F: net movement at each anti-node is zero in a non-standing wave
FALSE: only standing waves have nodes and antinodes
for a pipe closed at both ends, the distance between the first and fourth node in a standing wave is?
for pipe closed at both ends, distance between nodes is wavelength/2
so between 1st and 4th would be
3wavelength/2
could also be written as 3(velocity)/2(frequency) because
v=f(wavelength)
when waves pass between mediums what NEVER changes
frequency
if the speed of electron A is 3x speed of electron B, which shows ratio of force on A to force on B due to electric field?
Fa=Fb
3Fa=Fb
Fa=3Fb
Fa=Fb
F=Eq, there is nothing in here about velocity
how does velocity of light waves and sound waves differ when passing through different mediums?
light waves travel slower in denser mediums
sound waves travel faster in denser mediums (increased frequency because of density, faster recoil)
to increase current, add resistors in parallel or in series?
Ohm’s law: V=IR
increase current by decreasing resistance
can decrease resistance by adding another resistor in parallel- resistors in parallel always have total resistance lower than lowest resistor in parallel (1/Rtotal = 1/R1 + 1/R2)
allows for alternative pathways for current
in a circuit, resistors are:
conductors
insulators
batteries
conductors- must allow for a current to pass through (insulator would block current)
venturi effect
decrease in fluid pressure when fluid passes through narrowed section and velocity increases
explained by Beroulli equation
if a gas at STP has a volume less than 22.4L, it is deviating from ideal behavior why?
intermolecular attractions cause molecules to move closer together, occupy less space
gas above 22.4L indicates volume of gas molecules is not negligible
dispersion is the separation of light into its colors. which will refract more, red or blue light?
lower frequency colors refract less- lower index of refraction; higher frequency refract more
blue light refracts more than red light
chromatic aberration
formation of blurry images due to light dispersion
put these in order of increase frequency: red, infrared, violet, microwave, radio, ultraviolet, gamma, x-ray
radio < microwave < infrared (infra RED) < red < violet < ultraviolet (ultra VIOLET) < xray < gamma
what is the velocity of a light wave with index of refraction of 3?
n = c/v 3 = 3x10^8 / v v = 1x10^8 m/s
given a lens with a focal length of 3 and a lens with a focal length of 6, which is stronger?
stronger lens bends light more
strength of lens = 1/f
focal length of 3 is stronger
what is the strength of a lens with an image distance of 5 and an object distance of 2? What kind of lens is it?
S = 1/f = 1/do + 1/di
S = 1/f = 1/2 + 1/5
S = 0.5 + 0.2 = 0.7
positive image distance = converging (convex) lens- round on both sides, converges light rays
what kind of lens is eye
convex lens (converging)- round on both sides, converges light rays
object distance is 2 focal lengths from center of converging lens. what is ratio of height of image to height of object?
1/f = 1/do + 1/di
1/f = 1/2f + 1/di when object distance is twice focal length
ratio of image/object distances = ratio of image/object heights (because of right triangle geometry)
di = 2f
object/image distances are the same. heights will also be the same
1:1 ratio
your eye has a focal length of 2cm. what is the combined strength when you wear glasses with optical power of -4D?
S = 1/f
your eye is convex lens (converging), so positive strength and focal length. Glasses are negative strength, so it’s a concave (diverging) lens
-4D + (1/0.02) = -4D + 50D = 46D
what is the volumetric flow rate of a 1m radius circle with fluid flowing through at 3m/s?
Q = AV Q = [pi]r^2 x V Q = (3.14)(1^2)(3) Q = ~9
define: alpha decay beta - decay beta + decay electron capture gamma decay
alpha- decrease atomic number by 2, mass by 4
beta (-)- lose electron, increase atomic number by 1
beta (+)- lose positron, decrease atomic number by 1
electron capture- gain electron, decrease atomic number by 1
gamma- no change
describe viscous flow for closed channel
fastest at center, slower along top and sides (drag along walls)
what kind of mirrors are:
grocery store security cameras
passenger side mirrors
cosmetic mirrors
security camera- convex (round outside), diverging
side mirror- convex, diverging
cosmetic mirror- concave, converging
which is before visible light, which is after: ultraviolet and infrared
ULTRA VIOLET is after violet (higher energy)
INFRA RED is before red (lower energy)
which of these are diverging? convex mirror convex lens concave mirror concave lens
convex mirror (image comes back at you with light rays dispersing) concave lens (image is behind with light rays spreading, remember for lens just consider the shape of the front)
how can you find magnification and what does it mean when it’s negative
m = -i/o
negative magnification = inverted (real) image
for what kinds of mirrors and lenses is focal point negative?
convex mirrors- diverging
concave lens- diverging
when does total internal reflection occur
angle of incidence is greater than critical angle
critical angle is when angle of refraction = 90*, and refracted light passes along interface of two media
can only occur when light travels from higher to lower index of refraction (will cause angle to move away from normal)
what kind of lens for reading? what kind of lens for seeing the board at school? what are these conditions called?
myopia = nearsighted --> diverging (concave) lens hyperopia = farsighted --> converging (convex) lens
if the first lens in a two lens system has a magnification of 5 and the second has a magnification of 2, what’s the total magnification?
m total = m1 x m2 x m3…
5x2 = 10
what causes prism
dispersion
different wavelengths of light refract differently
spreading of light, as seen in single slit experiment
diffraction
light with parallel electric field vectors is said to be
plane polarized
what kind of image is formed when an object placed in front of a convex lens at a distance smaller than the focal length
virtual and upright
real if the object is farther than the focal length
which of these will not result in splitting of white light into its component colors? (consider everything is ideal) dispersion diffraction refraction reflection
dispersion can (prism) diffraction can (diffracting grating, separates by wavelengths) refraction can (thin film, colors refracted at slightly different angles in film)
reflection cannot if mirror is ideal. if not ideal, significant aberration could lead to separation of light
when a light’s frequency is above threshold frequency, the magnitude of the resulting current is directly proportional to…
directly proportional to intensity and amplitude of light beam
emission
photon emitted when electron falls from higher energy to lower energy level
this is used to determine chemical structure because the different bonds absorb different wavelengths of light
infrared (IR) spectroscopy
basic principle of fluorescence
multi step emission (of different frequencies)
mass defect
result of matter being converted into energy in the nucleus
nuclear fission vs fusion
fission- absorption of lower energy neutron (large nucleus splits into smaller nucleus)
fusion- small nuclei combine
compare effects of: alpha decay beta (-) decay beta (+) decay gamma decay electron capture
alpha- alpha particle (He) emission (has +2 charge and no electrons)–> reduce atomic # by 2, mass # by 4
beta (-)- electron and anti-neutrino emission–> increase atomic # by 1
beta (+)- positron and neutrino emission–> reduce atomic # by 1
gamma- just decreases energy
electron capture- doesn’t emit, but absorbs electron from inner shell–> increase atomic # by 1
what is pH of solution with pKa of 1, [2] of acid, and [4] of base?
pH = pKa + log[base/acid]
= 1 + log[base] - log[acid]
~ 1 + 0.4 - 0.2
= 1.2
simplify x^4/3
x^4/3 = root of 3
simplify square root
[sqrt]180 =
[sqrt]4 x [sqrt]9 x [sqrt]5
= 6[sqrt]5
[sqrt]2
[sqrt]3
[sqrt]2 = 1.4 [sqrt]3 = 1.7
simplify logA^b
logA^b = blogA
convert log to ln
logx = lnx/ 2.3 (e = 2.3)
log(a x 10^b)
log(a) + log(10^b) =
0.a + b
SOH CAH TOA
sin- opposite/ hypotenuse
cos- adjacent/ hypotenuse
tan- sin/cos = opposite/adjacent
What is magnitude of electric field between two electrodes 3cm apart with 5V potential?
E=v/d
E=5/0.03
E=5/1/3/100 = 166N/C
How does the change in frequency due to the Doppler effect vary for sound waves and radio waves?
delta frequency/ frequency = -v/c
a slower wave will have a greater change in frequency
sound waves are slower than radio waves, so sound waves will have a greater change in frequency
on earth an ice cube floats with 9/10 of its volume submerged. How would this change for a planet where gravity is 1/6 earth’s?
weight = mg =
p(density of fluid)v(volume submerged)g
because weight is balanced by buoyant force
since both weight and buoyant force are proportional to g, the value of g is irrelevant
ice cube will still be 9/10 submerged
When the number of photons incident on a cathode with energies above the work function increase, what also increases?
- potential energy of each electron ejected
- number of electrons ejected
- speed of electrons at anode
number of electrons ejected
number of incident photons affects number of electrons, not their energies (energies depend on photon energy, not quantity). Energy of electrons also depends on work function, and potential between cathode/anode
increasing frequency of each photon incident on cathode will have what effect?
increase speed of ejected electrons- only effect photon frequency has on ejected electrons is on its kinetic energy
a particle with a charge of 8x10^-19C and speed of 1m/s is placed in between capacitor plates. if the speed of the particle is doubled, the electric force on the particle will:
remain the same
F=qE
nothing about speed here!
If you add a second capacitor plate in series to your circuit, what will the equivalent capacitance of the new circuit be?
in series, C are added by inverse rule
it will be 1/2 the original value
what is the length of a pipe that is closed at one end and has a wavelength of 2m at the second harmonic?
for pipe closed at one end, L=n(wavelength)/4
L = 2(2)/4 = 1m long
What is the intensity of the threshold of pain, 120dB, when the human threshold of hearing is 10^-12W/m^2?
dB = 10log(I/I0) where I0 = 10^-12
120 = 10log(I/10^-12)
to make log(I/I0) = 12,
intensity must be 10^0 (=1) W/m^2
how does the magnitude of a detected sound’s frequency shift change as an object is throw up and falls back down?
falls to zero, then increases
as object goes up it has negative acceleration, and instantaneously stops at peak (shift decreases to zero)
on the way down the shift increases as the object gains velocity
why does visible light (unlike sound) travel more slowly through denser medium?
the light is absorbed and re-emitted by the atomic structure of the optically dense medium
a block of weight W is pulled at a constant speed by a rope that gives tension T while a frictional force F resists movement. what is the magnitude of F?
constant speed means frictional force = tension
F = Tcos(theta)
if molecule A has stronger intermolecular bonds than molecule B, which one will have lower surface tension?
stronger bonds = higher surface tension
(B will have lower surface tension)
surface tension (J/m^2) is measure of intermolecular forces between molecules on surface of liquid
paramagnetic vs diamagnetic
paramagnetic = unpaired electrons
diamagnetic = paired electrons (di = pair), aka even number of electrons
pauli exclusion principle
even in excited state, none of electrons can have same four quantum numbers
what is the strength of a magnetic field that exerts a force of 2N on a 2C charge going 3m/s?
F = qvB, units are N/C(m/s)
2N = (2C)(3m/s)B
B=0.3 T
what is heat capacity defined as
c = Q/(delta)T
change in heat per unit time
what is ratio of fundamental frequency to frequency of 3rd overtone?
3rd overtone = 4th harmonic, so ratio is 1:4
what is current and its unit
charge per time, C/s
first law of thermodynamics
deltaU = Q - W
from Point S to Point T, electric potential increases continuously from 100V to 200V. Where do the field lines point?
from T to S- in direction of decreasing electric potential
R1 and R2 are connected in series to a battery with no internal resistance. How does the current through R1 and R2 change when a third resistor is added in parallel?
current through R1 and R2 decreases- the third resistor in parallel decreases total resistance. with another option for current to go through, there would be less current through R1 and R2
You bike on a stationary bike at Crossfit with a load of 30W. After 3 mins, how much work have you done?
P = W/t, so W = Pt 30x(3x60) = 5400J
kinetic energy of a photoelectron?
KE = hf - Work function h = 7x10^-34 m^2kg/s
what is the the velocity of a 5kg child going around a 5m ride in a circular motion with a centripetal force of 10N?
Fc = (mv^2)/r 10N = 5kg v^2 / 5m v = [sqrt]10 m/s
remember that centripetal acceleration is v^2/r, and F=ma, so Fc=(mv^2)/r makes total sense
what is the centripetal acceleration if an object is going 2m/s around a 4m radius circle?
ac = v^2 / r ac = (2^2) / 4 = 1m/s^2
Fc = (mv^2)/r
what is the index of refraction of light passing from air into a wall going 2x10^8m/s?
n = c/v n = (3x10^8)/ (2x10^8) = 1.5
if a person’s lungs have an air pressure of 380mmHg, what percentage of standard atmospheric pressure is this?
standard atm pressure = 760mmHg
this would be 50%
what happens in beta minus decay
neutron –> proton –> increase atomic number by 1
photon emission is type of what decay
gamma
which is not a unit of power:
J/s
ftxlb/s
m^2/s^3xkg
units of power:
J/s
ftxlb/s
kgxm^2/s^3
(mass/distance/energy should be on top, time on bottom)
