### SAT Physics Subject Test - Practice Test 2

##
**SAT Physics Subject Test - Practice Test 2**

Do not use a calculator. To simplify numerical calculations, use g= 10 m/s^{2}.

**PART A**

**Directions:**In this section of the exam, the same lettered choices are used to answer several questions. Each group of questions is preceded by five lettered choices. When answering questions in each group, select the best answer from the available choices and fill in the corresponding bubble on the answer sheet. Each possible answer may be used once, more than once, or not at all.

**Questions 1-3:**

The motion of five separate objects is shown in the following velocity-time graph.

**1.**Which object is slowing the most during the entire 6-second elapsed time?

**2.**Which object has the greatest magnitude of acceleration?

**3.**Which object undergoes the greatest displacement during the 6-second time interval?

**Questions 4-6:**

**(A)**Kinetic energy

**(B)**Potential energy

**(C)**Total mechanical energy

**(D)**Work

**(E)**Power

Choose the correct term from above to answer the following questions.

**4.**The rate at which energy changes from one form to another or the rate at which energy is transferred into or out of a system.

**5.**The sum of the potential and kinetic energies of a system at a specific instant in time.

**6.**A quantity associated solely with the instantaneous position of an object.

**Questions 7-9:**

The diagram below depicts an electron located between two charged plates. In addition, a uniform magnetic field is in the space between the plates. Use the diagram and the answers below to answer questions 7 to 9.

**(A)**+x-direction

**(B)**-jc-direction

**(C)**+y-direction

**(D)**-y -direction

**(E)**none, zero magnitude, and no direction

**7.**The direction of the electric field of the charged plates.

**8.**The direction of the electric force acting on the electron.

**9.**The direction of the magnetic force acting on the electron at the instant it begins to move.

**Questions 10-12:**

**(A)**Diffraction

**(B)**Interference

**(C)**Reflection

**(D)**Refraction

**(E)**Total internal reflection

Choose the correct term from above to answer questions 10 to 12.

**10.**The change in direction of light as it moves from one medium into another.

**11.**The spreading of waves that results when waves pass through an opening or encounter an obstacle.

**12.**The result of wave superposition.

**Questions 13-15**:

**(A)**Gold foil experiment

**(B)**Heat-work experiment

**(C)**Michelson-Morley interferometer

**(D)**Photoelectric effect experiment

**(E)**Young’s double-slit experiment

Choose the correct experiment from above to answer questions 13 to 15.

**13.**Provided evidence that light has a particle characteristic.

**14.**Provided evidence that light has a wave characteristic.

**15.**A failed experiment, but its negative result indicated that the speed of light is constant regardless of the motion of the light source

**PART B**

**Directions:**This section of the exam consists of questions or incomplete statements followed by five possible answers or completions. Select the best answer or completion, and fill in the corresponding bubble on the answer sheet.

**16.**Which of the following is NOT true for every possible motion involving a constant speed?

**(A)**The magnitude of velocity is constant.

**(B)**The object may be changing direction.

**(C)**The acceleration is zero.

**(D)**The magnitude of the net force acting on the object can be equal to or greater than zero.

**(E)**The net work done on or by the object is zero.

**17.**An object traveling at 10 meters per second undergoes an acceleration of 4.0 meters per second while moving a distance of 100 m. Determine the final velocity of the car.

**(A)**30 m/s

**(B)**60 m/s

**(C)**90 m/s

**(D)**120 m/s

**(E)**150 m/s

**18.**A mass initially at rest experiences a constant acceleration a and is displaced a distance x, resulting in a final speed, v. What would be the final speed of the object if it moved the same distance x but with twice the acceleration, 2a?

**(A)**v

**(B)**√2(v)

**(C)**2v

**(D)**2√2(v)

**(E)**4v

**19.**A ball is thrown horizontally from the top of a 20-meter-tall platform. The ball travels 40 meters horizontally before striking the ground. Determine the initial velocity of the ball.

**(A)**10 m/s

**(B)**20 m/s

**(C)**40 m/s

**(D)**80 m/s

**(E)**120 m/s

**20.**Which of the following is true for the acceleration of an object that is thrown straight upward?

**(A)**It is initially decreasing and negative.

**(B)**It decreases until it becomes zero and then increases.

**(C)**It is increasing throughout the entire motion.

**(D)**It is decreasing throughout the entire motion.

**(E)**It is constant throughout the entire motion.

**Questions 21-22:**

The object shown in the diagram below has mass m and weight w. The object is pulled to the right at constant velocity along a rough, horizontal surface by a string. The tension in the string has a magnitude T and is directed at an angle 8 as measured from the horizontal.

**21.**Determine the magnitude of the friction force.

**(A)**0

**(B)**T cos θ

**(C)**T sin θ

**(D)**T

**(E)**cannot be determined without knowing the coefficient of friction

**22.**Which of these correctly describes the relationship between the magnitude of the normal force, N, and the weight of the object, w?

**(A)**N = 0

**(B)**N = m

**(C)**N = w

**(D)**N < w

**(E)**N > w

**Questions 23-24:**

A 2.0-kilogram mass and a 1.0-kilogram mass are connected by a string. The masses are pulled along a horizontal surface by a 12-newton force.

**23.**What is the acceleration of the 2.0-kilogram mass?

**(A)**1.0 m/s

^{2}

**(B)**2.0 m/s

^{2}

**(C)**3.0 m/s

^{2}

**(D)**4.0 m/s

^{2}

**(E)**6.0 m/s

^{2}

**24.**Determine the magnitude of the tension in the string between the masses.

(A) 2.0 N

(B) 3.0 N

(C) 4.0 N

(D) 6.0 N

(E) 8.0 N

**25.**A 60-kilogram person rides in an elevator that is accelerating upward at 1.0 meter per second squared. What is the apparent weight of the person?

**(A)**54 N

**(B)**66 N

**(C)**540 N

**(D)**600 N

**(E)**660 N

**26.**A 3.0-kilogram mass lies on a rough horizontal surface. It is attached to a 1.0-kilogram mass by a string draped over a pulley as shown in the diagram above. What minimum coefficient of friction is needed in order for the blocks to remain at rest?

**(A)**0.25

**(B)**0.33

**(C)**0.50

**(D)**0.67

**(E)**0.75

**27.**A car completes a turn that has a radius of 20 meters. The coefficient of friction between the tires and road is 0.50. What maximum speed can the car safely maintain in order to complete the turn without skidding?

**(A)**5 m/s

**(B)**10 m/s

**(C)**15 m/s

**(D)**20 m/s

**(E)**25 m/s

**28.**A mass m is in uniform circular motion with a speed v and a radius r. How is the centripetal acceleration, ac, affected if the radius is doubled while the speed remains constant?

**29.**A roller coaster loop has a radius of 10.0 meters. What minimum speed is required at the top of the loop in order to complete the loop successfully?

**(A)**2.5 m/s

**(B)**5.0 m/s

**(C)**7.5 m/s

**(D)**10.0 m/s

**(E)**12.5 m/s

**Questions 30-31:**

An 8.0-kilogram mass is attached to a vertical spring. The mass is lowered 0.50 meters to equilibrium where it remains at rest. The stretching motion of the spring is plotted in the following force-displacement graph.

**30.**Determine the spring constant.

**(A)**20 N/m

**(B)**40 N/m

**(C)**80 N/m

**(D)**160 N/m

**(E)**240 N/m

**31.**How much work is done on the spring to stretch it 0.50 meters?

**(A)**10 J

**(B)**20 J

**(C)**40 J

**(D)**80 J

**(E)**160 J

**32.**A mass m of 3.0 kilograms is released from rest on a surface that forms a quarter circle with a radius of 0.80 meters. When it reaches the bottom of the circular portion, the track is horizontal for a distance d of 1.2 meters. All surfaces are smooth and frictionless. Determine the speed of the mass when it reaches the end of the horizontal section of track.

**(A)**2 m/s

**(B)**4 m/s

**(C)**6 m/s

**(D)**12 m/s

**(E)**16 m/s

**33.**A projectile with a mass of 2.0 kilograms is launched with a speed of 20 meters per second at an angle of 53° above the horizontal, as shown in the figure above. It lands at point P on a building that is 16 meters tall. Determine the total mechanical energy of the projectile at point P, relative to the initial launch height.

**(A)**100 J

**(B)**200 J

**(C)**400 J

**(D)**800 J

**(E)**1,600 J

**34.**Which of the following quantities is conserved in a perfectly elastic collision?

**(A)**Total velocity of the system

**(B)**Total linear momentum of the system

**(C)**Total kinetic energy of the system

**(D)**Both A and C

**(E)**Both B and C

**35.**The graph above shows the force acting on an object during a 6-second time interval. What is the change in momentum during this elapsed time?

**(A)**10 kg • m/s

**(B)**60 kg • m/s

**(C)**90 kg • m/s

**(D)**135 kg • m/s

**(E)**185 kg • m/s

**Questions 36-37:**

A 3.0-kilogram mass moving with a speed of 2.0 meters per second is closing on a 2.0-kilogram mass moving with a speed of 1.0 meters per second, as shown in the diagram below. The masses collide and stick together.

**36.**What is the speed of the combined masses after the collision?

**(A)**1.2 m/s

**(B)**1.6 m/s

**(C)**1.8 m/s

**(D)**2.0 m/s

**(E)**2.4 m/s

**37.**What impulse is experienced by the 3.0-kilogram mass during the collision?

**(A)**-1.2 kg • m/s

**(B)**-1.6 kg • m/s

**(C)**-1.8 kg • m/s

**(D)**-2.0 kg • m/s

**(E)**-2.4 kg • m/s

**38.**Kepler’s three laws describe the orbit of a planet with a mass m around a star of mass M. Which statement below is NOT consistent with Kepler’s three laws?

**(A)**Planetary orbits are elliptical.

**(B)**The central star is located at one of the foci of the elliptical orbit.

**(C)**A circular orbit is an ellipse where the two foci coincide.

**(D)**The period of the orbit depends on the mass of the planet.

**(E)**As the radius of the orbit decreases, the speed of the orbiting mass increases.

**39.**A very large star of mass Mand radius r undergoes a transformation into a neutron star. Assume that the mass remains constant while the radius of the star becomes 1/1,000 its original size, (1 × 10

^{-3})r. How does the change in the radius of the star affect the force of gravity, F

_{g}, acting between the star and a planet that is orbiting the star?

**(A)**The force of gravity between the planet and the star remains unchanged.

**(B)**The new force of gravity between the star and the planet is (1 × 10

^{-3})F

_{g}.

**(C)**The new force of gravity between the star and the planet is (1 × 10

^{-6})F

_{g}.

**(D)**The new force of gravity between the star and the planet is (1 × 10

^{-9})F

_{g}.

**(E)**The new force of gravity between the star and the planet is (1 × 10

^{-12})F

_{g}.

**40.**In the diagram above, two neutral, uncharged, conducting spheres mounted on insulating stands are in contact with each other. A negatively charged rod is brought near the spheres but does not touch either sphere. While the negative rod is held in this position, the spheres are separated. As a result, sphere 1 now has a charge of Q. Which of these statements is true?

I. Sphere 2 now has a -Q charge.

II. The spheres have been charged by induction.

III. If the spheres touch again, their total charge will be 2Q.

**(A)**I only

**(B)**II only

**(C)**III only

**(D)**I and II only

**(E)**I, II, and III

**Questions 41-42:**

In the diagram below, two charges, q = -1 coulomb and Q = +4 coulombs, are separated by a distance d of 1.0 meter.

**41.**Determine the location, as measured from charge q, where the electric field due to both charges has zero magnitude.

**(A)**0.25 m to the left of charge q

**(B)**0.33 m to the right of charge q

**(C)**0.33 m to the left of charge q

**(D)**1.00 m to the right of charge q

**(E)**1.00 m to the left of charge q

**42.**Charges q and Q attract one another with the electric force, F

_{E}If the magnitude of both charges is doubled and the distance between the charges is also doubled, determine the new electric force acting on these charges.

**(A)**F

_{E}

**(B)**2F

_{E}

**(C)**4F

_{E}

**(D)**8F

_{E}

**(E)**16F

_{E}

**Questions 43-45:**

Two charged plates each hold a charge Q of 3.0 coulombs, and they have a potential difference Vof 6.0 volts. The plate spacing, d, is 20 centimeters. A positive charge, q = 0.40 coulomb, is located at the midpoint between the plates as shown in the diagram below

**43.**Determine the magnitude of the electric field between the plates.

**(A)**0.33 V/m

**(B)**1.5 V/m

**(C)**3.0 V/m

**(D)**30 V/m

**(E)**33 V/m

**44.**Determine the capacitance of the plates.

**(A)**0.33 F

**(B)**0.50 F

**(C)**2.0 F

**(D)**9.0 F

**(E)**18 F

**45.**What is the electric potential energy of charge eft

**(A)**0.20 J

**(B)**1.2 J

**(C)**1.5 J

**(D)**2.0 J

**(E)**2.4 J

**46.**What is the equivalent resistance for the portion of the circuit shown in the above

diagram?

**(A)**1 Ω

**(B)**2 Ω

**(C)**4 Ω

**(D)**6 Ω

**(E)**12 Ω

**47.**The lightbulbs connected in the circuit above all have identical resistances. Rank the light bulbs in order from brightest to dimmest.

**(A)**1 > 2 > 3 = 4

**(B)**3 = 4 > 2 > 1

**(C)**1 > 3 = 4 > 2

**(D)**2 > 3 = 4 > 1

**(E)**1 = 2 > 3 = 4

**Questions 48-50:**

Use the following diagram to answer questions 48 to 50.

**48.**What is the resistance of R

_{1}?

**(A)**0.5 Ω

**(B)**1 Ω

**(C)**2 Ω

**(D)**4 Ω

**(E)**16 Ω

**49.**What is the potential difference across R

_{2}?

**(A)**1 V

**(B)**2 V

**(C)**4 V

**(D)**6 V

**(E)**12 V

**50.**What is the power consumption of R

_{3}?

**(A)**1 W

**(B)**3 W

**(C)**6 W

**(D)**9 W

**(E)**12 W

**51.**A sphere with a mass of 0.20 kilograms and a positive charge of 0.10 coulombs is moving at a speed of 10 meters per second in the +x-direction. The sphere enters a uniform 5.0-tesla magnetic field that is directed into the page (-z) as shown above. What is the resulting motion?

**(A)**The charge will circle clockwise with a 2.0 m radius.

**(B)**The charge will circle counterclockwise with a 2.0 m radius.

**(C)**The charge will circle clockwise with a 4.0 m radius.

**(D)**The charge will circle counterclockwise with a 4.0 m radius.

**(E)**The charge will circle clockwise with a 40 m radius.

**52.**Which of the following fields CANNOT change the speed of the object that is acted upon by the field?

I. Uniform gravity field

II. Uniform electric field

III. Uniform magnetic field

**(A)**I only

**(B)**II only

**(C)**III only

**(D)**Both I and II

**(E)**Both II and III

**53.**A rectangular loop of wire with length L, width w, and resistance R is moved into a magnetic field, B, at a constant velocity v. What is the magnitude of induced current in . the loop as it enters the magnetic field?

**54.**A pendulum with a string length L oscillates with a period T. What does the string length need to be changed to in order to double the period?

**55.**Which graph correctly depicts the total energy during the oscillation of a frictionless spring-mass system?

**56.**Sort the following electromagnetic waves in order from shortest to longest wavelength: infrared, gamma rays, microwaves, visible light, and radio waves.

**(A)**Microwaves, radio waves, visible light, infrared, gamma rays

**(B)**Gamma rays, infrared, visible light, radio waves, microwaves

**(C)**Gamma rays, visible light, infrared, microwaves, radio waves

**(D)**Radio waves, microwaves, visible light, infrared, gamma rays

**(E)**Microwaves, gamma rays, visible light, infrared, radio waves

**57.**Which term describes the separation of white light into separate colors in a glass prism due to small differences in the index of refraction for each wavelength?

**(A)**Diffraction

**(B)**Dispersion

**(C)**Interference

**(D)**Polarization

**(E)**Refraction

**58.**A 5-meter-long string is set into a vibration that creates the standing wave pattern in the diagram above. The speed of the wave in the string is 420 meters per second. What is the frequency of this vibration?

**(A)**84 Hz

**(B)**105 Hz

**(C)**140 Hz

**(D)**210 Hz

**(E)**420 Hz

**59.**The object viewed by a convex lens is positioned outside of the focus, as shown in the .

diagram above. In which location will the image be formed? >

**(A)**A

**(B)**B

**(C)**C

**(D)**D

**(E)**E

**60.**Light passes from glass (medium 1), into air (medium 2). The angle of the light in the glass (θ

_{1})is adjusted until total internal reflection is observed. Which of these represents the index of refraction of the glass, n

_{1}?

**61.**An incident ray of white light passes from air into glass. Which color of light will ; experience the greatest refraction?

**(A)**Red

**(B)**Green

**(C)**Blue

**(D)**Violet

**(E)**None. All colors of light will be refracted at the same angle.

**62.**Monochromatic light is incident upon a single slit. The light passes through the slit and is projected on a screen behind the slit. Which of these describes the pattern seen on the screen?

**(A)**There is a single maximum consistent with a single slit.

**(B)**Light spreads out completely and fills the entire screen evenly.

**(C)**There is a large central maximum with faint secondary maxima.

**(D)**The pattern is identical to the results obtained using a double slit.

**(E)**The light converges into a single bright line.

**63.**When light passes from air into glass, how are its frequency, wavelength, and speed affected?

**Questions 64-65:**

Mercury is used in thermometers to measure temperatures. The specific heat of mercury is 140 joules/kilogram • kelvin, and the coefficient of linear expansion for mercury is 60 × 10

^{-6 }K

^{-1}.

**64.**How much heat must be added to increase the temperature of 0.002 kilograms of mercury by 10°C?

**(A)**0.028 J

**(B)**2.8 J

**(C)**4.2 J

**(D)**42 J

**(E)**420 J

**65.**Determine the change in length of a 0.20-meter column of mercury when the temperature increases by 10°C.

**66.**A gas is trapped in a cylinder with a movable piston. During several thermodynamic processes, the pressure, P, and volume, V, of the gas are changed in order to increase the temperature of the gas from TtoGT. Which of the following is NOT capable of creating this change in temperature?

**67.**A gas trapped in a cylinder with a movable piston undergoes an adiabatic process. During this process, the gas does 1,200 joules of work. Which of the following statements is true?

**(A)**The change in internal energy is zero.

**(B)**The internal energy of the system increases by 1,200 joules.

**(C)**The temperature of the gas remains unchanged.

**(D)**The temperature of the gas increases.

**(E)**The heat transferred into or out of the system is zero.

**68.**A heat engine absorbs 2,500 J of heat and exhausts 1,500 J to a cold reservoir. What is the efficiency of this engine?

**(A)**25%

**(B)**40%

**(C)**50%

**(D)**75%

**(E)**80%

**69.**Each of the following scientists and experiments contributed to the development of atomic theory EXCEPT

**(A)**J. J. Thomson’s work with cathode rays passing through charged plates

**(B)**Rutherford’s gold foil experiment

**(C)**Michelson and Morley’s work with the interferometer

**(D)**Planck’s analysis of emission spectra

**(E)**Einstein’s work on the photoelectric effect

**Questions 70-71:**

A photoelectric effect experiment is conducted, and the results are graphed in the following kinetic energy versus frequency graph.

**70.**Which answer below correctly states the work function, Ø, the threshold frequency, ƒ

_{0}, and the value of Planck’s constant, h, as calculated from these experimental results?

**71.**If the photoelectric material is replaced with a new material that has a greater work function, how will the graph change?

**(A)**The graph will not change at all.

**(B)**The y-intercept will remain the same, but the slope of the graph will decrease.

**(C)**The y-intercept will remain the same, but the slope of the graph will increase.

**(D)**The y-intercept will change, and the slope of the graph will increase.

**(E)**The y-intercept will change, but the slope of the graph will remain the same.

**72.**An isotope of polonium,

^{218}Po

_{84. }undergoes beta decay. In the process, the atom becomes an isotope of astatine. Which of the following is the result of this transmutation?

**73.**How many neutrons are liberated during the following nuclear reaction?

**(A)**1

**(B)**2

**(C)**3

**(D)**4

**(E)**5

**74.**An object moving in the x-direction accelerates rapidly. As the object nears the speed of light, a stationary observer would report that the object’s

**(A)**mass increases due to mass-energy equivalence

**(B)**mass decreases due to mass-energy equivalence

**(C)**mass increases and its length in the x-direction decreases

**(D)**mass decreases and its length in the x-direction decreases

**(E)**mass increases while its length, width, and depth all decrease

**75.**The mass of the universe seems inconsistent with observed gravitational effects. Which of the following has been proposed to account for the missing mass in the universe?

**(A)**Chaos theory

**(B)**Dark matter

**(C)**String theory

**(D)**The general theory of relativity

**(E)**The special theory of relativity

**ANSWER KEY**

Practice Test 2

Practice Test 2

**DIAGNOSTIC CHART**

**SCORING YOUR TEST**

**How to Determine Your Raw Score**

**Answer 1:**

**(D)**To identify if an object is speeding up or slowing down, assess the trend in the speed (absolute value of velocity) of each object. Object A is speeding up from 0 to 30 m/s. Object B has a constant speed of 15 m/s. Object Cis slowing during the first 3 seconds and then speeding up during the next three seconds. Object D is slowing during the entire interval from 15 m/s to zero and is therefore the correct answer. Object E does have negative velocity. However, its speed (absolute value of velocity) is increasing from 20 m/s to 30 m/s.

**Answer 2:**

**(A)**Acceleration is the slope of the velocity-time graph. The magnitude of acceleration is the absolute value of the slope. The greatest acceleration will have the steepest slope. Object A has the steepest slope and therefore the greatest acceleration, 5 m/s

^{2}.

**Answer 3:**

**(E)**The area between the velocity-time graph and the x-axis is the displacement of an object. The area between the graph of object E and the x-axis represents a displacement of 135 m from the origin in the negative direction. Although negative, it is still the largest displacement.

**Answer 4:**

**(E)**Work is a change in energy. Power is the rate of work, which is also the rate of change in energy.

**Answer 5:**

**(C)**Total mechanical energy is the sum of the kinetic and potential energies of a system.

**Answer 6:**

**(B)**Potential energy is the energy associated with the instantaneous position of an object.

**Answer 7:**

**(B)**The direction of the electric field is the same as the direction of the force on a positive test charge. This means the electric field lines are drawn away from positive plates, or charges, and toward negative plates or charges.

**Answer 8:**

**(A)**Negative charges move in the direction opposite that of electric field lines.

**Answer 9:**

**(D)**The electric force described in answer 8 will begin to accelerate the electron to the right. Use the right-hand rule to find the force of magnetism on the moving charge. The thumb of the right hand points in the direction of motion of a charged particle, the extended fingers point in the direction of the magnetic field (into the page in this case), and the palm of the hand points in the direction of force (upward in this case). The right-hand rule applies to positively charged particles. Since this is a negatively charged particle, it will do the opposite and be forced downward in the -y-direction. As an alternative, you can use the left hand to solve for negative charges moving in magnetic fields.

**Answer 10:**

**(D)**Refraction is the bending of light, or any wave, as it moves from one medium into another.

**Answer 11:**

**(A)**Diffraction is the spreading of waves that results when waves pass through an opening or encounter an obstacle.

**Answer 12:**

**(B)**Wave superposition causes interference patterns in waves.

**Answer 13:**

**(D)**The photoelectric effect experiment provided evidence that light behaves as a particle made up of discrete packets of energy known as quanta.

**Answer 14:**

**(E)**The interference patterns observed by passing light through two small slits in Young’s experiment imitated the behavior of water waves passing through two small slits.

**Answer 15:**

**(C)**While trying to prove the existence of the ether, the medium in space in which light waves supposedly travel, the Michelson-Morley experiment failed to find the ether but did determine an accurate measurement for the speed of light.

**Answer 16:**

**(C)**An object moving at a constant speed may be turning. When an object turns, it is changing direction and is therefore changing it velocity. If the velocity is changing, the object is accelerating. Uniform circular motion is an example. The magnitude of velocity is constant (A), the object is changing direction (B), and centripetal force is the net force acting on the object and is greater than zero (D). The work-kinetic energy theorem states that the net work is equal to a change in kinetic energy. If an object is moving at constant speed, then the change in kinetic energy and net work are both zero (E).

**Answer 17:**

**(A)**

**Answer 18:**

**(B)**

**Answer 19:**

**(B)**The horizontal and vertical motions solve independently. The y- direction accelerates under the influence of gravity. In a horizontal launch, the initial velocity in the y-direction is zero, v

_{iy}= 0.

**Answer 20:**

**(E)**Acceleration due to gravity is a constant 10 meters per second squared during the entire flight of the object. Even at the top of its arc, when the instantaneous velocity becomes 0, the acceleration remains 10 meters per second squared.

**Answer 21:**

**(B)**

The friction force must be equal but opposite to the horizontal component of force, T

_{x}, in order to maintain a constant velocity.

ƒ = T cos θ

**Answer 22:**

**(D)**The string is lifting the object by an amount equal to T sin 0. The sum of the normal force, N, and T sin 0 is equal to the weight of the object. Therefore, the normal force must be less than the weight of the object.

N + T sin θ = w

**Answer 23:**

**(D)**Treat the blocks as a single system with a combined mass.

**Answer 24:**

**(E)**The string between the two blocks provides the force accelerating the 2.0 kg block at the same rate as the acceleration of the system.

**Answer 25:**

**(E)**Apparent weight is equal to the normal force acting on the person.

**Answer 26:**

**(B)**In order for the system to remain at rest, the opposing forces acting on the two masses must be equal and opposite. The tension in the string cancels. Set the magnitude of the friction force acting on mass 1 equal to the force of gravity acting on mass 2.

**Answer 27:**

**(B)**The friction force, f holds the car in the turn and creates the net centripetal force, F

_{c}, acting toward the center of the circular motion.

**Answer 28:**

**(B)**

**Answer 29:**

**(D)**At the top of the loop, both the normal force to the track and the force of gravity act downward toward the center of the circle. Both forces are positive.

The mass, radius, and gravity are all fixed variables that cannot be reduced. However, as the speed of the roller coaster is reduced, the normal force of the track decreases. The minimum speed occurs when the normal force reaches zero at the top of the loop.

**Answer 30:**

**(D)**The spring constant is the slope of a force-displacement graph.

**Answer 31:**

**(B)**The work is the area underneath a force-displacement graph.

**Answer 32:**

**(B)**This is conservation of energy. The potential energy at the top of the curved section of track is transformed into kinetic energy. The initial height is equal to the radius of the curved section of track, h = r.

**Answer 33:**

**(C)**Even though the question asks for the total energy at point P, you do not need to solve for projectile motion and then determine the landing velocity. Total mechanical energy is conserved and is the same at the beginning and at the end of the problem. It is easier to solve for the total mechanical energy at the beginning where it consists entirely of kinetic energy.

**Answer 34:**

**(E)**Linear momentum is conserved during both elastic and inelastic collisions. In perfectly elastic collisions, kinetic energy is conserved as well.

**Answer 35:**

**(D)**Change in momentum is equal to the area underneath a force-time graph.

**Answer 36:**

**(B)**This is conservation of momentum. This collision is perfectly inelastic. The mass sticks together to form one large, combined mass.

**Answer 37:**

**(A)**Impulse is equal to the change in momentum. This question is asking for the change in momentum of only the 3.0 kg mass.

**Answer 38:**

**(D)**Regardless of the mass of an object in orbit around a planet or a star, the velocity at a specific distance from the center of the planet or star is constant for that specific distance. All of the other statements are true.

**Answer 39:**

**(A)**The universal law of gravitation which can be expressed as:

The radial distance, r, between the two masses is a line drawn from the center of one mass to the center of the other mass. The actual radius of the masses is not a factor in the equation. Since the star did not lose any mass as it collapsed, the force between the star and planet remains unchanged.

**Answer 40:**

**(D)**The negative rod near sphere 1 causes negative charges to be repelled from sphere 1 onto sphere 2. As a result, sphere 1 has a greater positive charge while sphere 2 has a greater negative charge. If the spheres are separated, the spheres become charged. Since the rod did not touch either sphere, this was accomplished by induction. If sphere 1 receives a charge of Q, then due to conservation of charge sphere 2 must have an equal and opposite charge of -Q. If the spheres are again touched, they will neutralize and neither sphere will then have a charge.

**Answer 41:**

**(E)**For the total electric field to equal zero, the individual electric field vectors of the two charges must be opposite and equal to one another. The electric field vector due to q points toward q and the electric field vector due to Q points away from Q. The only locations where these two field vectors are opposite each other is to the left of charge q and to the right of charge Q. However, in order for the magnitudes of the vectors to be equal, the zero point has to be closer to the smaller charge q. Therefore, the only location where the electric fields can cancel is to the left of charge q. This narrows the choices to A, C, or E. The magnitude of the electric field of each point charge can be found using the following equations:

**Answer 42:**

**(A)**

**Answer 43:**

**(D)**

**Answer 44:**

**(B)**

**Answer 45:**

**(B)**The electric potential energy, U

_{E}, of charge, q, located a distance, d, from the charged plate that it is attracted to can be determined as follows.

U

_{E}= qEd = (0.40 C)(30 N/C) (0.10 m)= 1.2 J

The charge is located at the midpoint between the plates. Its energy is related to its position, not the distance between the plates. If the positive charge had been located initially on the positive plate, then the distance between the plates would have been used.

**Answer 46:**

**(D)**

**Answer 47:**

**(A)**Brightness is determined by the power dissipated in the bulb. Power can be determined by using the following formula:

P= I

^{2}R

All of the bulbs have the same resistance, R, so their brightness is determined by the amount of current flowing through them. All of the current must pass through bulb 1. After flowing past bulb 1, the current reaches a junction. Some current must go down the path leading to bulb 2, and the rest of the current must go down the path leading to bulbs 3 and 4. Current will take the path of least resistance, so more current will flow down the path leading to bulb 2 than the path leading to bulbs 3 and 4. However, the exact same amount of current will pass through both bulbs 3 and 4 because they are in series and receive the same current. As a result, bulbs 3 and 4 will have the same brightness.

**Answer 48:**

**(C)**The voltage of R

_{1}is shown to be 4 V. The current flowing through R

_{2}is shown to be 2 A. This same current must also flow through R

_{1}because they are in series with each other. Using Ohm’s law, V= IR, the resistance of R

_{1}can be determined:

**Answer 49:**

**(B)**The components in any loop of the circuit must use the voltage supplied by the battery. A loop exists containing R

_{1}, R

_{2}, and R

_{3}?. These must add up to the voltage of the battery.

**Answer 50:**

**(D)**Power can be determined using the following formula:

P = IV

The voltage drop across R

_{3}? is shown to be 6 V. The current across R

_{3}? is equal to the total current flowing in the circuit minus the current flowing through the parallel resistor, R

_{4}?. The total current of 2 A is flowing through R

_{2}? and splits up between R

_{3}? and R

_{4}?. Since the current flowing through R

_{4}? is 0.5 A, the current flowing in R

_{3}must be 2.0 A - 0.5 A = 1.5 A.

P = IV = (1.5AK6V) = 9 W

**Answer 51:**

**(D)**The right-hand rule states that the thumb of the right hand points in the direction of motion of a charged particle, the extended fingers point in the direction of the magnetic field (into the page in this case), and the palm of the hand points in the direction of the force (upward in this case). The right-hand rule applies to positively charged particles. The charge will circle counterclockwise. The magnitude of its radius can be determined by setting the centripetal force, F

_{c}, equal to the force of the magnetic field on a moving charge.

**Answer 52:**

**(C)**Magnetic fields apply a force in a direction that is perpendicular to the motion of the object. As a result, the forward speed is not changed, only the velocity is changed. Velocity changes because there is a change in direction but not in magnitude.

**Answer 53:**

**(B)**The induced emf,

**ε**, is caused by a change in flux, Ø. Flux can be determined by the area of the loop multiplied by the magnetic field passing through the loop. The amount of flux will change as the loop is moved with velocity v through the magnetic field, B. The equation to describe this is

**ε**= BLν. The

**ε**is essentially an induced voltage. The current can be found by applying Ohm’s law:

**ε**= V = IR.

**Answer 54:**

**(E)**

**Answer 55:**

**(E)**During the oscillation, the total amount of energy will not change. The kinetic energy and potential energy will transform between each other, but their sum will remain constant.

**Answer 56:**

**(C)**This is the order of the electromagnetic spectrum listed from shortest to longest wavelength. It is also the electromagnetic spectrum listed from highest to lowest frequency.

**Answer 57:**

**(B)**Dispersion is caused by the slightly different indexes of refraction within a particular medium depending upon the wavelength. White light is made up of multiple wavelengths that experience dispersion in a prism.

**Answer 58:**

**(D)**There are 2.5 wavelengths visible in the drawing: 2.5λ = 5 m.

**Answer 59:**

**(E)**An object placed between the focal point, ƒ and twice the focal point, 2ƒ will form a real and inverted image beyond the 2ƒ point on the opposite side of a convex lens.

**Answer 60:**

**(A)**

**Answer 61:**

**(D)**Different wavelengths of light have slightly different indexes of refraction in glass. The shorter the wavelength, the greater the refraction resulting in the dispersion of the colors of light.

**Answer 62:**

**(C)**This pattern is caused by the interference of the light upon itself as it passes through the single slit and is evidence of the wave nature of light.

**Answer 63:**

**(C)**When light passes from one medium into another, the frequency does not change. Light moving from air, which has nearly the same index of refraction as a vacuum, will slow down.

v = ƒλ

When the frequency is constant, wavelength is directly proportional to wave speed. If the speed decreases, then the wavelength also decreases.

**Answer 64:**

**(B)**Heat, Q, is equal to the mass, m, multiplied by the specific heat, c, and the change in temperature, ΔT.

Q = mc ΔT

Q = (0.002 kg) (140 J/kg • K)(10 K) = 2.8 J

The coefficient of linear expansion is not needed for this part. When in doubt, use kelvins. However, if the formula involves a change in temperature, ΔT, then either the Celsius or the Kelvin scale can be used; 1° is equal to 1 K.

**Answer 65:**

**(C)**The change in length, ΔL, is equal to the coefficient of linear expansion, α , multiplied by the original length, L

_{0}, and the change in temperature, ΔT:

**Answer 66:**

**(D)**Use the ideal gas law. The change in both pressure and volume must offset the increase, by a factor of 6 in temperature.

**Answer 67:**

**(E)**During an adiabatic process, the pressure and volume change so rapidly that no heat is exchanged with the surroundings, which is consistent with the correct answer, E. Why are the other answers wrong? Examine the first law of thermodynamics: ΔU= Q + W. In an adiabatic process, heat exchange is zero (Q = 0). This modifies the first law to AU = W. In this process, the 1,200 joules of work are done by gas. When work is done by gas, the gas loses energy, AU = W = -1,200 J. This means the internal energy decreases, invalidating answers A and B. If the internal energy decreases, then the temperature decreases, invalidating answers C and D.

**Answer 68:**

**(B)**

**Answer 69:**

**(C)**Michelson and Morely’s experiment provided evidence that light travels through space without the need of a medium. It became evidence of the particle nature of light in addition to confirming the speed of light.

**Answer 70:**

**(A)**When the threshold frequency is reached, photoelectrons will be emitted with a kinetic energy above 0. According to the graph, that occurs when the frequency is equal to 1.0 × 10

^{15}Hz. That narrows the choices to A and C. The work function is the amount of energy that must be added to reach the threshold frequency. The y-intercept of the graph, -4 eV, indicates the energy of the electrons occupying the lowest energy level inside the atom. To reach the threshold frequency, +4 eV of energy must be added to these electrons. Therefore, the work function is +4 eV, which is also consistent with answers A and C. Planck’s constant is the slope of the function.

**Answer 71:**

**(E)**The slope of the line is Planck’s constant. Constants do not change, so the slope of the line cannot change.

**Answer 72:**

**(D)**Beta decay occurs when a neutron releases an electron and becomes a proton. The result will be an increase in the atomic number by 1 but no change to the atomic mass because the mass of a neutron is essentially the same as that of a proton. The loss of mass from the release of an electron is insignificant.

**Answer 73:**

**(C)**In a balanced nuclear equation, the sum of the mass numbers on the left side of the equation must equal the sum of the mass numbers on the right side of the equation. Similarly, the sum of the atomic numbers on both sides of the equation must be equal. The sum of the mass numbers on the left side is 236. A liberation of 3 neutrons would result in a total mass number of 236 on the right side of the equation.

**Answer 74:**

**(C)**The result of an object reaching the speed of light is that its mass will increase and its length will shorten in the direction of travel.

**Answer 75:**

**(B)**The motion of stars and galaxies is not consistent with the mass that can be seen with telescopes. Mathematically, a large portion of the mass of the universe is missing. Since the missing mass cannot be observed directly, it has been called dark matter. A search is underway to identify the validity, composition, and properties of dark matter.

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