MCAT physics
total flight time =
(time from launch to top) + (time from top to landing)
cos180
-1
density of water
-1000 kg/m³ -1 g/cm³
colors of the visible spectrum
-ROYGBV -in order from lowest frequency (longest wavelength) to highest frequency (shortest wavelength)
electromagnetic wave
-composed if oscillating electric and magnetic fields -are transverse waves -do not require a material medium to propagate and can travel through empty space (vacuum)
acceleration
-how fast an object's velocity changes -an object's velocity changes if the speed or direction changes, so an object can be accelerating even if its speed is constant
longitudinal wave
-if the direction in which the particles of the conducting medium oscillate is parallel to the direction in which the wave travels -sound waves are longitudinal waves
formula for location of the center of masses
-multiply each mass by its location and add -divide by the total mass -x stands for location -m stands for mass
pauli exclusion principle
-no two electrons, protons, or neutrons can occupy the same quantum state within a small space -the photoelectric effect occurs when light incident upon a metal surface causes electrons to be ejected by that surface. individual photons provide energy hf to individual electrons, and if that energy is enough to overcome the binding energy of the metal, the electrons are ejected.
Bohr model of the atom assumes:
-the atom is made up of a dense, massive positive nucleus orbited by negative electrons -the energy levels of an atom are quantized. they are determined by the discrete orbital states of the electrons which are numbered. higher number states correspond to higher energies. n=1 is the ground state -atoms can change quantized energy states by absorbing or emitting a photon. the energy of the photon must correspond exactly to the energy difference between the two states -atoms can change states thermally by interacting with other particles. as with the case of photon absorption, though, the changes in atomic energy are quantized, and the excited atoms will tend to return to the ground state by emitting photons
simple harmonic motion
-the ideal type of oscillatory motion -a mass oscillating on a spring exhibits simple harmonic motion
center of mass
-the point that behaves as if the object were a single particle -the point at which we could consider all the mass of the object to be concentrated
flow rate
-the volume of fluid that passes a particular point per unit time -f=Av A=area of pipe at any point v=average speed of the flow
bernoulli's equation
-used on ideal fluids -the fluid is incompressible -negligible viscosity -laminar flow -steady flow rate
cos90
0
dropped means Vo equals
0
horizontal velocity does NOT equal what at the top of its trajectory
0
if an objects starts from rest, Vo equals
0
vertical velocity equals what at the top of its trajectory
0
cos60
0.5
sin30
0.5
tan30
0.6
cos30
0.85
sin60
0.9
cos0
1
tan60
1.7
frequency equals
1/T where T represents period
period equals
1/f where f represents frequency
gravitational acceleration
10 m/s²
kilo
10³
mega
10⁶
giga
10⁹
centi
10⁻²
milli
10⁻³
pico
10⁻¹²
micro
10⁻⁶
nano
10⁻⁹
if the object's density is 3/4 the density of the fluid, then
3/4 of the object will be submerged (and vice versa)
An electrocardiogram responds to changes in the electric potential of the heart from a number of different angles and distances, and represents a different pair combinations of these signals (voltages) as deflections of several needles under which runs graph paper moving horizontally at a constant speed. Suppose a patient has a resting heart rate of 60 beats per minute and the tape runs through the machine at 4 cm/s. What is the wavelength over which the pattern should repeat?
60 beats/min= 1 beat/s or a period of 1 s and frequency of 1 Hz. The wave speed, v, is simply the speed at which the tape runs under the needle: v=4 cm/s. Thus λ=v/f=4 cm/s / 1 Hz=4 cm
An ammonia molecule (NH₃) contains 3 hydrogen atoms that are positioned at the vertices of an equilateral triangle. The nitrogen atom lies 38 pm (1 pm=1 picometer=10⁻¹² m) directly above the center of this triangle. If the N:H mass ratio is 14:1, how far below the N atom is the center of mass of the molecule?
7 pm Since the 3 hydrogen atoms have equal masses and are symmetrically arranged at the corners of an equilateral triangle, the center of mass of just the 3 hydrogen's is at their geometric center, or the center of the base triangle. Let the position of the nitrogen atom be the 0 mark. (14)(0 cm) + (3 x 1)(38 pm) all divided by (14)+(3 x 1)
What a doctor injects someone with a hypodermic needle, she exerts about 15 N of force to pierce adult skin. Once the skin has been pierced, considerably less force is required to push the needle deeper. If a force of 5 N on the plunger is required to initiate the injection, how hard should one pull back on the barrel to minimize risk of hematoma to the patient once the needle is inserted into the vein?
According to Newton's second law, Fnet=ma. Minimizing risk of hematoma implies that the acceleration of the stationary needle should be zero (so it won't move deeper in or out of the vein during the injection). Thus Fnet=0 and Fplunger=Fbarrel or Fbarrel=5 N
Turpentine has a specific gravity of 0.9. What is the density of this liquid?
Density of turpentine= (specific gravity of turpentine)(density of water)=(0.9)(1000 kg/m³)=900 kg/m³
total mechanical energy formula
E=KE+PE
hooke's law
F=-kx k=spring constant
force of gravity acting on a fluid
Fgrav=(density)(volume)(acceleration due to gravity)
newton's third law of motion
For every action there is an equal and opposite reaction and form an action-reaction pair
A typical ion channel in a cellular membrane might allow the passage of 10⁷ sodium ions to flow through in one second. What is the magnitude and direction of this ionic current?
I=Q/t (10⁷)(1.6x10⁻¹⁹ C)=1.6x10⁻¹² A
impulse
J
impulse momentum theorem
J=∆p=∆(mv)=F∆t
elastic collisions conserve
KE
angular momentum formula
L=lmv=iw l=lever arm/radius of the circle i=inertia w=angular velocity
joule
Newton x meter used to describe work
power formula
P=IV
power of circuit element
P=IV=I²R=V²/R
power dissipated by a resistor: joule heating law
P=I²R
elastic potential energy
PEelastic=½kx²
hydrostatic gauge pressure
Pgauge=(density of fluid)(acceleration due to gravity)(depth of sheet)
charge on a capacitor formula
Q=VC C=proportionality constant V=potential difference between the plates of a charged capacitor
current formula
Q=charge t=time
Within a metal wire, 5x10¹⁷ conduction electrons drift past a certain point in 4 seconds. What is the magnitude of the current?
Q=ne (5x10¹⁷)(1.6x10⁻¹⁹ C)=8x10⁻² C I=Q/t=(8x10⁻² C)/4 s=0.02 A
When the potential difference between the ends of a wire is 12 V, the current is measured to be 0.06 A. What's the resistance of the wire?
R=V/I 12 V/0.06 A=200 Ω
resistance formula
R=V/I V=voltage applied I=resulting current
newton's second law of motion
The acceleration of an object depends on the mass of the object and the amount of force applied.
inertia
The tendency of an object to resist a change in motion
2 forces act on an object of mass m= 5 kg. One of the forces has a magnitude of 6 N, and the other force, perpendicular to the first, has a magnitude of 8 N. What's the acceleration of the object?
To find the net force, find the hypotenuse of the right triangle made from the forces. The hypotenuse will be 10 N. Since Fnet=10 N, the acceleration of the object will be a=Fnet/m=(10 N)/(5 kg)= 2 m/s²
The wavelength of the red Hα spectral line characteristic of the visible hydrogen spectrums 656 nm. How much energy does a hydrogen atom lose when it emits an Hα photon? Use h=6.63x10⁻³⁴ Js.
Use the equation for the energy of a photon in terms of wavelength. Ephoton=hc/λ=[(6.63x10⁻³⁴ Js)(3x10⁸ m/s)]/656x10⁻⁹ m=3x10⁻¹⁹ J
For 6 seconds, you push a 120 kg crate along a frictionless horizontal surface with a constant force of 60 N parallel to the surface. If the crate was initially at rest, what will its velocity be at the end of this 6 second time interval?
Using Newton's second law, we find that the acceleration of the crate is a=F/m=(60 N)/(120 kg)=0.5 m/s². using the equation V=Vo+at, 0+(0.5m/s²)(6s)= 3 m/s
kinematics equation no displacement
V = Vo + at
Ball 1 and Ball 2 are rolling toward each other at the same speed, 5 m/s. Ball 1 has a mass of m1=8 kg, and Ball 2 has a mass of m2=2 kg. After the collision, Ball 1 is observed to move with a velocity of 2 m/s in the same direction as V1. What's the velocity of Ball 2 after the collision?
V2'=7 m/s P total before = P total after m1v1+m2v2=m1v1'+m2v2' (8 kg)(5 m/s)+(2 kg)(-5 m/s)=(8 kg)(2 m/s)+(2 kg)(v2') 30=16+(2 kg)(v2') 14=(2 kg)(v2') v2'=7 m/s since v1 and v2 point in opposite directions, pick one direction to call positive. to the right was chosen as the positive direction.
ed's formula
V=Ed d=distance E=electric field
ohm's law
V=IR
projectile motion horizontal velocity
Vx = Vo (constant)
projectile motion vertical velocity
Vy = Voy + (-g)t
kinematics equation no time
V² = Vo² + 2ad
work done by an electric field
W=-∆PE
work formula
W=Fd
work formula where θ is the angle between F and d
W=Fdcosθ
efficiency formula
Woutput/Feffort
work energy theorem
Wtotal=∆KE
photon
a bundle of energy associated with electromagnetic radiation
pulley
a device that changes the direction of the tension that pulls on the object that the string is attached to
capacitor
a pair of conductors that can hold equal but opposite charges
electric circuit
a pathway for the movement of electric charge, consisting of a voltage source, connecting wires, and other components
force
a push or pull exerted by one object on another
mass
a quantitative measure of an object's inertia
mechanical wave
a series of disturbances (oscillations) within a medium that transfers energy from one place to another
mirror
a surface, usually made of glass or metal, that forms an image of an object by reflecting light
A box of mass m is sitting on an incline of 45 degrees and it requires an applied force F up the incline to get the box to begin to move. What is the maximum coefficient of static friction? a. (√2F/mg)-1 b. (√2F/mg) c. (√2F/mg)+1 d. (2F/mg)-1
a. (√2F/mg)-1 the force of static friction and the force of gravity are acting down the incline in this situation. when the box just begins to move upwards the forces in both directions are equal and the force of static friction is at its maximum. therefore, you have the equation F=µsmgcos(45)+mgsin(45). solving for µs, we find the correct answer choice to be A.
An experiment is conducted where a cue ball (mass 0.25 kg) moves at 10 m/s towards an adjacent numbered ball of same mass at rest. In trial 1, the collision is elastic. In trial 2, the collision is perfectly inelastic. What is the speed of the cue ball immediately after the collision in trial 1 and trial 2 respectively? a. 0 m/s and 5 m/s b. 0 m/s and 10 m/s c. 5 m/s and 0 m/s d. 5 m/s and 5 m/s
a. 0 m/s and 5 m/s in a perfectly inelastic collision, recall that total momentum is conserved but not total kinetic energy and that the balls stick together. initial momentum must be equal to final momentum. Pi=Pf=(m₁v₁)=(m₁+m₂)v'=v'=(m₁v₁)/(m₁+m₂)=(0.25 x 10)/(0.25 + 0.25)=5 m/s. this is the value for trial 2, eliminating choices B and C. for the elastic collision, kinetic energy must be conserved in addition to total momentum, and both objects can move at different velocities after the collision. since momentum is conserved Pinitial=Pfinal=m₁v₁=m₁v₁f+m₂v₂f. since m₁=m₂, then v₂f=v₁-v₁f. similarly, if kinetic energy is conserved, then KEinitial=KEfinal=½m₁v₁²=½m₁v₂²f+½m₂v₂²f. in order for these 2 equations to hold true, v₁f must equal either 0 m/s or 10 m/s. since 10 m/s would indicate the 2 balls did not collide at all, the cue ball must have a velocity of 0 m/s immediately following the elastic collision, transferring all kinetic energy to the numbered ball.
The gravitational force the sun exerts on earth is F. Mars is 1.5 times further from the sun than earth and its mass is 1/6 of the earth's mass. What is the gravitational force that the sun exerts on mars? a. 2/27 F b. 1/9 F c. 9 F d. 27/2 F
a. 2/27 F the gravitational force of the sun on the earth is F=GMm/r², the force exerted on mars is Fmars=((GM)(1/6M))/(3r/2)²=((GMm)(1/6))/((r²)(9/4))=4/54F=2/27F
In optics, spontaneous paramedic down conversion is often used to create two photons from one photon. Thus, it is possible for a blue photon with a frequency of 700 THz to be split into two identical red photons when incident on a nonlinear crystal. What is the wavelength of the red photons with respect to the blue photon, λB, given that energy is conserved? a. 2λB b. 4λB c. 1/2λB d. 1/4λB
a. 2λB the energy of a photon is E=hf=hc/λ since EB=2ER, we know that fB=2fR, and consequently λR=2λB
A particular eucalyptus tree has a density of 667 kg/m³ and a mass of 6000 kg. What volume of the tree would float above the surface of water? a. 3 m³ b. 5 m³ c. 6 m³ d. 9 m³
a. 3 m³ for floating objects, Po/Pf=Vsub/V since the density of the object is 667 kg/m³ and the density of water is 1000 kg/m³, two thirds of the object will be submerged and one third will be above the surface of the water. since p=m/v, then v=m/p=6000/667=9m³. the total volume of the object is 9 m³, and one third of that is 3 m³
A 100 kg skier's knee can withstand a lateral torque of 500 Nm before dislocating. As the skier loses control going around a corner, one ski comes up off the snow and the other boot and lower leg remain vertical, such that the knee starts the bend laterally. If the distance from the skier's knee to his center of mass is 1 m, at what angle θ from vertical will the knee dislocate due to the torque of gravity alone? a. 30 degrees b. 45 degrees c. 60 degrees d. 90 degrees
a. 30 degrees rearranging the formula for torque, we find that sinθ=τ/rF. the force of gravity is acting at the center of mass, 1 m from the knee, which is the fulcrum. substituting the values, being careful to use 1000 N of gravitational force rather than 100 kg, we find that sinθ=0.5. therefore θ=30 degrees
A person listening to music on a stereo system experiences a sound level of 70 dB. If the volume dial is turned up to increase the intensity by a factor of 500, what sound level would this person hear now? a. 97 dB b. 105 dB c. 115 dB d. 120 dB
a. 97 dB if the intensity had increased by a factor of 100, which is 10 x 10, the sound level would have increased by 10+10=20 dB. if the tensity has increased by a factor of 1000, which is 10x10x10, the sound level would have increased by 10+10+10=30 dB. the fact that the intensity increased by a factor of 500, which is between 100 and 1000, means that the sound level increased by between 20 dB and 30 dB. if the original sound level was 70 dB, then the new sound level must be between 70 + 20=90 dB and 70 + 30=100 dB
The explanation for the fact that radioactive isotopes of an element exhibit the same chemical behavior as the stable isotopes of the element is that each has the same: a. atomic number b. number of neutrons c. mass number d. atomic weight
a. atomic number
During adiabatic compression of a mass the temperature: a. increases because no heat is transferred b. remains constant because heat is transferred c. remains constant because no heat is transferred d. decreases because heat is transferred
a. increases because no heat is transferred
Visible light travels more slowly through an optically dense medium than through a vacuum. A possible explanation for this could be that the light: a. is absorbed and re-emitted by the atomic structure of the optically dense medium b. is absorbed and re-emitted by the nucleus of the material in the optically dense medium c. bounces around randomly inside of the optically dense medium before emerging d. loses amplitude as it passes through the optically dense medium
a. is absorbed and re-emitted by the atomic structure of the optically dense medium
a pilot wanting to travel northeast in a wind blowing from the west at a speed similar to her airspeed should direct her plane in which direction? a. north b. south c. east d. west
a. north
Sound of a known frequency, wavelength, intensity, and speed travels through air and bounces off an imperfect reflector which is moving toward the source. Which of the following properties of the sound remains the same before and after reflections? a. speed b. intensity c. frequency d. wavelength
a. speed within still air, the speed of sound remains constant
2 crates are moving along a frictionless horizontal surface. The first crate, of mass M=100 kg, is being pushed by a force of 300 N. The first crate is in contact with the second crate, of mass m=50 kg. a. What's the acceleration of the crates? b. What's the force exerted by the larger crate on the smaller one? c. What's the force exerted by the smaller crate on the larger one?
a. the force is pushing on a combined mass of 150 kg so the acceleration will be a=(300 N)/(150 kg)= 2 m/s² b. let F₂ be the force that M exerts on m. F₂=ma so F₂=(50 kg)(2 m/s²)= 100 N c. by newton's third law, the force that m exerts on M will be -F₂, which will be -100 N
A siren produces sound waves in the air. If the frequency of the waves is gradually decreasing, which of the following changes to the waves is most likely also occurring? a. the wavelength is increasing b. the wave speed is decreasing c. the amplitude is decreasing d. the period is decreasing
a. the wavelength is increasing because the wave speed is set by the medium (the air, in this case), the wave speed is a constant. since v=λf, this means that λ and f are inversely proportional. so if f is decreasing, then λ must be increasing. so choice A.
on earth, a tennis player can hit a tennis ball normally, causing the ball to travel on a path that is a symmetrical parabola. a tennis player can also hit a tennis ball with a "slice" which causes the ball to spin and deviate to one side of its normal path. What is the best explanation for this deviation? a. there is an additional acceleration on the ball. b. the spin on the ball caused the acceleration from gravity to change direction. c. the spin on the ball used energy so the ball could not travel in a straight line. d. the gravitational field was not uniform.
a. there is an additional acceleration on the ball.
average acceleration formula
a=∆v/∆t
charged particle
accelerates in an electric field
density
amount of mass contained in a unit of volume
perfectly inelastic
an inelastic collision in which the objects stick together afterwards
mass
an intrinsic property of an object and does not change with location
if no net force acts on an object ...
an object at rest will remain at rest an object in motion will remain in motion with a constant velocity
newtons first law of motion
an object in motion will remain in motion unless acted upon by another force
periodic/harmonic motion
any motion that regularly repeats
projectile motion horizontal acceleration
ax=0 Vox = Vo(cosθo)
projectile motion vertical acceleration
ay= -g Voy = Vo(sinθo)
In a crash simulation, a car traveling at x m/s can stop at a distance d m with a maximum deceleration. If the car is traveling at 2x m/s, which of the following statements is/are true, assuming maximum deceleration? 1. the stopping time is doubled 2. the stopping distance in doubled 3. the stopping distance is quadrupled. a. 1 and 2 only b. 1 and 3 only c. 2 only d. 3 only
b. 1 and 3 only according to the formula v²=vo²+2ad, if v is 0, the equation can be rearranged for d becoming d=vo²/2a. since the car is decelerating, a will be negative. if vo is doubled, the stopping distance, d, will be quadrupled. according to the formula v=vo + at, if v is 0, the equation can be rearranged for t becoming t=-vo/a. a will be negative. is vo is doubled, the stopping time, t, is doubled.
Light travels through water at an approximate speed of 2.25 x 10⁸ m.s. What is the refractive index of water? a. 0.75 b. 1.33 c. 1.50 d. 2.25
b. 1.33 answer A can be eliminated immediately since an index of refraction can never be less than 1. n=c/v n=(3x10⁸)/(2.25x10⁸)=about 1.33
The linear thermal expansion of a metal rod is given by ∆L=αL₀∆T. By how many degrees Celsius would the temperature of a rod have to increase for the rod's length to increase by 20%? a. αL₀/5 b. 1/5α c. it depends on the original length of the rod d. cannot be determined because kelvins must be used for ∆T
b. 1/5α an increase of 20% in length is the same as saying ∆L/L₀=0.20. this eliminates choice C. substituting into the given equation yield α∆T=∆L/L₀=0.2→∆T=0.2/α=1/5α
The density of ice is 920 kg/m³, and the density of seawater is 1025 kg/m³. Approximately what percent of an iceberg floats above the surface of the ocean (in other words, how much is "the tip of the iceberg")? a. 5% b. 10% c. 90% d. 95%
b. 10% because the ice has lower density than seawater, we know that the iceberg will float. the fraction of the iceberg's volume that will be submerged is: 920/1025= about 900/1000= 90% since 90% is submerged, then 10% floats above the surface
if an airplane has an airspeed of 100 km/hr southwest but is traveling 140 km/hr south relative to the ground, what is the wind velocity? a. 40 km/hr to the east b. 100 km/hr to the southeast c. 100 km/hr to the east d. 170 km/hr to to the southeast
b. 100 km/hr to the southeast
neglecting air resistance, if a parachutist drops from an airplane when it is flying horizontally at 100 m/s to the west at an altitude of 1 km, and the parachute never engages, what will be his final horizontal velocity? a. 0 m/s b. 100 m/s to the west c. 40 m/s to the west d. 170 m/s to the west
b. 100 m/s to the west since air resistance is neglected, the horizontal velocity will be constant at the initial velocity inherited from when the parachutist was aboard the airplane.
Assume that a ray of sunlight strikes the water, making an angle of 60 degrees with the surface. What is the angle of reflection? a. 15 degrees b. 30 degrees c. 60 degrees d. 90 degrees
b. 30 degrees if the incident ray makes an angle of 60 degrees with the surface, then it makes an angle of 30 degrees with the normal. therefore, the angle of incidence is 30 degrees. by the law of reflection, the angle of reflection is also 30 degrees.
The speed of a transverse traveling wave along a certain 4-meter-long rope is 24 m/s. Which of the following frequencies could cause a standing wave to form on this rope, assuming both ends of the rope are fixed? a. 32 Hz b. 33 Hz c. 34 Hz d. 35 Hz
b. 33 Hz the fundamental frequency for this rope is f₁=(1/2L)v=3 Hz. all harmonic frequencies are whole-number multiples of the fundamental, so any frequency that could cause a standing wave to form on the rope must be a multiple of 3 Hz. of the choice five, only choice B, 33 Hz, is a multiple of 3 Hz.
A sound wave of frequency 440 Hz travels at a speed of 344 m/s through the air in a concert hall. How fast would a note one octave higher, 880 Hz, travel through the same concert hall? a. 172 m/s b. 344 m/s c. 516 m/s d. 688 m/s
b. 344 m/s altering the frequency will not affect the wave speed.
An organ pipe that is closed at one end has a length of 3 m. What is the second longest harmonic wavelength for sound waves in this pipe? a. 3 m b. 4 m c. 6 m d. 9 m
b. 4 m because the end of the pipe is closed, the length of the pipe L, must be an odd number of quarter wavelengths: L= 1(λ/4), 3(λ/4), 5(λ/4) in order to support standing waves. therefore, the possible harmonic wavelengths are λ=4L/1, 4L/3, 4L/5, and so on. the second longest is λ= 4L/3= 4(3 m)/3= 4 m
A 2 kg ball is sliding east (without friction) down a hill that makes an angle of 30 degrees with the horizontal. A child kicks the ball north with a force of 10 N. What is the net acceleration of the kicked ball? a. (5√3)/2 m/s² b. 5√2 m/s² c. 5√3 m/s² d. 10√2 m/s²
b. 5√2 m/s² the force of gravity that is parallel to the surface of the hill FG-parallel is the initial force acting on the ball (there is no kinetic friction force acting on the ball.) The FG that is parallel to the surface of the hill can be calculated using mgsinθ=(2 kg)(10 m/s²)sin30=20(1/2)=10 N. this 10 N force is acting in the east direction. the child kicks the ball with a 10 N force in the north direction. these 2 forces are vectors and can be added tip to tail to find the resulting force vector. the 3 force vectors make an isosceles right triangle, so the hypotenuse must be equal to a leg of the triangle multiplied by √2, or in this case, 10√2 N. the question is asking for the acceleration of the ball, and a=F/m=(10√2 N)(2 kg)=5√2 m/s².
A person is leaning on his elbow on a table. If the amount of force the table must exert to keep the person upright is F, the area of contact between the person and the table is A, and the angle that the person's arm makes with the table's surface is θ, how much pressure is exerted by the person on the table? a. F/A b. Fsinθ/A c. Fcosθ/A d. since the force exerted by the person on the table is not given, the pressure exerted by the person on the table cannot be determined
b. Fsinθ/A the way that pressure, forced DNA area are related is P=F/A. since the given angle is between the arm and the table, the vertical component of the force will be related to the sine of that angle
A ray of light in air strikes the flat surface of a liquid, resulting in a reflected ray and a refracted ray. If the angle of reflection is known, what additional information is needed in order to determine the relative refractive index of the liquid compared to air? a. angle of incidence b. angle of refraction c. refractive index of air d. wavelength of the light
b. angle of refraction
If an object is placed very far from a concave mirror, where will the image be formed? a. halfway between the focal point and the mirror b. at the focal point c. at the center of curvature d. at infinity
b. at the focal point
A small negatively charged particle is placed near a fixed positively charged particle (Q). Which of the following describes the motion of the negatively charged particle? a. it accelerates away from Q b. it accelerates toward Q c. it moves with constant speed away from Q d. it moves with constant speed toward Q
b. it accelerates toward Q
A typical medical ultrasound scan uses frequencies in the MHz range. What would happen to an ultrasound signal as it passed from air into body tissues? a. its wavelength and speed would both decrease b. its wavelength and speed would both increase c. its wavelength would decrease and its speed would increase d. its wavelength would increase and its speed would decrease
b. its wavelength and speed would both increase when a wave passes into a new medium, its frequency does not change (the specific frequency range is irrelevant). therefore, when traveling through the body, the frequency of the sound wave will be the same as it was in the air. however, we know that sound waves generally travel faster through liquids and solids than they do in gases, so we'd expect the wave speed through the body to be faster. because the equation v=λf is always true, the same f at a faster v means a greater wavelength. therefore the answer is B.
When you pet a cat, you rub electrons off the cat's fur, which are transferred to your hand. Assuming that you transfer 5 x 10¹⁰ electrons to your hand, what is the electric charge on your hand? What is the charge on the cat?
because each electron carries a charge of -e=-1.6 x 10⁻¹⁹, you've gained 5 x 10¹⁰ of them, the charge on your hand will be (5 x 10¹⁰)(-e)=-8 x 10⁻⁹ C since the cat lost 5 x 10¹⁰ electrons, the charge on the cat will be (5 x 10¹⁰)(+e)=8 x 10⁻⁹ C
A brick that weighs 25 N is lifted from the ground to a shelf that's 2 m high. What is its change in gravitational potential energy?
because mg=25 N, we have ∆PEgrav=mgh=(25 N)(2 m)= 50 J. notice that since the brick was lifted up, its change in gravitational potential energy is positive
A book of mass m=2 kg slides across a flat tabletop. If the coefficient of kinetic friction between the book and table is 0.4, what's the magnitude of the force of kinetic friction on the book?
because the magnitude of the normal force is Fn=mg=(2 kg)(10 m/s²)= 20 N, the magnitude of the force of kinetic friction is Ff=µkFn=(0.4)(20 N)=8 N
Which has more gravitational potential energy: an object of mass 2 kg at a heigh of 50 m or an object of mass 50 kg at a heights of 2 m? (set PEgrav=0 at the ground for both objects)
both objects have the same gravitational potential energy relative to the ground. use the formula PE=mgh
A 200 kg roller coaster starts from rest 50 m above the ground. It falls toward the ground without any friction, then once it reaches ground level, the brakes are applied over 30 m in order to bring the coaster to a complete stop. How much work is done by the brakes? a. 10 x 10⁴ J b. 10 x 10⁵ J c. -10 x 10⁴ J d. -10 x 10⁵ J
c. -10 x 10⁴ J this problem requires the work-kinetic energy theorem, stating W=∆KE. the kinetic energy at the bottom is equal to the potential energy at the top, by conservation of energy, which is mgh=(200)(10)(50)=10⁵ J. the change in kinetic energy is the final kinetic energy minus the initial. therefore, the work done by friction to bring the roller coaster to a stop is equal to ∆KE=-10⁵ J or -10 x 10⁴ J
An object that is totally immersed in benzene (specific gravity = 0.7) is subject to a buoyancy force of 5 N. When the same object is totally immersed in an unknown liquid, the buoyancy force is 12 N. What is the approximate specific gravity of the unknown liquid? a. 0.3 b. 0.9 c. 1.7 d. 2.3
c. 1.7 The buoyant force on an immersed object is the product of: (density of the liquid) × (volume of the object) × (acceleration of gravity). Forming the ratio of buoyant forces in the two cases gives: 12/5 = (density of the unknown liquid)/(density of benzene, 0.7). Solving for the specific gravity of the unknown liquid, which is the ratio of its density to that of water, gives (12/5) × 0.7 = 1.7. Answer C is correct.
A 1000 kg gondola is operated on a cable between 2 towers 340 m apart. When the gondola is exactly between the towers, it is 100 m below their heights. What is the tension in the cable at this midpoint? a. 5 kN b. 8 kN c. 10 kN d. 20 kN
c. 10 kN looking at the symmetrical triangles formed by the cable, one finds that the top side is 170 m on each while the vertical displacement of the gondola is 100 m. this is a 1-2-√3 triangle, so the hypotenuse must be 200 m, though the actual distance does not matter, just the proportion. we find that the gravitational force is 10,000 N, which is divided evenly between the vertical components of the 2 tensions, giving each a Ty of 5000 N. stopping here would give you choice A, which is wrong. because of the nature of the triangle, we know that the total tension is twice the value of this vertical component. so each tension must be 10,000 N. note that if you add up the tension of the 2 spans acting on the gondola, which is not what the question is taking, you get D.
neglecting air resistance, what is the total velocity of a parachutist just before engaging his parachute, 8 seconds after dropping from an airplane flying horizontally at 60 m/s a. 60 m/s b. 80 m/s c. 100 m/s d. 140 m/s
c. 100 m/s use the equation V=Vo+at to calculate the vertical component of velocity starting at rest and accelerating at 10 m/s² for 8 s. the parachutist will be falling at 80 m/s. her horizontal velocity will be constant at 60 m/s. use the pythagorean theorem to calculate the hypotenuse which will be 100 m/s
At a distance of 1 m, the intensity level of a soft whisper is about 30 dB, while a normal speaking voice is about 60 dB. How many times greater is the power delivered per unit area by a normal speaking voice than by a whisper? a. 2.5 b. 30 c. 1000 d. 3000
c. 1000 the normal speaking voice has an intensity that's 30 dB greater than the whisper. therefore the intensity must be 10³ times greater
If the density of a person is approximately the density of water and the density of air is approximately 1 kg/m³, how many times greater is the weight of the person than the buoyant force from the air on the person? a. 10 b. 100 c. 1000 d. 10000
c. 1000 the wight of a person, in terms of density, is Wp=PpVg, where V is the volume of the person. The buoyant force from air on the person is Fb=PairVg, where V is again the volume of the person because the whole person is submerged in air. This means that the only difference is the density of the person as compared to the density of air, and since we are told that the density of the person is approximately the density of water (1000 kg/m³) and air has a density of approximately 1 kg/m³, the relevant factor is 1000.
You have 4 frictionless, massless pulleys, arranged next to each other. If you have enough force to lift a 40 kg object without any pulleys, what is the maximum mass of the couch, attached to the 2 lower pulleys, than can be raised with the pulley system? a. 80 kg b. 120 kg c. 160 kg d. 240 kg
c. 160 kg with 4 pulleys you have 4 times the tension force acting upwards, allowing you to lift 4 times the wight. since the maximum tension force is (40 kg)(10 m/s²)=400 N, the maximum force that can be applied to the couch is 4 x 400 N=1600 N. this corresponds to a mass of 160 kg
What is the maximum weight of an object that a 50 kg person could lift by standing on one piston of a hydraulic jack, if the jack's pistons are circular and have radii of 5 m and 10 m? a. 500 N b. 1000 N c. 2000 N d. 4000 N
c. 2000 N F₂=(F₁A₂)/A₁ F₂=(mg)(πr₂²)/πr₁² F₂=(50x10)(10²)/5²
A piano tuner strikes a tuning fork at the same time he strikes a piano key with a note of similar pitch. If he hears 3 beats per second, and the tuning fork produces a standard 440 Hz tone, then what must be the frequency produced by the struck piano string? a. 437 Hz b. 443 Hz c. 437 Hz or 443 Hz d. 434 Hz or 446 Hz
c. 437 Hz or 443 Hz if the beat frequency is 3 Hz, then the frequencies of the tuning fork and piano string are "off" by 3 Hz. the frequency produced by the piano string might be 3 Hz lower or 3 Hz higher than the tuning fork; without more information, we don't know which one. If the tuning fork produces a tone of frequency 440 Hz, the piano strong produces a frequency of either 440-3=437 Hz or 440+3=443 Hz
A closed system consisting of a balloon expands by 5 x 10⁻² L at constant temperature in an environment with a pressure of 1.0 x 10⁵ Pa. What is the value of heat transfer in this process? a. -5.0 J b. -5.0 kJ c. 5.0 J d. 5.0 kJ
c. 5.0 J for a closed system at constant pressure, the magnitude of work can be calculated as W=P∆V W=(1.0 x 10⁵ Pa)(5 x 10⁻² L)
In human legs, 20% of the body's mass is in the upper legs (acting at 20 cm from the hip), 10% is in the lower legs (acting at 90 cm), and 3% is in the feet (acting at 120 cm). Find the center of mass of an outstretched leg for a person who is 70 kg. a. 30 cm from the hip b. 40 cm from the hip c. 50 cm from the hip d. 60 cm from the hip
c. 50 cm from the hip
a surfer searching for the perfect wave paddles out to sea on her surfboard. she heads west from her beach spot and paddles at a rate of 8 meters per minute. there is a constant current in the water that day, pulling the surfer south at 6 meters per minute. after 5 minutes of paddling, how far is the surfer from her original beach spot? a. 40 m west b. 40 m southwest c. 50 m southwest d. 70 m southwest
c. 50 m southwest pythagorean theorem
an airplane capable of an airspeed of 100 km/hr is 60 km/hr off the coast above the sea. if the wind is blowing from the coast out to see at 40 km/hr, what is the least amount of time it will take for the plane to get to shore? a. 26 minutes b. 36 minutes c. 60 minutes d. 100 minutes
c. 60 minutes
An automobile with a certain shape experiences a drag force due to air resistance that is, in Newtons, equal to one-third the square of the car's speed, in meters per second. How much power would the engine have to supply to the wheels to balance this drag force when the car is moving at a constant speed of 30 m/s? a. 10 W b. 300 W c. 9 kW d. 27 kW
c. 9 kW Fdrag=(1/3)v² P=Fv P=(1/3)(v²)(v)=(1/3)v³ P=(1/3)(30)³=9 kw
Which circuit elements store energy? I. capacitors II. resistors III. batteries a. I only b. I and II only c. I and III only d. II and III only
c. I and III only
An expanding spring pushes a ridge cylinder of gas across a horizontal frictionless table. Consider the system to be the gas inside the cylinder. Which of the following sets of relations best describes what happens? a. W on system > 0, Q > 0, ∆KE > 0 b. W on system = 0, Q = 0, ∆KE = 0 c. W on system > 0, Q = 0, ∆KE > 0 d. W on system > 0, Q < 0, ∆KE > 0
c. W on system > 0, Q = 0, ∆KE > 0 an expanding spring exerts a force that causes a mass (the gas and its container, but even the gas has a mass of its own) to displace, so it does positive work on the system. the work done is mechanical, and because the gas is neither expanded nor compressed, simply translated, kinetic energy increases. there is no friction and no mention of temperature that would move heat in or out of the system.
a bubble in a glass of beer releases from rest at the bottom of the glass and rises at acceleration a to the surface in t seconds. if t>2, how much farther does the bubble travel between times t=1s and t=2s than it does between times t=0s and t=1s? a. 2a meters b. 3a/2 meters c. a meters d. a/2 meters
c. a meters the distance traveled in the first second can be found with the equation d=Vot + 1/2at² using Vo=0 (since the bubble begins at rest) and t=1s, resulting in 1/2a. Use the same equation to find the distance traveled from t=0 to t=2, resulting in 2a. the distance traveled between t=1 and t=2 equals 2a-a/2=3a/2. Subtract the distance traveled during the first second of travel from the distance traveled during the next second. 3a/2-a/2=a
Which of the following best explains why people with bicep attachment points farther from their elbows tend to have greater elbow flexion strength, and thus an improved ability to perform a dumbbell curling exercise? a. an attachment that is farther from the elbow increases the force provided by muscle contraction b. an attachment that is farther from the elbow decreases the force provided by muscle contraction c. an attachment point that is farther from the elbow results in a greater torque produced by the bicep as it contracts c. an attachment point that is closer to the hand results in a lesser torque produced by the bicep as it contracts
c. an attachment point that is farther from the elbow results in a greater torque produced by the bicep as it contracts choices A and B are eliminated because they discuss a difference in the muscle's contraction force which is a function of muscle fibers, not its point of attachment. an attachment point farther from the elbow increases r, the distance from the pivot point, to where the force is applied, so according to the torque equation τ=rFsinθ, this would increase the torque created by the biceps contraction.
Glasses that correct for nearsightedness have a negative power associated with them. Are these lenses diverging or converging, and do they have a focal length that is positive or negative? a. diverging lens with positive focal length b. converging lens with negative focal length c. diverging lens with negative focal length d. converging lens with positive focal length
c. diverging lens with negative focal length
When a sound source moves away from an observer, the observer has the impression that the sound source is: a. rotating b. louder than it actually is c. lower in frequency than it actually is d. higher in frequency than it actually is
c. lower in frequency than it actually is
When spinning a coin on a flat surface, two equal forces with opposite directions are applied to the opposite sides of a coin. Which of the following is true about the coin after it leaves the hand? (assume ideal frictionless motion) a. the coin does not rotate because equal but opposite forces cancel each other out b. the coin does not rotate because equal but opposite torques cancel each other out c. the coin rotates and the rotational acceleration is zero d. the coin rotates and the rotational acceleration is equal to the nonzero net torque divided by the moment of inertia
c. the coin rotates and the rotational acceleration is 0 after the coin leaves the hand, it undergoes rotational equilibrium, as no net torque is applied. in this case, the rotational acceleration is 0, with the coin undergoing a constant angular rotation
If the blood in the body is taken to be an ideal fluid, which of the following is true of blood flow in arteries? a. the flow speed of blood is the same through the complete peripheral vascular system at any given moment, but it varies over time b. the flow speed of blood is the same through the complete peripheral vascular system and does not vary over time c. the flow rate of blood is the same through the complete peripheral vascular system at any given moment, but it varies over time d. the flow rate of blood is the same through the complete peripheral vascular system and does not vary over time
c. the flow rate of blood is the same through the complete peripheral vascular system at any given moment, but it varies over time
If the magnification of a mirror is 2, where are the focal point and the image? a. the image is on the same side of the mirror as the object and the focal point is twice as far from the mirror as the object b. the image is on the same side of the mirror as the object and the focal point is held as far from the mirror as the object c. the image is on the opposite side of the mirror as the object and the focal pint is twice as far from the mirror as the object d. the image in on the opposite side of the mirror as the object and the focal point is half as far from the mirror as the object
c. the image is on the opposite side of the mirror as the object and the focal pint is twice as far from the mirror as the object
relative to the typical dropping parachutist, one who thrusts himself downward on exiting the airplane (ignoring air resistance and assuming both parachutists open their parachutes after the same amount of time) will have: a. lower acceleration but the same velocity just before engaging his parachute b. the same acceleration and the same velocity just before engaging his parachute c. the same acceleration but greater velocity just before engaging his parachute d. greater acceleration and greater velocity just before engaging his parachute
c. the same acceleration but greater velocity just before engaging his parachute
A pipe of constant cross-sectional area carries water at a constant flow rate from the host water tank in the basement of a house up to the second floor. Which of the following will be true? a. the speed at which the water arrives at the second floor must be lower than the speed at which it left the water tank b. the speed at which the water arrives at the second floor must be greater than the speed at which it left the water tank c. the water pressure at the second floor must be lower than the water pressure at the tank d. the water pressure at the second floor must be greater than the water pressure at the tank
c. the water pressure at the second floor must be lower than the water pressure at the tank because the flow rate is constant and the cross sectional area the pipe is constant, the flow speed will be constant.
Describe the image formed in a plane mirror. a. real and upright b. real and inverted c. virtual and upright d. virtual and inverted
c. virtual and upright real always goes with inverted. virtual always goes with upright. from common experience, the image formed in a flat mirror is upright, so the answer must be C
a ball is thrown in a projectile motion trajectory with an initial velocity v at an angle θ above the ground. if the acceleration due to gravity is -g, which of the following is the correct expression of the time it takes for the ball to reach its highest point, y, from the ground? a. v²sinθ/g b. -vcosθ/g c. vsinθ/g d. v²cosθ/g
c. vsinθ/g at the highest point from the ground, the ball has a velocity of 0. applying the formula Vy=Voy +ayt and rearranging for t, it becomes t=-Voy/-g. substituting Voy=Vsinθ into the equation, t=vsinθ/g
speed of light in a vacuum
c=3x10⁸ m/s
tensile or compressive strain
change in length/original length
the magnetic force never
changes the speed of a particle, and does NO work on the particle
for conductors
charge rests on the outer surface and the electric field inside is 0
f is positive for
concave mirrors
f is negative for
convex mirrors
90<θ≤180 for work
cosθ is negative work is negative
0≤θ<90 for work
cosθ is positive work is positive
θ=90 for work
cosθ is zero work is zero
kinematics equation no acceleration
d = 1/2 (Vo + V)t
kinematics equation no final velocity
d = Vot + 1/2at²
kinematics equation no initial velocity
d = Vt - 1/2 at²
A 7 kg ball is dropped from 20 m. If the speed just before it hits the ground is 18 m/s, what is the work done by air resistance? a. 266 J b. 13 J c. -13 J d. -266 J
d. -266 J the initial energy is mgh=(7)(10)(20)= 1400 J. the final energy is completely kinetic, ½(mv²)=1134 . the equation for conservation of energy with friction is Ei+W by friction=Ef. thus, the work done by friction is negative and equal to 1134-1400=-266 J
A young child is sliding down a hill at an incline of 30 degrees on a self with a total combined mass of 10 kg. If the coefficient of friction between the hill and the sled is 0.3 and the length of the hill is 50 m, how much work has been done by gravity when the child reaches the bottom of the hill? a. 1000 J b. 2500 J c. 3535 J d. 4330 J
d. 2500 J F and d are in the same direction. F=mgsinθ where θ=30 W=Fd W=(10)(10)(sin30)(50)=2500 J
A fully unraveled yo-yo is being swung around in a vertical circle. The yo-yo is 100 g on a string that is 90 cm long. A yo-yo guru manages to make his yo-yo travel three complete circles in 1 second. Determine the centripetal acceleration on the yo-yo. a. 28 m/s² b. 32 m/s² c. 284 m/s² d. 320 m/s²
d. 320 m/s² the formula for centripetal acceleration is ac=v²/r. to determine speed, we must know what distance the yo-yo traveled. it makes 1 revolution in 1/3 s. thus v=(2πr/t)=2π(0.9)/(0.33)=17 m/s. given the speed of the yo-yo, the centripetal acceleration is given as ac=v²/r=(17²)/(0.9)=320 m/s²
A person is pulling a block of mass m with a force equal to its weight directed 30 degrees above the horizontal plane across a rough surface, generating a friction f on the block. If the person is now pushing downward on the block with the same force 30 degrees below the horizontal plane across the same rough surface, what is the friction on the block? (µk is the coefficient of kinetic friction across the surface.) a. f b. 1.5f c. 2f d. 3f
d. 3f the friction f on the block is represented by the formula f=µkN, where N is the normal force acting on the block. when the force is applied 30 degrees above the horizontal, N=mg-mgsin30. since sin30 is 0.5, N=mg-0.5mg=0.5mg substituting N into the formula for friction, it becomes f1=0.5µkmg. when the force applied is 30 degrees below the horizontal, N=mg+mgsin30=mg+0.5mg=1.5mg. substituting N into the formula for friction, it becomes f2=1.5µkmg=3f1
an object is thrown with an initial speed of 7 m/s directed 45 degrees above the horizontal from a cliff. after reaching the peak of its trajectory, it falls 20 m to the ground below. what is the approximate ratio of the time it takes to hit the ground from the peak of the trajectory to the time it takes from its release to the peak of the trajectory? a. 0.5 b. 1 c. 2 d. 4
d. 4 use the formula d=Vot + 1/2at² to calculate the time it takes for the object to hit the ground. t will equal 2 s. use the formula V=Vo + at to calculate the time it takes to reach the peak. t will equal 0.5 s. 2/0.5 = 4
Ethyl alcohol has a specific gravity of 0.8. If a cork of specific gravity 0.25 floats in a beaker of ethyl alcohol, what fraction of the cork's volume is submerged? a. 4/25 b. 1/5 c. 1/4 d. 5/16
d. 5/16 because the cork has a lower density than the ethyl alcohol, we know that the cork will float. the fraction of the cork's volume that will be submerges is: Vsub/V=density of object/density of fluid=(0.25)/(0.8)=(1/4)/(4/5)=5/16
How much work is needed to lift a box of mass 2 kg up a height of 3 m using a pulley system with 75% efficiency? a. 4 J b. 8 J c. 45 J d. 80 J
d. 80 J without the pulley system, lifting this box would require doing the work to increase the potential energy by mgh which is (2 x 10 x 3)=60 J. with a pulley system that has less than 100% efficiency, it will require more work, so the answer has to be greater than 60 J. D is the only answer larger than 60 J.
An amount of heat Q is added to a system. Which of the following can result? I. its temperature increases II. its phase changes III. it undergoes isothermal expansion a. I only b. I or II only c. I or III only d. I, II, or III
d. I, II, or III
Which of the following concerning uniform circular motion is true? a. the centrifugal force is the action-reaction pair of the centripetal force b. unlike the centrifugal force, the centripetal force is a type of force akin to that of friction, gravity, and tension forces c. the velocity of the object in motion changes, whereas the acceleration of the object is constant d. a satellite undergoing uniform circular motion is falling towards the center in a circular path
d. a satellite undergoing uniform circular motion is falling towards the center in a circular path
Which of the following statements is true regarding red photons and blue photons traveling through vacuum? a. red light travels faster than blue light and carries more energy b. blue light travels faster than red light and carries more energy c. red light travels at the same speed as blue light and carries more energy d. blue light travels at the same speed as red light and carries more energy
d. blue light travels at the same speed as red light and carries more energy all electromagnetic waves travel at the same speed through a vacuum. because blue light has a higher frequency than red light, they have greater energy
An object is placed in front of a convex mirror. If the objet is moved closer to the mirror, the image will move: a. farther from the mirror and become smaller b. farther from the mirror and become larger c. closer to the mirror and become smaller d. closer to the mirror and become larger
d. closer to the mirror and become larger
Which of the following is true? a. compression in length increases with an increased area of applied force b. compression in length increases with a decreased area of applied force c. compression in length is larger with a smaller original length d. compression in length is larger with a smaller Young's modulus
d. compression in length is larger with a smaller Young's modulus
A beam of light passing through brown glass (n=1.5) strikes the surface between the glass and air and experiences Total Internal Reflection. Which of the following changes to the experiment would ensure that the beam of light continues to experience this phenomenon? a. have the light originate in air b. decrease the angle of incidence c. immerse the glass in water (n=1.33) d. decrease the wavelength of light
d. decrease the wavelength of light
Which of the following describes the direction of motion of alpha, beta, and gamma rays in the presence of an external magnetic field? a. they all travel straight b. they are all bent in the same direction c. gamma rays travel straight; alpha and beta rays are bent in the same direction d. gamma rays travel straight; alpha and beta rays are bent in opposite directions
d. gamma rays travel straight; alpha and beta rays are bent in opposite directions magnetic fields exert a force on moving electric charge. the magnitude of the force is directly proportional to the electric charge and particles of opposite sign experience forces of opposite direction. gamma rays possess zero charge, and thus experience no form from a magnetic field and will travel in a straight line. alpha and beta particles possess charges of opposite sign, and thus will experience forces in opposite directions
Which one of the following statements is true concerning the amplitude of a wave? a. amplitude increases with increasing frequency b. amplitude increases with increasing wavelength c. amplitude increases with increasing wave speed d. none of the above
d. none of the above amplitude is determined by how much energy we put into the wave to get it started and does not depend on frequency, wavelength, or wave speed
When an object falls from a very large height, it accelerates towards earth because of the force of gravity. are resistance also acts on the object as it falls, and the air resistance increases as the speed of the object increases. Eventually, the force due to air resistance equals that of gravity and the object reaches terminal velocity. What best describes this situation? a. the acceleration of the object at terminal velocity is the largest it will ever be b. the speed of the object increases until it hits the ground c. the speed of the object at terminal velocity is zero d. the acceleration of the object at terminal velocity is zero
d. the acceleration of the object at terminal velocity is zero the net force on the object is the difference between the force due to gravity and the force due to air resistance. therefore, as the force due to air resistance grows larger, the net force decreases, as does the acceleration, eliminating choice A. when the force due to larger air resistance equals that of gravity, the net force is 0, as is the acceleration which makes D correct. when there is 0 acceleration, velocity is constant, eliminating choice B and the object does not stop moving once it reaches terminal velocity, eliminating choice C.
In order to determine the relative speed of approach of a sound source by Doppler measurements, three of the following items of data are necessary. Which one is NOT required? a. the speed of sound in the medium b. the frequency of the emitted sound c. the frequency of the observed sound d. the distance between source and observer
d. the distance between the source and observer
A man on earth weighing 200 pounds floats with 1/10th of his body weight above water. This man would NOT float on a planet whose gravitational pull is: a. 1/10 g b. 2 g c. 10 g d. the man would always float
d. the man would always float to float, the buoyant force must be equal in magnitude to the gravitational force (Fb=Fg) or pgv=mg. because g is present on both sides of this equation, it can be factored out and won't determine if he will float
When rapidly turning a corner of a flat road, a cyclist leans into the center of the turn. The frame of the bike is nearly parallel to which vector? a. the force of gravity on the bicycle and rider b. the normal force on the pair c. centripetal force d. the sum of the normal and friction forces
d. the sum of the normal and friction forces gravity always acts downward meaning A cannot be correct. the normal force is always perpendicular to the surface, so B is incorrect. the centripetal force will be toward the center of the turn, which will be horizontal on a flat road, so C is wrong. D is correct because the friction is the source of that horizontal centripetal force and the normal fore is up. if you add them, it will be similar to the angle at which the bike leans.
A 100 g block is sitting at rest on a horizontal table. According to Newton's third law, which of the following indicates the correct action-reaction pair of the 2 forces? a. the gravitational force exerted by the table on the block and the normal force exerted by the block on the table b. the gravitational force exerted by the block on earth and the normal force exerted by the table on the block c. the weight of the block and the normal force exerted by the table on the block d. the weight of the block and the gravitational force exerted by the block on earth
d. the weight of the block and the gravitational force exerted by the block on earth the correct action-reaction pairs are as listed: -the weight of the block and the gravitational force exerted by the block on earth -the normal force exerted by the block on the table and the normal force exerted by the table on block -the gravitational force exerted by the table on the block and the gravitational force exerted by the block on the table
Will an object with more mass but the same volume as another object sink faster in a non-viscous fluid? a. no, because acceleration due to gravity is independent of the mass of the object being accelerated b. no, because the buoyant force is greater on an object with more mass c. yes, because it weighs more, and the object induces greater acceleration for the heavier object than for the lighter one d. yes, because the buoyant force impedes the downward acceleration of a greater mass less than it does a lesser mass
d. yes, because the buoyant force impedes the downward acceleration of a greater mass less than it does a lesser mass
pressure
density x g x height
A 2 cm³ sample of osmium, one of the densest substances on earth, has a mass of 45 grams. What's the specific gravity of this metal?
density=mass/volume=(45 grams)/(2 cm³)=22.5 g/cm³
free fall
describes an object moving only under the influence of gravity
when light is traveling through material (not a vacuum)
different frequencies will have different speeds
average velocity formula
displacement/time
shear strain
distance of shear/original length
wave particle duality
electromagnetic radiation travels like a wave but interacts with matter like a particle
second law of thermodynamics
entropy of an isolated system either stays the same or increases during any thermodynamic process
the amount of current entering a parallel combination of resistors is
equal to the sum of the currents that pass through the individual resistors
the sum of the voltage drops across the resistors in any complete path is
equal to the voltage of the battery
How much positive charge is contained in 1 mole of carbon atoms?
every atom of carbon contains 6 protons, so the amount of positive charge in one carbon atom would be q₊=+6e Q₊=(6.02x10²³)(6)(1.6x10⁻¹⁹)=6x10⁵ C
index of refraction
every medium has an index of refraction that tells us how much slower light travels through that medium than through empty space n=index of refraction c=speed of light in a vacuum (3x10⁸ m/s) v=speed of light in medium
doppler effect equation
f'=frequency heard by detector f=frequency emitted by source vo=speed at which detector is moving vs=speed at which source is moving v=speed of wave
fundamental frequency
fn=nf₁
work
force x distance
stress
force/area
For a particular rope, it's found that the fundamental frequency is 6 Hz. What's the third-harmonic frequency?
from the equation fn=nf₁, we get f₃=3f₁= 3(6 Hz)=18 Hz
Find the mass of an object whose weight is 50 N.
g= 10 N/kg m=w/g=(50 N)/(10 N/kg)=5 kg
Find the weight of an object whose mass in 50 kg.
g= 10 m/s² or 10 N/kg w=mg=(50 kg)(10 N/kg)=500 N
photon energy formula
h=planck's constant (6.6x10⁻³⁴ Js)
specific gravity
how dense something is compared to water
velocity
how fast an object's position changes
power
how fast work gets done
simple pendulum
if the connecting rod or string between the suspension point and the object at the end of a pendulum has a negligible mass (so that all the mass is in the object at the end of the rod or string), and if there is no friction at the suspension point during oscillation, then the pendulum is a simple pendulum
The net force on an object of mass 10 kg is zero. What can you say about the speed of this object?
if the net force on an object is zero, all we can say is that it will not accelerate; its velocity may be zero, or it may not. without more information, we cannot determine the object's speed; all we know is that whatever the speed is, it will remain constant.
An object of mass 50 kg moves with a constant velocity of magnitude 1000 m/s. What is the net force on this object?
if the object moves with constant velocity, then the net force it feels must be zero, regardless of the object's mass or speed.
m is negative for
inverted images
the ground
is at potential 0
displacement
its change in position
an object's velocity is always tangent to
its path
when a wave passes into another medium
its speed changes, but its frequency DOES NOT
an object moving in a circular path is said to have uniform circular motion if
its speed is constant
when an electromagnetic wave travels through a vacuum
its speed is constant
polarized light
light whose direction of polarization has been restricted somehow
magnification equation
m=magnification factor o=object's distance from the mirror
speed
magnitude of the velocity vector
weight formula
mass x gravitational acceleration
collisions always conserve
momentum
momentum formula
momentum (p)=mv
An object of mass m is moving with velocity v. What will happen to its momentum if v doubles? What will happen to its kinetic energy?
momentum has something in common with kinetic energy: namely, only moving objects have it. also, the more massive an object, or the greater its velocity the greater its momentum (and kinetic energy.) however, there are 2 important differences. first, kinetic energy is a scalar, while momentum is a vector. second, kinetic energy is proportional to v² whereas the magnitude of momentum is proportional only to v. so, if the object's speed doubles, then its momentum doubles while its kinetic energy increases by a factor of 4.
uniformly accelerated motion
motion in which the object's acceleration is constant
quantization of angular momentum
mvr=nh/2π where n=1,2,3...
electric field vectors point toward
negative source charges
no net force means
no acceleration
conduction electrons
non localized electrons
law of refraction (snell's law)
n₁=refractive index of medium through which the incident ray is traveling n₂=refractive index of the medium through which the transmitted ray is traveling -if the transmitting medium has a higher index of refraction than the incident medium, then the ray will bend towards the normal -if the transmitting medium has a lower index of refraction than the incident medium, the the ray will bend away from the normal
A ray of light traveling through air is incident on a piece of glass whose refractive index is 1.5. If the sine of the angle of incidence is 0.6, what's the sine of the angle of refraction?
n₁sinθ₁=n₂sinθ₂ (1)(0.6)=(1.5)(sinθ₂) sinθ₂=0.6/1.5=6/15=2/5=0.4 notice that sinθ₂ is less than sinθ₁, this immediately tells us that θ₂<θ₁. the light is traveling from air (n₁=1) into glass, whose refractive index is higher. if the transmitting medium has a higher index of refraction than the incident medium, then θ₂ will be less than θ₁ and the ray will bend towards the normal
isobaric process
occurs at constant pressure W=P∆V
isochoric process
occurs at constant volume ∆E=Q
isothermal process
occurs when heat is allowed to pass freely between a system and its environment ∆E=0 Q=W
adiabatic process
occurs when no heat is transferred between the system and the environment and all energy is transferred as work Q=0 ∆Einternal=-W
equilibrium position
on a spring, its when the spring is at its natural length
the direction of friction is
opposite to the direction of motion (or intended direction of motion)
plane mirror
ordinary flat mirror
power formula
p=work/time
the direction of the force of static friction is always
parallel to the surface and in the opposite direction to the object's intended velocity
electric field vectors point away from
positive source charges
energy=
power x time
concave mirror can create
real and virtual images
i is positive for
real images (in front of the mirror)
compressions
regions of high pressure
negative charges move to
regions of higher potential
rarefractions
regions of low pressure
positive charges move to
regions of lower potential
resistance and resistivity formula
resistivity=P L=length A=cross sectional area
sound travels
slowest through gases faster through liquids fastest through solids
velocity includes both
speed and direction
frequency of light
speed of light/wavelength
stress vs strain
stress is pressure, strain is change
hookes law
stress= modulus x strain
the slope of a velocity vs time graph gives
the acceleration
law of reflection
the angle of reflection is equal to the angle of incidence
angle of refraction
the angle that the transmitted (or refracted) ray makes with the line that's perpendicular to the plane of interface between 2 media
launch angle
the angle the initial velocity vector makes with the horizontal
refraction
the bending of light as it enters water
coulomb's law
the calculation of the electric force between 2 charged particles q₁ and q₂ represents their charges and r represents the distance between them and k being the proportionality constant
in a unifirm gravitational field
the center of mass equals the center of gravity
trajectory
the curved path of an object thrown into space
kinematics
the description of motion in terms of an objects position, velocity, and acceleration
polarization of the wave
the direction in which the wave's electric field oscillates
in the equation F=ma, because m is a positive number, the direction of a is always the same as
the direction of Fnet, meaning an object will accelerate in the direction of Fnet. (this does not mean than an object will always MOVE in the direction of Fnet)
the area under a velocity vs time graph gives
the displacement
lever arm
the distance from the pivot to the line along with F is applied which is always perpendicular to the line of action of F
intensity of s sound wave
the energy it transmitters per second per unit area
For a particular rope, it's found that the second-harmonic frequency is 8 Hz. What's the fifth-harmonic frequency?
the equation fn=nf₁ gives us f₂=2f₁. this means that f₁=f₂/2=(8 Hz)/2=4 Hz. therefore, f₅=5f₁=5(4 Hz)=20 Hz
dynamics
the explanation of motion in terms of the forces that act on an object
inclined plane mgsinθ
the force due to gravity acting parallel to the incline plane
inclined plane mgcosθ
the force due to gravity acting perpendicular to the inclined plane
tension
the force exerted by a stretched string, cord, or rope
restoring force
the force that maintains oscillations in a spring
weight
the gravitational force exerted on an object by the earth (changes whatever planet the object happens to be on/near)
the farther away the mass is from the axis of rotation
the greater the rotational inertia will be
the work done by gravity depends only on
the initial and final heights of the objects, not on the path the object follows, making gravity a conservative force
if the ray's angle of incidence exceeds a certain critical angle
the light will undergo internal reflection. all of the incident ray's energy will be reflected back into its original medium and there will be no refracted ray
3 blocks hang below a massless meter stick. Block m₁ hangs from the 20 cm mark, block m₂ hangs from the 70 cm mark, and block m₃ hangs from the 80 cm mark. If m₁=2 kg, m₂=5 kg, and m₃=3 kg, at what mark on the meter stick should a string be attached so that this system would hang horizontally?
the location of the center of mass would be at 63 cm
archimedes' principle
the magnitude of the buoyant force is equal the weight of the fluid displaced by the object
in the case of sliding/kinetic friction, the magnitude of the force of friction is directly proportional to
the magnitude of the normal force
amplitude
the maximum displacement from equilibrium
A crate that weighs 1000 N rests on a horizontal floor. The coefficient of static friction between the crate and the floor is 0.4. If you push on the crate with a force of 250 N, what is the magnitude of the force of static friction?
the maximum force of static friction that the floor could exert on the crate is Ffmax=µsFn=(0.4)(1000 N)= 400 N. however, if you exert a force of only 250 N on the crate, then static friction will only be 250 N.
torque
the measure of a force's effectiveness at making an object spin or rotate
projectile motion
the motion of an object, experiencing only the constant, downward acceleration due to gravity (free fall)
current
the movement of charge
You push a 50 kg block of wood across a flat concrete driveway, exerting a constant force of 300 N. If the coefficient of kinetic friction between the wood and concrete is 0.5, what will be the acceleration of the block?
the normal force acting on the block has a magnitude of Fn=mg=(50 kg)(10 m/s²)= 500 N. therefore, the force of kinetic friction acting on the sliding block has a magnitude of Ff=µkFn=(0.5)(500 N)= 250 N. this means that the net force acting on the block (and parallel to the driveway) is equal to F-Ff=(300 N)-(250 N) = 50 N. if Fnet=50 N and m= 50 kg, then a=Fnet/m=(50 N)(50 kg)=1 m/s²
frequency
the number of cycles that occur in one second
if Density of object < Density of fluid
the object will float, and the fraction that's submerged is the same as the ratio of its density to the fluid's density
What happens if an object is denser than the fluid it is in?
the object will sink
acceleration being perpendicular to velocity means
the object's speed is constant
acceleration being in the opposite direction to velocity means
the object's speed is decreasing
acceleration at an angle between 90 and 180 to velocity means
the object's speed is decreasing and the direction of the velocity is changing
acceleration in the same direction as velocity means
the object's speed is increasing
acceleration at an angle between 0 and 90 to velocity means
the object's speed is increasing and the direction of the velocity is changing
normal force
the perpendicular component of the contact force exerted by a surface on an object
diffraction
the redistribution of a wave's intensity such as when they encounter an obstruction
the greater the value of n (index of refraction) for a medium
the slower light travels through that medium
period
the time it takes an object to move through one full cycle of motion
for an object undergoing uniform circular motion, the period is
the time it takes to make one revolution
first law of thermodynamics
the total energy of the universe is constant ∆E=Q-W Q=heat W=work
total power supplied by a battery equals
the total power dissipated by the resistors
the speed of a wave is determined by
the type of wave and the characteristics of the medium, NOT by the frequency
normal force
the upward, supporting force exerted by the ground
dispersion
the variation in wave speed for different frequencies
the slope of a position vs time graph gives
the velocity
at the top of an objects trajectory thrown straight upward into the air
the velocity at the highest point is 0
What if Fnet = 0?
then a=0. this means that the object's velocity does not change and that the object won't accelerate
For 6 seconds you pull a 120 kg crate along a frictionless horizontal surface with a constant force of 60 N directed at an angle of 60 degrees to the surface. If the crate was initially at rest, what will its horizontal velocity be at the end of this 6 second time interval?
to find the horizontal velocity, we need to find the horizontal acceleration. using newton's second law, we find that the horizontal acceleration of the crate is ax=Fx/m=(Fcosθ)/m=(60 N)(cos60)/(120 kg)=0.25 m/s². using the equation Vx=Vox + axt = 0+(0.25 m/s²)(6s)= 1.5 m/s
elastic collision
total momentum and total kinetic energy are conserved
inelastic collision
total momentum is conserved but total kinetic energy is not
the acceleration of an object undergoing uniform circular motion always points
towards the center of the circle
free fall acceleration of an object does not depend on its mass/size/shape, so in the absence of effects due to the air
two objects will hit the ground at the same time if dropped at the same time even if one is larger than the other
m is positive for
upright images
Two charges, q1=-2x10⁻⁶ C and q2=5x10⁻⁶ C, are separated by a distance of 10 cm. Describe the electric force between these particles.
using coulombs law (9x10⁹)[(2x10⁻⁶ C)(5x10⁻⁶ C)]/(10⁻¹m)²=9 N convert the length of cm to m to match the units of coulomb's constant
A wave of frequency 12 Hz has a wavelength of 3 m. What is the speed of this wave?
using the equation v=λf, we find that v=(3 m)(12 Hz)= 36 m/s
When a longitudinal compression wave of frequency 700 Hz travels through a brass rod, its wavelength is 5 m. How fast does sound travel through brass?
using v=λf, we find that v=(5 m)(700 Hz)=3500 m/s
What is the wavelength of a sound wave of frequency 170 Hz if the wave speed is 340 m/s²?
using v=λf, we find that λ=v/f=(340 m/s)/(170 Hz)= 2 m
Ball 1 and Ball 2 are rolling toward each other at the same speed, 5 m/s. Ball 1 has a mass of m1=8 kg and Ball 2 has a mass of m2=2 kg. After the collision, Ball 1 and Ball 1 stick together and slide frictionlessly across the table. What's their common velocity after the collision?
v'=3 m/s choosing to the right as the positive direction. P total before = P total after m1v1 + m2v2= (m1+m2)v' (8 kg)(5 m/s)+(2 kg)(-5 m/s)=(8 kg+2 kg)(v') 30=(10 kg)(v') V'=3 m/s
A roller coaster car drops from rest down the track and enters a loop. If the radius of the loop is R, and the initial height of the car is 5R above the bottom of the loop, how fast is the car going at the top of the loop? Assume that R=15 m and ignore friction.
v=30 m/s let's call the bottom of the loop our h=0 level. at the car's initial position, we have hi=5R and vi=0 (so KEi=0). at the top of the loop (the final position) we have hf=2R. the question is to find the car's speed, v, at this point. KEi+PEi=KEf+PEf 0+mghi=½mv²+mghf ghi=½v²+ghf v=√2g(hi-hf) v=√2g(5R-2R) v=30 m/s
A skier begins at rest at the top of a hill of height 125 m. If friction between her skis and the snow is negligible, what will be her speed at the bottom of the hill?
v=50 m/s let the bottom of the hill be h=0, and call the top of the hill the skier's initial position and the bottom of the hill her final position. KEi+PEi=KEf+PEf 0+mgh=½mv²+0 v=√2gh v=√2(10 m/s²)(125 m) v= 50 m/s
convex mirrors can only create
virtual images
i is negative for
virtual images (behind the mirror)
electric field
volts per meter
emission spectrum
when a diffused elemental gas is energized by heating or passing a current through it, the gas glows with a particular hue specific to that element. if that light is passed through a prism, then dispersion will cause the light to separate into its component colors, corresponding to frequencies and wavelengths. the pattern of distinct bright lines of color is called the element's emission spectrum
A block of mass 200 g is oscillating on the end of a horizontal spring of spring constant 100 N/m and natural length of 12 cm. When the spring is stretched to a length of 14 cm, what is the acceleration of the block?
when the spring is stretched by 2 cm, hooke's law tells us that the force exerted by the spring has a magnitude of F=kx=(100 N/m)(0.02 m)=2 N. therefore, by Newton's second law, the acceleration of the block will have a magnitude of a=F/m=(2 N)/(0.2 kg)=10 m/s²
static friction
when there is no relative motion between the surfaces that are in contact
kinetic/sliding friction
when there is relative motion between the surfaces that are in contact
magnetic field lines created by a magnet
will point north to south
torque formula
with a level arm = LF
projectile motion horizontal displacement
x = Voxt
projectile motion vertical displacement
y = Voyt + ½(-g)t²
kinetic energy formula
½mv²
A square metal plate (of side length s) rests on a flat table, and we exert a force F at one corner, parallel to one of the sides. What is the torque of this force? (use the center of the plate as the pivot point)
τ=LF=½sF the line of action of the force F is simply the bottom side of the square. the perpendicular distance from the pivot to the side of the square is half the length of the side of the square, ½s, so that this lever arm, L, is perpendicular from the center of the square to the center of the bottom side of the square.
change in kinetic energy
∆KE=-∆PE
displacement formula
∆x=xf-xi (final position minus initial position)
