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AP Physics Final Review 2014-2015

You should look over old tests, labs, homework, and study guides. Questions on this study guide are not meant to be all-inclusive or 100% representational of the final exam; it is merely a guide.

MULTIPLE CHOICE:

1) If the sum of all the forces acting on a moving object is zero, the object willa. Slow down and stopb. Change the direction of its motionc. Accelerate uniformlyd. Continue moving with constant velocity

2) The graph represents the relationship between gravitational force and mass for objects near the surface of Earth. The slope of the graph represents the

a) Acceleration due to gravityb) Universal gravitational constantc) Momentum of objectsd) Weight of objects

3) As the car goes around the curve, the centripetal force is directeda) Toward the center of the circular curveb) Away from the center of the circular curvec) Tangent to the curve in the direction of motiond) Tangent to the curve opposite the direction of motion

4) The diagram shows a block sliding down a plane inclined at angle θ with the horizontal. As angle θ is increased, the coefficient of kinetic friction between the bottom surface of the block and the surface of the incline will

a) Decreaseb) Increasec) Remain the same

5) The amount of work done against friction to slide a box in a straight line across a uniform, horizontal floor depends most on the

a) Time taken to move the boxb) Distance the box is movedc) Speed of the boxd) Direction of the box’s motion

6) Which graph best represents the motion of a block accelerating uniformly down an inclined plane?

a b c d


7) A child is riding on a merry-go-round. As the speed of the merry-go-round is doubled, the magnitude of the centripetal force acting on the child

a) Remains the same b) is halved c) is doubled d) is quadrupled


8) Which of the following correctly applies to a projectile in the absence of friction?

a) The vertical velocity is changing.b) The horizontal velocity is changing.c) The vertical acceleration is changing.d) The horizontal acceleration is changing.

9) A ball is thrown at an angle of 38° to the horizontal. What happens to the magnitude of the ball’s vertical acceleration during the total time interval that the ball is in the air?

a) It decreases, and then increases.b) It decreases, and then remains the same.c) It increases, and then decreases.d) It remains the same.

10) A man standing on a scale in an elevator notices that the scale reads 30 Newtons greater than his normal weight. Which type of movement of the elevator could cause this greater-than-normal reading?

a) Accelerating upwardb) Accelerating downwardc) Moving upward at constant speedd) Moving downward at constant speed

11) Projectile A is launched horizontally at a speed of 20m/s from the top of a cliff and strikes a level surface below, 3.0 seconds later. Projectile B is launched horizontally from the same location at a speed of 30m/s. The time it takes projectile B to reach the level surface is

a) 4.5 s b) 3.0 s c) 2.0 sd) 10 s

The motion of a circus clown on a unicycle moving in a straight line is shown in the graph at right.

12) What would be the acceleration of the clown at 5 s?

a) 1.6 m/s2 b) 8.0 m/s2 c) 2.0 m/s2 d) 3.4 m/s2

e) none

13) After 12 seconds, how far is the clown from her original starting point?a) 100 m b) 56 m c) 34 m d) 47 m

e) 74 m

14) A 15 kg rock is projected horizontally from a very high cliff at a speed of 65m/s as shown. What is the speed of the rock after it has fallen a vertical distance of 35m?

a) 26 m/s b. 59 m/s c. 65 m/s d. 70 m/s

15) A 45 kg steel ball is projected vertically with an initial speed of 280m/s. While the ball is rising, 8.5x105 J of heat energy are produced due to air


friction. What is the maximum height reached by the ball using 2 significant figures?

a) 1900 m b. 2100 m c. 4000 m d. 5900 m

16) The net work done in accelerating an object along a frictionless horizontal surface is equal to the change in the object’s

a) net force b) potential energy c) velocity d) kinetic energy

17) Forces A and B have a resultant R. Force A and resultant R are represented in the diagram. Which vector best represents force B?

a b c d

18) Two stones, A and B, are thrown horizontally from the top of a cliff. Stone A has an initial speed of 15 meters per second and stone B has an initial speed of 30. m/s. Compared to the time it takes stone A to reach the ground, the time it takes stone B to reach the ground is

a) the same b) half as great c) twice as great d) four times as great

19) Using the graph at the left, what was the average speed during the 10.0-second time interval?

a) 2.4m/s b) 1.6 m/sc) 2.0 m/sd) 7.2m/s

20) A satellite is placed in an orbit at a distance 8R away from the center of the earth. It is then moved to a new orbit of radius 2R away from the earth’s center. Which of the following is the correct ratio of the gravitational force in the new orbit to that in the old orbit?

a) 2 :1 b) 4 :1 c) 8 :1 d) 16 :1

21) A ball is dropped from the top of a building. Taking air resistance into account, which best describes the speed of the ball while it is moving downward?

a) It will increase at a steady rate b) It will remain constant c) It will decrease d) Its rate of acceleration will decrease until the ball moves at a constant

speed


22) Which graph best represents the relationship between the acceleration of an object falling freely near the surface of Earth and the time that it falls?

a b c d

23) Is it possible for an object’s velocity to increase while its acceleration decreases?

a) No, this is impossible because of the way in which acceleration is defined.

b) No, because if acceleration is decreasing the object will be slowing down.

c) No, because velocity and acceleration must always be in the same direction.

d) Yes, an example would be a falling object near the surface of the moon.

e) Yes, an example would be a falling object in the presence of air resistance.

24) A hypothetical planet orbits a star with mass one-half the mass of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth years does it take for the planet to complete one orbit?

a) ½ b) 1/(2)1/2 c) 1 d) (2)1/2 e) 2

25) Bales of hay are dropped from an airplane to a herd of cattle below. Assume the airplane flew horizontally at an altitude of 180m with a constant velocity of 50m/s. Neglect air resistance. About how far horizontally will the bale move prior to landing on the ground?

a) 9000 m b) 300 m c) 180 m d) 100 m e) 50 m

26) What is the shape of the velocity time graph for an object with the position time graph shown in the diagram at right?


27) Snail A is travelling at 0.001 m/s [E] toward Snail B, travelling at 0.001 m/s [W]. What is the velocity of Snail A relative to Snail B?

a) zero b) 0.001 m/s [E] c) 0.002 m/s [E] d) 0.002 m/s [W]

A banana boat is travelling at 4 m/s [E] relative to still water. The river is flowing at 1 m/s [W] relative to earth. A monkey on the boat is moving at 2 m/s [E] relative to boat and throwing a banana behind him at 3 m/s relative to himself. A bird is flying over the boat at a velocity of 1 m/s [W] relative to earth. An observer is standing on the riverbank watching everything.

28) How long will it take the boat to move 50m east and then 50m west (ignore time for turning around)?

a) 26.6s b) 20.3s c) 15.4s d) 34.8s

29) How fast is the banana moving relative to the river?a) 1m/s E b) 2m/s W c) 3m/s W d) 3m/s E e) 4m/s W

KinematicsMake sure you know how to:

a) Draw motion graphs for a moving objectb) Interpret x vs. t and v vs. t graphs in terms of position, velocity,

displacement, and acceleration.c) Know definitions of key terms and understand situations when velocity

and acceleration might be negative, positive or zero.1. What is the difference between initial position, final position, displacement,

and path length?

2. The position vs. time graph for a moving object is a straight line with a slope equal to -15.0 m/s and starts at x = 3. Explain what this means about the motion of the object.

3. Give an example in which an object has negative acceleration and is speeding up. Give an example in which an object with positive acceleration is slowing down. Be able to draw graphs and motion diagrams for each.

4. A car’s motion is described by the following function:

x(t) = (-2)t2 + (12)t + (-48 )

a) What is the car’s position and velocity at time zero?

b) What is its acceleration?

c) At what time (if any) does the car’s velocity become zero?

5. While driving along a flat stretch on the highway, there is a policeman parked behind a bush. As you drive by he uses his speed gun to track your speed over

a period of 10 seconds. The data he includes in his report is given in the table below.

a) Plot a velocity vs. time graph.

b) What type of relationship does the graph show?

c) What is the equation of the graph?

Time (s) Velocity (mph)

0 452 604 786 948 10810 125


6. A car goes from rest to 100 km/hr in 10 seconds. It then travels at that rate for the following hour. After that hour, it brakes to a stop in 15 seconds.

a) What is the car's acceleration during the 1st 10 seconds?

b) What is the car’s acceleration during the last 15 seconds?

c) What is the total distance (in meters) that the car travels during the trip: speeding up, constant velocity and slowing down?

d) What is the car's average velocity during the whole trip?

7. If you throw a tennis ball straight up in the air with a velocity of 30m/s, how long will it take to come back to the ground?

What is the acceleration of the ball at the maximum height of the flight?

8. Ashleigh and Rachael are bored with attending choral lessons inside the high school and decide instead to practice their singing while skydiving. They pick their new favorite song, Ring of Fire by Johnny Cash, and get into the airplane. Ignore air resistance.

a) Draw a motion diagram and a separate force diagram while they are falling before deploying the parachute.

b) If Ring of Fire is 2 min 36 sec long, at what altitude do they have to fall from in order to finish the song right before they deploy the parachutes?

c) What will their final velocity be right before deploying the parachutes?

9. Kelsey is playing in a lacrosse game against North’s rival South. She catches a pass and has a breakaway past the defense. Her initial speed is 2 m/s and she accelerates at a rate of 4 m/s2 for 3.4 s until she shoots the ball.a) How fast is she going when she releases the ball?

b) How far did she run while accelerating?

Forces and Newton’s Laws

a) Plot a velocity vs. time graph.

b) What type of relationship does the graph show?

c) What is the equation of the graph?


Make sure you know how to:a) Draw a force diagram, and use the force diagram to apply Newton’s second

law.b) Connect descriptions of motion and motion graphs with Newton’s concepts.c) Understand and apply Newton’s First, Second, and Third Laws to word

problems.d) Understand static and kinetic friction, force of friction and coefficients

10.You slide toward the right at decreasing speed on a horizontal wooden floor. What objects interact with and exert forces on you?

11.Why do you need to keep pushing a grocery cart in a store in order to keep it moving? Doesn’t this go against Newton’s 1st Law?

12.An elevator in a tall office building moves downward at constant speed. How does the magnitude of the upward force exerted by the cable on the elevator compare to the magnitude of the downward force exerted by Earth on the elevator? Explain your reasoning.

13.Three friends are arguing about the type of information a bathroom scale reports. Eugenia says that it reads the weight of a person. Alan says that it reads the sum of the forces exerted on the person by Earth and the scale. Mike says that the scale reads the force that the scale exerts on the person. Who do you think is correct? Why?

14.Identify third law force pairs for the following interactions: A rollerblader and the floor, a volleyball player and the volleyball, and a speeding up car’s tires and the road.

15.Draw all of the forces for the following rocks.no acceleration moving at constant speed moving in a circle

around post

16.Alex’s car (900 kg) stalls 10 m from the Amwell Road parking lot. Alex gets

two of his strong physics friends, Sam and Tim, to help him move the car.

The 3 students push horizontally with a force of 500 N each. a. Draw and label a force diagram for the object of interest


b. Solve for any of the forces that you can.

c. What is the acceleration of the car?

d. How long does it take them to reach the parking lot?

17. You are pulling a sled on snow with your cousin on it. Together the mass is 40 kg. The coefficients of static and kinetic friction are 0.30 and 0.20.

a. How hard do you have to pull to just get them moving?

b. How hard would you have to pull to keep them moving at a constant velocity?

c. You pull with a force that’s 10 N higher than your answer to part b. What is the resulting acceleration?

d. Now you are pulling on a slippery section of snow and ice. If you have to pull with 60N to keep moving at a constant velocity, what is the coefficient of friction?

Two Dimensional Motion

Make sure you know What information or data determines the time in the air, Which component of velocity is constant, Which component of velocity is accelerating, How to determine the components of a velocity vector.

18.Michelle stands on the Millstone River Bridge kicking stones into the water below.

a. If Michelle kicks a stone with a horizontal velocity of 3.50 m/s, and it lands in the water with a horizontal distance of 5.40 m from where Michelle is standing, what is the height of the bridge?

b. If the stone had been kicked harder, how would this affect the time it takes to fall?

19. A pumpkin is launched out of a cannon at an angle of 30° with an initial velocity of 50 m/s.

a. What is the horizontal velocity? (horizontal component)

b. What is the initial vertical velocity? (vertical component)

20.A boy on a 250 m high tower throws a ball that lands 100 m away in the horizontal direction.

a. How long (in seconds) does the ball take to hit the ground?

b. What was the ball’s initial velocity?


Impulse and MomentumMake sure you can solve problems using the conservation of momentum principle and the impulse/momentum theorem

21.Two identical cars are traveling toward each other at the same speed. One of the carts has a piece of modeling clay on its front. The carts collide, stick together, and stop; the momentum of each cart is now zero. If the system includes both carts, did the momentum of the system disappear? Explain your answer.

22.Robin Hood has a mass of 35kg and shoots a 0.1kg arrow at a speed of 150m/s, causing him to move in the opposite direction. What is the recoil speed of the archer?

23.A 0.3-kg tennis ball, traveling at 15 m/s to the right, is hit back to the left by Daria. It leaves her racket with a speed of 44 m/s in the opposite direction from which it came. If the racket and the ball are in contact for 0.05 s, calculate the average force the racket exerts on the ball.

24.A carnival game requires you to knock over stuffed clowns at the NJ shore. You are given the option of picking a ball that is very bouncy or a big lump of clay. Both options have the same amount of mass. Assume you can throw them with equal speed and accuracy and you only get one throw. Which option would you choose? Why?

25.A 40 kg skater traveling at 4 m/s overtakes a 60 kg skater traveling at 2 m/s in the same direction and collides with her. If they remain in contact after the collision, what is their final velocity?

Work and EnergyMake sure you can:

a) Choose a system and the initial and final states of a physical processb) Solve problems using kinetic/potential energy formulasc) Apply energy conservation principles to solve problems.d) Understand and apply the definition of work

26.If an object’s speed increases by a factor of 5, by what factor would the kinetic energy increase?

27.In Metropolis, the comic book hero Superman uses his incredible strength to save the lives of countless ordinary citizens. One day, the braking system on


a passenger bus fails when the bus is 50 m away from a busy intersection. The bus is moving towards the intersection at 5 m/s. If Superman exerts a force of 300 N on the bus, which has a mass of 1000 kg, will he be able to stop the bus before it reaches the busy intersection?

28.A 4 kg bowling ball is raised 15 m to the top of a ramp. It is released from rest and travels to the bottom.

a) How much PE does the ball have when it is at the top of the ramp? The bottom of the ramp?

b) How fast is it traveling when it reaches the bottom (ignore friction)?

29.A 51.7-kg hiker ascends a 43.2-meter high hill at a constant speed of 1.20 m/s. If it takes 384 s to climb the hill, then determine:

a) The potential energy change of the hiker.b) The kinetic energy of the hiker.c) The work done by the hiker’s muscles.d) The power generated by the hiker.

Circular Motion Use your understanding of Newton’s laws to explain why you tend to slide across the car seat when the car makes a sharp turn.

30.A 13 g holiday ornament is attached to a 0.93 m string. The stopper is swung in a horizontal circle making one revolution in 1.18 s.

a. What is the linear/tangential speed of the ornament?

b. Determine the force exerted by the string on the ornament.

c. In what direction will it go if you let it go (besides down)?

31.A 5 kg metal ball is swung in a circle attached to a 1-meter chain. The ball is traveling at 5 m/s.

a. Determine the centripetal acceleration of the ball

b. Determine how hard you need to pull on the chain to maintain this rotation.


Rotational Motion

32.Two children push tangentially counterclockwise on the edge of a 1.8-meter-radius merry-go-round to accelerate it from rest. Each child pushes continuously with a constant force of Fp = 120 N.

a. Calculate the magnitude of the total torque on the merry-go-round. (Use proper units on your final answer.)

b. Suppose that I = 320 kg·m2 for the merry-go-round. After 3.5 s of being pushed with constant torque, what is the period of rotation of the merry-go-round?

c. How much total work did the children do during the same 3.5 s? State your assumptions/show your work.

d. According to the diagram shown above, in which direction does the merry-go-round’s angular momentum vector point?

i. Into the pageii. To the leftiii. Out of the page

iv. To the right

v. Toward top of the page

vi. Toward bottom of the page

33.A 6.0-meter-long boom has a television camera suspended at its right end, as shown above. When used properly, the weight of the camera (mc = 8.0 kg) and of the boom itself (mb = 26 kg) is counterbalanced by an adjustable metal weight mounted at the boom’s left end. Assume that the pivot is frictionless, and that the boom has uniform thickness and density.

a. At present, the boom is exactly horizontal, and an 85-kg metal weight is mounted on the left end of the boom. Calculate the net torque about the pivot. (Note that the system is NOT currently balanced.)

b. The vector of the net torque you calculated in part (a) is directed:i. into the pageii. to the rightiii. toward the top of

the page

iv. out of the pagev. to the leftvi. toward the bottom

of the page

c. When the entire system is released from rest in its current position, the boom will begin to accelerate about its pivot in which direction?

i. Clockwise ii. Counter-clockwised. Suppose that, immediately after it is released, the system accelerates

at 0.15 rad/s2. Calculate the entire system’s moment of inertia.

34.Determine the gravitational force between two objects that are 100 km apart if one has a mass of 100 kg and the other has a mass of 6.5 x 1019 kg.


Mixed Problems:

1. A car travels 10.0 km north in 400.0 s. Then it travels 25.0 km south in 850.0 s. What is the (a) average speed and (b) average velocity of the car?

2. A body with initial speed of 8.0 m/s moves along a straight line with constant acceleration and travels 640 m in 40.0 s. Find the (a) average velocity, (b) final velocity, and (c) acceleration.

3. A string is wound around the outer edge of a toy top (radius 3.5 cm). When the string is pulled with a constant acceleration, the top “spins up” from rest to an angular speed of 66 rad/s during a period of 2.5 s. (The toy’s center and bottom remain stationary: as the string is pulled, the toy rotates, but it does not translate.)

a. What is the linear acceleration of the string? _______________b. How many revolutions does the toy complete during the 2.5 s of

acceleration? _______________c. On the picture of the toy top, draw a vector representing the vector

direction of ω.

4. A truck starts from rest and moves with a constant acceleration of 5.0 m/s². Find its a) speed and b) the distance traveled after 4.0 s has elapsed.

5. A marble dropped from a bridge strikes the water in 5.0 s. Calculate (a) the speed with which it strikes and (b) the height of the bridge.

6. A baseball is thrown straight upward with a speed of 30.0 m/s. (a) How long will it rise? (b) How high will it rise? (c) How long after it leaves the hand will it return to the starting point?

7. A boat is pointed straight across a river (east) and is moving at a speed of 0.55 m/s relative to the water. The current of the river is south at 0.30 m/s. (a) What is the velocity of the boat relative to the riverbank? (b) How long does it take the boat to cross the river if the river is 65 m wide?

8. A grand piano (m = 350. kg) starts at rest on a wheeled dolly that allows it to move without friction in any direction on level ground. Four people push on the piano with the four constant forces shown above. (Assume that the four forces do NOT change in magnitude or direction as the piano moves.) The +x and +y-directions are given. Show your work completely.

a. What is the net force on the piano (magnitude &

direction)?b. What is the acceleration of the piano?

(magnitude & direction)?


9. A ball, rolling with a speed of 20.0 cm/s, rolls off the edge of a table that is 80.0 cm high. (a) How long does it take to drop to the floor? (b) How far, horizontally, from the table edge does the ball strike the floor?

10.A body projected upward from level ground at an angle 55 with the horizontal has an initial speed of 40. m/s. (a) How long does it remain in the air? (b) How far from the starting point will it strike?

11.During an episode of the animated TV show Family Guy, Brian tries to demonstrate to Peter just how badly Peter needs to go on a diet: Brian takes an apple and tosses it into a circular orbit around Peter’s midsection. (To see this short joke on YouTube, visit: http://www.youtube.com/watch?v=MD7urmuSeEg or else search the www.youtube.com website for “family guy gravitational”.) Suppose the apple has a mass of 250 g, and that it orbits Peter’s center-of-mass in a circular orbit of radius 1.0 m and period 5.0 s. Assume that both the apple and Peter are spherical and uniform-density. (Assume that NO other masses, including the Earth, are nearby)

a. Find the apple’s linear speed. Show your work.b. What is Peter’s mass, in kilograms? Show your work completely. (Your

answer will be many orders of magnitude greater than the mass of a typical human… more like the mass of a small mountain!)

12.A mortar shell is launched from the ground with a speed of 100. m/s, at an angle of 60° to the horizontal. If it comes down and lands on top of a plateau 20. m above the level of the launch, calculate the horizontal distance traveled by the shell.

13.A plane flying at 100. m/s at an angle of 35° below horizontal releases a package when it is 1500 m above the ground. Calculate the horizontal distance the package travels from the instant of its release until the time it hits the ground.

14.Two posts at a distance, L, apart from each other support a shelf. Three canisters, each of mass M, are located at distances of (1/5)L, (2/5)L, and (3/5)L from post A. The shelf itself also has mass M. The entire configuration is at rest in equilibrium. For both parts (a) and (b): Express each final answer ONLY in terms of M, L, g, and any necessary

mathematical constants. Simplify each final answer to its most compact algebraic form.

a. Find the upward force exerted by post A on the shelf: _______________b. Find the upward force exerted by post B on the shelf: _______________

15.A force acts on a 2.0-kg mass and gives it an acceleration of 3.0 m/s². (a) What acceleration is produced by the same force when acting on a mass of 4.0 kg? (b) How large is the force?


16.A 95-kg box is sliding along a level floor with an initial speed of 15 m/s. (a) How large of a constant frictional force is required to stop the box in a distance of 15 m? (b) What is the coefficient of friction between the box and the floor?

17.A floating barge is held against a pier by two cables, as shown in the diagram below (viewed from above, looking down). The tension in cable #1 is 1250 N. Find the tension in cable #2 and the compression in the pier.

18.A mass of 1.5 kg moves in a circle of radius 25 cm at 2.0 rev/s, calculate the required centripetal force for the motion.

19.A car moving at 5.0 m/s tries to round a flat corner that has a radius of curvature of 8.0 m. How large must the coefficient of friction be between the wheels and the roadway if the car is not to skid?

20.A 22-kg wagon is pulled along the level ground by a rope inclined at 33 above the horizontal. A frictional force of 31 N opposes the motion. How large is the pulling force if the wagon is moving with (a) constant speed and (b) an acceleration of 0.40 m/s²?

21.Find the accelerations and string tensions of each of the following systems:

22.A suitcase slides down a loading ramp that makes an angle of 35 with the ground. If the coefficient of kinetic friction between the ramp and the suitcase is 0.555, find the magnitude of the acceleration of the suitcase.

23.A pilot attempts a vertical loop during an air show. While upside-down at the top of the 245-meter radius loop he experiences a g-force of 2.75 g’s. Calculate the speed of the plane at this point.

24.How much would a German shepherd of mass 34.0 kg weigh on earth? How much would it weigh on Uranus? [massUR = 8.80 x 1025 kg; radiusUR = 2.67 x 107 m]


25.During 2007 & 2008, the Cassini spacecraft has been exploring Saturn and its very large moon, Titan. Suppose that one day, in the distant future, astronauts can visit Titan and live in a base-station on its surface, where the surface gravity is 1.35 m/s2.

a. Suppose that fly-by photographs show that the radius of Titan is 2680 km (not actually true, but pretend for the purposes of this problem). Calculate Titan’s mass: ____________________ kg

b. When an astronaut drops a 1.25-kg hammer from rest, and lets it fall through a distance of 2.00 m in her room on Titan, how much gravitational potential energy does it lose? ____________________

c. The hammer’s final speed on Titan is ___________________. (Ignore air resistance.)

d. A heavy crate (245 kg) sits at rest on a level platform, with a coefficient of static friction μs = 0.95. The horizontal force strength needed to dislodge the crate (to start it moving) on Titan is ________________.

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