### SAT Physics Subject Test - Practice Test 1

##
**SAT Physics Subject Test - Practice Test 1**

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:**

**(A)**Alpha decay

**(B)**Beta decay

**(C)**Gamma ray

**(D)**Fission

**(E)**Fusion

Select the term from above that identifies the nuclear reactions described in questions 1 to 3.

**Questions 4-6:**

The following diagrams depict sound waves moving outward from a sound source.

4. Which diagram depicts the sound waves created by a source moving with a speed v that is equal to the speed of sound?

5. Which diagram depicts the sound waves created by a source moving with a speed v that is less than the speed of sound?

6. Which diagram depicts the sound waves created by a source moving with a speed v that is greater than the speed of sound?

**Questions 7-9:**

The following terms relate to circuits. Match the correct term with its definition.

**(A)**Capacitance

**(B)**Current

**(C)**Power

**(D)**Resistance

**(E)**Voltage

7. The rate of charge flow.

8. The rate of energy dissipation in a circuit.

9. The potential difference between the terminals of the battery.

**Questions 10-12:**

Match the correct image description with the optical instruments depicted in questions 10 to 12.

**(A)**Real and inverted

**(B)**Real and upright

**(C)**No image forms, ray traces never intersect

**(D)**Virtual and inverted

**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.

**Questions 13-15:**

Use the following speed-time graph for the motion of an object to solve questions 13 to 15.

**13**Determine the displacement during the first second (interval A).

*.***(A)**10 m

**15 m**

(B)

(B)

**(C)**20 m

**(D)**25 m

**(E)**30 m

**14**During which interval is the object moving with a constant velocity?

*.***(A)**A

**(B)**B

**(C)**C

**(D)**D

**(E)**A, B, D, and E

**15.**Which of the following is true when t = 6 seconds?

I. The object is accelerating.

II. The object has an instantaneous speed of zero.

III. The object has returned to the origin.

**(A)**I only

**(B)**II only

**(C)**III only

**(D)**I and II only

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

____________________________________________________________

**Question 16:**

If a ball is thrown straight upward with an initial velocity of v, it will reach a height of h. If the initial speed of the ball is doubled, what will be the new maximum height?

**Question 17:**

A mass, initially at rest, is accelerated uniformly at 5.0 meters per second squared.

Determine the displacement and final speed of the mass after 2.0 seconds have passed.

**Question 18:**

During a time of 5.0 seconds, an object moves through a half circle with a radius of 10 meters, as shown above. What is the magnitude of the object’s velocity during this motion?

**(A)**2 m/s

**(B) π**mls

**(C)**4 m/s

**(D)**2

**π**m/s

**(E)**4

**π**m/s

**Question 19:**

A boat capable of moving at 5 meters per second attempts to cross a 50-meter-wide river. The river flows downstream at 2 meters per second. The boat begins at point P and aims for point Q, a point directly across the river. How far downstream, from point Q, will the boat drift?

**(A)**0 m

**(B)**10 m

**(C)**20 m

**(D)**30 m

**(E)**40 m

**Question 20:**

A ball is thrown horizontally from the edge of a 5-meter-tall building. It lands 25 meters from the base of the building, as shown in the diagram above. With what initial speed was the ball thrown?

**(A)**5 m/s

**(B)**10 m/s

**(C)**15 m/s

**(D)**20 m/s

**(E)**25 m/s

**Question 21:**

A flat railroad car is moving to the right at 5 m/s. A person standing on the car throws a ball straight upward at 20 m/s. If air resistance is negligible, where will the ball be in relation to the person’s new position at the time when the ball returns to its original starting height?

**(A)**The ball will land 20 meters in front of the person.

**(B)**The ball will land 10 meters in front of the person.

**(C)**The ball will land in the person’s hand.

**(D)**The ball will land 10 meters behind the person.

**(E)**The ball will land 20 meters behind the person.

**Question 22:**

The diagram above depicts a projectile launched from point A with a speed of v at angle of 0, above the horizontal. Determine the speed of the projectile when it reaches its maximum height at point

**(A)**0

**(B)**ν

**(C)**½ν

**(D)**ν cos

**θ**

**(E)**ν sin θ

c

**Question 23:**

A 5.0-kilogram mass is pulled along a rough horizontal surface by a string, as shown above. The coefficient of kinetic friction between the surface and the object is 0.10. The tension in the string is 30 newtons. Determine the acceleration of the object.

**(A)**1 m/s²

**(B)**2 m/s²

**(C)**3 m/s²

**(D)**4 m/s²

**(E)**5 m/s²

**Question 24:**

Mass m is positioned on a frictionless 30° incline, as shown above. It is kept stationary by a string that is parallel to the incline. Determine the tension in the string.

**Question 25:**

Two masses, m

_{1}= 1 kg and = 3 kg, are connected by a string that is draped over a pulley, as shown above. Mass 1 is positioned on a frictionless horizontal surface, while mass 2 hangs freely. The masses are released from rest. Determine the acceleration of mass 2.

**(A)**2.5 m/s

^{2 }

**(B)**3.3 m/s

^{2 }

**(C)**5.0 m/s

^{2}

**(D)**6.7 m/s

^{2}

**(E)**7.5 m/s

^{2}

**Question 26:**

Earth (m = 5.98 X 10

^{24}kilograms) pulls a 60-kilogram person towards it with a force of 600 N. With what amount of force does the person pull Earth towards themselves?

**(A)**0 N

^{ (B) 1/600 N }

**(C)**60 N

**(D)**600 N

**(E)**5.98 X 10

^{24}N

**Question 27:**

Three forces act on a mass, m, as shown in the diagram above. The mass remains at rest. Determine the magnitude of force F.

**(A)**6N

**(B)**8 N

**(C)**ION

**(D)**12 N

**(E)**14 N

**Question 28:**

What is the apparent weight of a 60-kilogram astronaut that is experiencing a rocket launch with an acceleration of 40 meters per second squared?

**(A)**600 N

**1,200 N**

(B)

(B)

**1,800 N**

(C)

(C)

**(D)**2,400 N

**(E)**3,000 N

**Question 29:**

Three masses are stacked on top of each other and are resting on the floor, as shown above. Determine the net force acting on the 3-kilogram mass.

**(A)**0 N

**(B)**10 N

**(C)**20 N

**(D)**30 N

**(E)**40 N

**Questions 30-31:**

A 1.0-kilogram mass is attached to the end of a 1.0-meter-long string. When the apparatus is swung in a vertical circle, the tension in the rope at the very bottom of the circle has a magnitude of 110 newtons.

**30.**Determine the speed of the mass at the lowest point in the circle.

**(A)**5 m/s

**(B)**10 m/s

**(C)**25 m/s

**(D)**55 m/s

**(E)**110 m/s

**31.**Determine the minimum speed needed at the top of the loop in order for the mass to complete one cycle.

**(A)**1.0 m/s

**(B)**2.5 m/s

**(C)**√10 m/s

**(D)**5 √10 m/s

**(E)**10 m/s

**Questions 32-33:**

A 5.0-kilogram mass is moving in uniform circular motion with a radius of 1.0 meter and a frequency of 3.0 hertz.

**32.**Determine the tangential velocity of the mass.

**33.**Determine the centripetal acceleration of the mass.

_________________________________________________

**Question 34:**

A car of mass m makes a turn with a radius of r. The coefficient of friction between the tires and the road is /jl.The maximum speed that the car can make the turn without skidding is If the mass of the car is doubled, what is the new maximum speed in the turn?

**Question 35-37:**

A 2.0-kilogram mass is pulled up a frictionless 30° incline at a constant speed of 0.5 meters per second.

**35.**Determine the force, F, required to move up the incline at a constant speed of 0.5 m/s.

**(A)**5 N

**(B)**10N

**(C)**15 N

**(D)**20 N

**(E)**25 N

**36.**Determine the work done by force F to move the mass to a vertical height of 2.0 meters.

**(A)**0 J

**(B)**5 J

**(C)**10 J

**20 J**

(D)

(D)

**40 J**

(E)

(E)

**37.**Determine the power required to move the mass up the incline at constant speed.

**(A)**0 W

**(B)**2.5 W

**(C)**5.0 W

**(D)**10 W

**(E)**20 W

_________________________________________________________________________

**Question 38:**

A 3.0-kilogram block is pressed against a spring that has a spring constant of 300 newtons per meter, as shown above. The block is moved to the left until the spring has been compressed 0.10 meters. The block and compressed spring are held in this stationary position for a brief amount of time. Finally, the block is released and the spring pushes the block to the right. What is the maximum speed reached by the block?

**(A)**0 m/s

**(B)**1 m/s

**(C)**2 m/s

**(D)**5 m/s

**(E)**10 m/s

**Question 39:**

What amount of force is required to change the speed of a 1,500-kilogram car by 10 meters per second in a time of 5 seconds?

**(A)**500 N

**(B)**1,000 N

**(C)**2,000 N

**(D)**3,000 N

**(E)**6,000 N

**Question 40:**

Which of these is true during an inelastic collision, in which no external forces act?

I. Linear momentum is conserved.

II. Kinetic energy is conserved.

III. The system loses energy as heat.

**(A)**I only

**(B)**II only

**(C)**III only

**(D)**I and II only

**(E)**I and III only

**Question 41:**

Two carts with masses 3 m and m are placed on a horizontal track with a compressed spring positioned between them. The carts are released from rest. The 3 m cart moves to the left with a speed of v. What is the speed of the cart on the right in the diagram above?

**Question 42:**

A satellite of mass m orbits Earth at a height of h and a speed of v. What would the Speed be for a satellite of mass 3 m at a height of h?

**Question 43:**

**Question 44:**

Determine the magnitude of the electric force acting on the 1-coulomb charge in the diagram above in terms of the Coulomb’s law constant,

**(A)**¼ k

**(B)**½ k

**(C)**k

**(D)**2k

**(E)**4 k

**Question 45:**

The direction of an electric field is

**(A)**determined by Lenz’s law

**(B)**determined by the right-hand rule

**(C)**the same as the direction of force acting on any type of charge

**(D)**the same as the direction of force acting on a negative charge

**(E)**the same as the direction of force acting on a positive charge

**Question 46:**

In the diagram, a +l-coulomb charge is located 2 meters to the left of the origin. A -1-coulomb charge is located 2 meters to the right of the origin. Determine the electric potential, in terms of the Coulomb’s law constant, k, at point P located at the origin.

**(A)**zero

**(B) ¼**k

**(C) ½**k

**(D)**k

**(E)**2k

**Question 47:**

A conducting sphere with a mass of 1.0 kilograms and a charge of 3.0 coulombs is initially at rest. Determine its speed after being accelerated through a 6.0-volt potential difference.

**(A)**2.0 m/s

**(B)**3.0 m/s

**(C)**4.0 m/s

**(D)**5.0 m/s

**(E)**6.0 m/s

**Questions 48-50:**

Use the following circuit diagram to answer questions 48 to 50.

**48.**What current flows through the 1 Ω resistor?

**(A)**0.5 A

**(B)**1.0 A

**(C)**2.0 A

**(D)**3.0 A

**(E)**4.0 A

**49.**What is the voltage drop across the 1 Ω resistor?

**(A)**2 V

**(B)**4 V

**(C)**6 V

**(D)**8 V

**(E)**10 V

**50.**How much power is dissipated in the 1 Ω resistor each second?

**(A)**4 W

**(B)**10 W

**(C)**16 W

**(D)**20 W

**(E)**32 W

**Question 51:**

In the circuit diagrams above, the resistors represent identical lightbulbs. Which circuit will have the brightest lightbulbs?

**(A)**I only

**II only**

(B)

(B)

**III only**

(C)

(C)

**IV only**

(D)

(D)

**The brightness of the lightbulbs is the same in each circuit.**

(E)

(E)

**Question 52:**

Charge q moving with speed v in the +x-direction enters a uniform -z magnetic field, B, as shown in the diagram above. In what direction is the force of magnetism acting on the charge at the instant the charge first enters the magnetic field?

**(A)**

**+**x

(B)

(B)

**+**y

**- y**

(C)

(C)

**-z**

(D)

(D)

**+z**

(E)

(E)

**Question 53:**

The induced emf in the loop at the instant shown in the diagram above is

**Question 54:**

A pendulum is constructed with a string of length L and a mass m, as shown above. When the pendulum bob is displaced a distance x from equilibrium, its period of oscillation is T. What will be the new period if the mass, m, and the displacement from equilibrium, x, are both doubled?

**Question 55:**

Which graph correctly depicts the kinetic energy of a mass experiencing simple harmonic motion?

**Question 56:**

A sound wave emitted by a source has a frequency ƒ, a velocity ν, and a wavelength λ. If the frequency is doubled, how will the speed and wavelength be affected?

**Question 57:**

The two wave pulses shown above are moving toward one another. Which diagram depicts the waveform at the instant that the waves overlap and superimpose?

**Question 58:**

A guitar string vibrates in a manner resulting in a standing wave having a wavelength λ being formed in the string. A listener hears the fundamental frequency, f

_{1}for this particular string. The string is plucked a second time in a manner that produces the second harmonic for this string. How does the wavelength for the second harmonic compare with the wavelength at the fundamental frequency?

**Question 59:**

The object viewed by a convex lens is positioned just inside of the focus, as shown in the diagram above. Which of the following correctly describes the image?

**(A)**No image is formed

**(B)**Real and upright

**(C)**Real and inverted

**(D)**Virtual and upright

**(E)**Virtual and inverted

**Question 60:**

Which diagram below correctly illustrates the path of a light ray moving from point 1 in air (to the left of the solid line) to point 2 in glass (to the right of the solid line)?

**Question 61:**

An image formed by a convex mirror is

**(A)**real and upright

**(B)**real and inverted

**(C)**virtual and upright

**(D)**virtual and inverted

**(E)**No image is formed by this mirror.

**Question 62:**

Monochromatic light with wavelength X passes through two narrow slits that are a distance d The resulting interference pattern appears as a series of alternating bright and dark regions on a screen located a length L meters behind the slits. How could the experiment be altered so that the spacing between bright regions on the screen is decreased?

**(A)**Use light with a shorter wavelength.

**(B)**Decrease the distance from the slits to the screen.

**(C)**Increase the distance between the slits.

**(D)**Perform the experiment under water.

**(E)**All of the above.

**Question 63:**

The bending of light as it passes through a narrow opening, or slit, is known as

**(A)**absorption

**diffraction**

(B)

(B)

**(C)**interference

**(D)**polarization

**(E)**refraction

**Question 64:**

Unpolarized light is projected onto two polarizing filters, as shown above. The polarizing filters contain thin threads all oriented parallel to one another. The filters are rotated with respect to each other, and two key positions are identified. In one position, no light is transmitted through the filter. In the other position, the maximum amount of light is transmitted. How must the microscopic threads in the two filters be oriented so that these results are witnessed?

**Question 65:**

A gas is trapped in a cylinder with a movable piston. How is the temperature, T, of the gas affected if the pressure of the gas doubles while the piston is moved inward, reducing the volume by half?

**(A)**¼T

**(B)**½T

**T**

(C)

(C)

**2T**

(D)

(D)

**4T**

(E)

(E)

**Question 66:**

A metal washer is a flat, circular piece of metal with a hole through its center, as pictured above. What will be the effect of heating this washer?

**(A)**No change occurs as the effects on the diameters cancel.

**(B)**Diameter 1 will decrease, and diameter 2 will decrease.

**(C)**Diameter 1 will decrease, and diameter 2 will increase.

**(D)**Diameter 1 will increase, and diameter 2 will decrease.

**(E)**Diameter 1 will increase, and diameter 2 will increase.

**Question 67:**

The specific heat of a liquid is 2,000 joules/kilogram • kelvin. How much heat is required to raise the temperature of 3.0 kilograms of this liquid from 10°C to 30°C?

**(A)**300 J

**(B)**13,333 J

**(C)**30,000 J

**(D)**60,000 J

**(E)**120,000 J

**Question 68:**

During an isothermal process, 600 joules of heat are removed from a trapped gas. Determine the work done on or by the gas and the change in internal energy of the system.

**(A)**W = 0 J; ∆U = -600 J

**(B)**W = 0 J; ∆U = +600 J

**(C)**W= -600J; ∆U = 0J

**(D)**W

**=**+600 J; ∆U = 0 J

**(E)**None of the above.

**Question 69:**

Which of the following is true about an isometric process?

**(A)**No work is done.

**(B)**No change in volume occurs.

**(C)**No heat is exchanged.

**(D)**Both A and B.

**(E)**Both A and C.

**Question 70:**

A heat engine operates between 100°C and 500°C. The theoretical efficiency is most nearly

**(A)**10%

**(B)**20%

**(C)**50%

**(D)**70%

**(E)**80%

**Question 71:**

The energy level diagram above shows a sample of atoms initially in the ground state. The atoms are radiated by photons having 9 electron volts of energy. After the absorption, photons are emitted by the sample of atoms. Several energies for the emitted photons are listed below. Which of these energies is NOT possible for photons emitted by the atom diagrammed above?

**(A)**1 eV

**(B)**2 eV

**(C)**3 eV

**(D)**5 eV

**(E)**8 eV

**Question 72:**

In a photoelectric experiment, the frequency of light is steadily increased. Which statement below is NOT correct?

**(A)**Below the threshold frequency, no electrons are emitted.

**(B)**Above the threshold frequency, electrons are emitted.

**(C)**Increasing the frequency of light increases the energy of the emitted electrons.

**(D)**Increasing the frequency of light increases the potential difference of the photocell.

**(E)**Increasing the frequency of light increases the induced current.

**Question 73:**

A radioactive sample with a half-life of 25 days is analyzed after 100 days. The amount of remaining radioactive material as a fraction of the original sample is most nearly

**Question 74:**

A spacecraft with a speed of 0.99c in the +x-direction passes by a stationary observer.

The dimensions of the spacecraft will appear altered along which axis/axes?

**(A)**x only

**(B)**y only

**(C)**z only

**(D)**y and z only

**(E)**x, y, and z

**Question 75:**

Which scientist proposed three laws of planetary motion based upon observations of the orbit of Mars?

**(A)**Galileo Galilei

**(B)**Johann Kepler

**(C)**James Maxwell

**(D)**Albert Michelson

**(E)**Isaac Newton

**Question 75:**

Which scientist proposed three laws of planetary motion based upon observations of the orbit of Mars?

**(A)**Galileo Galilei

**(B)**Johann Kepler

**(C)**James Maxwell

**(D)**Albert Michelson

**(E)**Isaac Newton

**Answer Key**

**Practice Test 1**

**DIAGNOSTIC CHART**

**SCORING YOUR TEST**

**How to Determine Your Raw Score**

Your raw score is the amount of correctly answered questions minus the incorrectly answered questions multiplied by ¼. An incorrectly answered question is one that you bubbled in, but was incorrect. If you leave the answer blank, it does not count as an incorrect answer.

**ANSWERS EXPLAINED**

**Answer 1:**

**(B)**The atomic number (number of protons) increases from 83 to 84. For this to happen, a neutron must eject a beta particle (an electron) and become a proton. The overall mass of the atom remains virtually unchanged because the mass of the ejected electron is very small. As a result, the atomic mass remains unchanged.

**Answer 2:**

**(D)**Fission is the breaking apart of an atom with a large number of protons and neutrons into two smaller atoms. Free neutrons are often released along with a tremendous amount of energy.

**Answer 3:**

**(A)**An alpha particle is the nucleus of a helium atom,

_{2}He

^{4}. When two protons and two neutrons are released from thorium-227, the resulting isotope is radium-223. Adding together the atomic numbers of helium and radium-223 as well as adding together their atomic masses will reveal thorium-227.

**Answer 4:**

**(D)**The dot representing the sound source is located at the extreme boundary of the sound wave it has created. The sound waves are superimposing on each other at this point, creating the sound barrier.

**Answer 5:**

**(C)**The dot representing the sound source is located behind the boundary of the sound wave it has created.

**Answer 6:**

**(E)**The dot representing the sound source is located in front of the sound wave it has created.

**Answer 7:**

**(B)**Current is a measure of the amount of charge, Q, flowing per time, t. It is measured in units of amps (amperes).

**Answer 8:**

**(C)**Power is the rate of energy dissipation in a circuit. It is measured in units of watts.

**Answer 9:**

**(E)**Voltage is synonymous with potential difference. It is measured in joules per coulomb.

**Answer 10:**

**(A)**The rays will converge beyond the focal point on the right side of the lens, forming an inverted and real image.

**Answer 11:**

**(E)**The rays will diverge. The negative back ray traces will form an upright, virtual image.

**Answer 12:**

**(A)**The rays will reflect off the mirror beyond the focal point on the left side of the mirror, creating an inverted, real image.

**Answer 13:**

**(B)**The area under a speed-time graph is the displacement. Finding the area under interval A requires solving for the area of a triangle.

Displacement = Area = ½ (30 m/s) (1 s) = 15 m

**Answer 14:**

**(C)**During interval C, the object is moving at a constant speed of 20 m/s.

**Answer 15:**

**(D)**The slope of a speed-time graph is acceleration. At t = 6 seconds, there is a negative, nonzero slope, indicating an acceleration. At t = 6 seconds, the instantaneous speed is also zero. In order to return to the origin, the displacement must be zero. Displacement is the area under a speed-time graph. For the first 6 seconds, the accumulated area is positive, indicating that the object has moved away from the origin in the positive direction. The zero value at t = 6 seconds is the object’s instantaneous speed, not its position.

**Answer 16:**

**(D)**

**Answer 17:**

**(A)**

**Answer 18:**

**(C)**Velocity is a vector quantity and is calculated using the displacement vector. Displacement is the final position minus the initial position. It is the shortest straight-line distance from the initial position to the final position. Although the object moved along a circular path, its displacement is the diameter of the circle and is equal to 20 m. So the velocity equals 4 m/s.

**Answer 19:**

**(C)**The time for the boat to cross the river is independent of the motion of the flowing river. The boat takes 10 seconds to cross the 50-meter river at a speed of 5 meters per second. During these same 10 seconds, the boat drifts downstream because of the river flowing at 2 meters per second. In 10 seconds, the boat will have drifted 20 meters downstream.

**Answer 20:**

**(E)**Horizontal motion does not affect vertical motion. The amount of time the ball takes to hit the ground can be determined as follows:

**Answer 21:**

**(C)**Before throwing the ball vertically, both the person and the ball have a horizontal velocity of 5 meters per second. Even though the ball is thrown straight up at 20 meters per second in the vertical direction, it continues to move independently at 5 meters per second horizontally. The cart also maintains the same horizontal speed. As a result, the ball stays above the cart during its motion and lands where it started, in the thrower’s hand.

**Answer 22:**

**(D)**The horizontal velocity remains constant during flight at v cos 6. At the top of the flight, the vertical velocity becomes zero. However, the horizontal velocity remains unchanged.

**Answer 23:**

**(E)**

**Answer 24:**

**(B)**The component of gravity acting parallel to an incline is mg sin θ.

If the object is stationary, the forces acting along the incline must have equal magnitudes in opposite directions.

**Answer 25:**

**(E)**The direction of motion is parallel to the string. The sum of the forces acting on the system (both bodies simultaneously) will be the forces that are parallel to the string. The two equal and opposite tensions cancel.

**Answer 26:**

**(D)**Newton’s third law states that each force is balanced by an equal but opposite reactionary force. If Earth pulls on a person with a force of 600 N, then the person will also pull on Earth with a force of 600 N. The effect on the acceleration of the person, however, is much greater than the effect on the acceleration of the Earth. Given the same force, the more massive Earth does not accelerate as much as the less massive person

**.**

**Answer 27:**

**(C)**In order for the mass that is acted upon by these forces to remain at rest, the sum of the forces must be zero. Force F must cancel the combined pull of the 8 N and 6 N forces. When the 8 N and 6 N forces are added using vector addition, they form the sides of a 3-4-5 triangle. Their vector sum is 10 N directed in the third quadrant. In order to cancel this 10N force, force F must pull with 10 N in the opposite direction.

**Answer 28:**

**(E)**Humans sense weight by interacting with surfaces. When asked for the apparent (feeling of) weight of a person, solve for the normal force.

Essentially, the acceleration of the spacecraft is added to the force of gravity.

**Answer 29:**

**(A)**All three blocks are stationary. There is no acceleration. Therefore, there is no net force.

**Answer 30:**

**(B)**The centripetal force, F

_{c}, is the sum of the forces acting on the mass and is directed toward the center of the circular motion. When the mass reaches the bottom of the circle, tension is directed toward the center of the circle and is positive. Gravity acts downward, is directed away from the center of the circle, and is negative.

**Answer 31:**

**(C)**At the top of the circle, both tension and gravity act downward toward the center of the circle and both are positive.

The mass, radius, and gravity are all fixed variables that cannot be changed. However, as the speed of the circling mass is reduced, the tension in the string will decrease. The minimum speed occurs when the tension is zero at the exact instant that the mass is at the top of the loop.

**Answer 32:**

(E)

The mass does not affect the answer. Any object traveling under these conditions will have the same velocity.

**Answer 33:**

**(D)**

**Answer 34:**

**(C)**The centripetal force, F

_{c}, is the sum of the forces acting on the mass and directed toward the center of the circular motion. For a car making a turn, the force acting toward the center of the turn is friction.

While the car is moving in the horizontal plane, it is not moving vertically. Therefore, the normal and gravity are canceling in the y-direction. They must have equal magnitudes: N = mg.

Mass does not affect the outcome. It is not part of the equation.

**Answer 35:**

**(B)**As the speed is constant, the sum of the forces acting on the block is zero. The force acting on the block down the ramp is given by mg sin θ. The force pulling the block uphill, F, must therefore be equal but opposite to mg sin 0. The sine of 30° is equal to

**½.**

**Answer 36:**

**(E)**As there is no friction on the hill, the amount of work, W, done by force F pulling the block uphill is equal to the change in potential energy, ∆U

_{g}, of the block regardless of the path taken by the block.

**Answer 37:**

**(C)**Power, P, is the rate of work: work divided by time. However, the time needed for the block to move up the hill has not been given. An alternate solution is needed. Work, W, is equal to the force, F, parallel to the motion of an object multiplied by the displacement, ∆x, of the object.

The force and velocity must be parallel to use this formula. If they are not parallel, use the component of force that is parallel to the velocity.

**Answer 38:**

**(B)**This involves conservation of energy. The potential energy of the spring is converted into the kinetic energy of the block:

**Answer 39:**

**(D)**Impulse, /, is defined as a change in momentum, ∆p. Impulse can be calculated by multiplying the force, F, acting on an object by the elapsed time, t, that the force acts. The change in momentum is also equal to the mass, m, of an object multiplied by the change in velocity, ∆v.

**Answer 40:**

**(E)**Linear momentum and total energy are always conserved, regardless if the collision is inelastic or elastic. However, in an inelastic collision, some of the kinetic energy is transformed into thermal energy that is then lost as heat to the environment.

**Answer 41:**

**(E)**This is conservation of momentum. The total momentum of both objects added together must be the same before and after the collision. This is an explosion. Although the momentums of the two objects are in opposite directions, their magnitudes must be equal to conserve momentum.

**Answer 42:**

**(B)**Orbits involve circular motion. The centripetal force, F

_{c}, is the sum of the forces acting on the mass and directed toward the center of the circular motion. For planets, this is the force of gravity.

Fc = Fg

Two force of gravity equations can be substituted into this equation. Both are shown in the next step. Either one can be used to answer this question.

In both of these equations, the orbiting mass m cancels. The mass M in the right equation is the mass of the large central star. Since the mass of the orbiting body cancels, all planets at the same radius will have the same orbital speeds.

**Answer 43:**

**(A)**The measurement given is from the surface of Earth. The value needed for gravity calculations is the distance from the center of a planet. The point in space is located 3r

_{E }from the center of Earth. The acceleration of gravity, g, at a point in space can be found using the gravity equation.

Tripling the distance from the center of Earth will cause the gravity to be 1/9 the value it is on the surface of Earth.

**Answer 44:**

**(B)**Coulomb’s law can be expressed as:

**Answer 45:**

**(E)**By definition, the direction of an electric field is in the same direction as the force on a positive charge.

**Answer 46:**

**(A)**Electric potential, also called voltage, for a point charge can be determined by the following formula:

When there is more than one point charge, the electric potential is the sum of the individual potentials.

The sign on the charge is included. However, the distance from each charge to the point in question is an absolute value.

**Answer 47:**

**(E)**This is conservation of energy. The electric potential energy is converted into kinetic energy.

**Answer 48:**

**(C)**Add resistors R

_{3}and R

_{2}in parallel:

**Answer 49:**

**(A)**The current flowing through R

_{3}has been determined to be 2.0 A. Use Ohm’s law, V

_{3}= I

_{3}R

_{3}, to determine the voltage drop across R

_{3}:

**V = (2.0 A) (1 Ω) = 2 V**

**Answer 50:**

**(A)**Any of these three power formulas can be used:

**Answer 51:**

**(B)**Resistors in parallel receive the most current, dissipate the most power, and will also glow the brightest when they are lightbulbs.

**Answer 52:**

**(C)**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 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. This matches the answer if the left hand had been used instead of the right hand.

**Answer 53:**

**(B)**The induced emf,

**ε**, is caused by a change in flux, φ. 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 ν through the magnetic field, B. When a linear length of wire, I, enters a magnetic field, the emf generated in the wire can be determined with the following formula:

**Answer 54:**

**(C)**The period of a pendulum can be described as:

The period is affected only by changes in the length, L, of a pendulum’s string and the gravity field, g, it is in. Changes in the displacement, x, and mass, m, do not affect the period of a pendulum.

**Answer 55:**

**(A)**The kinetic energy is at maximum when the mass is passing through the position of zero amplitude. The kinetic energy is zero as the mass reaches the maximum and minimum displacements of +A and -A and velocity becomes zero. The potential energy of the system is depicted in B. Total mechanical energy is shown in E.

**Answer 56:**

**(E)**Wave speed is determined by the medium in which it travels. Since the medium has not changed the wave speed must remain a constant ν. The product of frequency and wavelength is the wave speed. Therefore, the wavelength must be reduced to ½λ when the frequency is doubled in order for wave speed to remain constant in the same medium.

**Answer 57:**

**(A)**When the two waves superimpose, they will add destructively since they are each on opposite sides of the axis of propagation. The wave pulse on the left is a larger and inverted version of the pulse on the right.

**Answer 58:**

**(A)**For strings and open tubes, the wavelengths of the harmonics can be found using the following formula where n is the number assigned to the harmonic:

**Answer 59:**

**(D)**For objects placed between the focus and a convex lens, the image will be magnified, virtual, and upright.

**Answer 60:**

**(C)**Light will refract toward a normal line drawn perpendicularly to the surface of the medium it is entering if that medium has a higher index of refraction than the one it is exiting. Glass has a higher optical density and a higher index of refraction than air.

**Answer 61:**

**(C)**A convex mirror is a divergent optical instrument. It can form only virtual images that are upright.

**Answer 62:**

**(E)**In the above formula, x

_{m}is a measure between the bright regions seen on the screen in Young’s double-slit experiment. If the space between the bright regions decreases, then x

_{m}will decrease and vice versa. Decreasing the wavelength (λ), decreasing the distance from the slits to the screen (L), and increasing the slit spacing (d), will all decrease the x

_{m}and the space between bright regions on the screen. If the experiment is performed under water, then the wave speed will decrease, causing a corresponding decrease in wavelength.

All of these alterations will result in a closer spacing pattern.

**Answer 63:**

**(B)**This is the definition of diffraction.

**Answer 64:**

**(C)**When polarizing fibers are oriented perpendicularly to each other, no light can pass through. When oriented in a parallel position, the maximum amount of light can pass through.

**Answer 65:**

**(C)**The ideal gas law describes the relationship among the pressure, volume, and temperature of a gas.

There is no change in the temperature.

**Answer 66:**

**(E)**Heating a metal will cause the metal to expand. The entire ring, outer diameter, and inner diameter will all expand proportionally.

**Answer 67:**

**(E)**

**Answer 68:**

**(D)**During an isothermal process, the temperature remains constant and the change in internal energy, ∆U, is zero. When heat is removed, the engine loses energy and heat is negative, Q = -600 J.

**Answer 69:**

**(D)**During an isometric process, the volume of gas remains unchanged. No work is done since there is no change in volume.

**Answer 70:**

**(C)**

The temperatures must be in kelvins.

**Answer 71:**

**(B)**9 eV is enough energy to raise the electron from the ground state, n= 1, to an excited state at n = 4. The possible photon’s energies emitted can be determined by taking the difference between any two energy levels on the electron’s way back to the ground state. All of those energies are possible except for 2 eV.

**Answer 72:**

**(E)**Once the threshold frequency has been reached, the current begins. The current cannot increase with increasing the frequency. To increase the current, the intensity of the light must be increased. Increasing the intensity of the light increases the number of photons. This would cause more electrons to be ejected.

**Answer 73:**

**(B)**If each half-life lasts for 25 days, then 100 days is four half-lives.

**Answer 74:**

**(A)**As objects approach the speed of light, their length in the direction of motion will appear to decrease to an outside observer. Since this spacecraft is moving in the x-direction, only this dimension appears shorter.

**Answer 75:**

**(B)**Kepler’s three laws of planetary motion are based upon observations of the orbit of Mars.

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