# Physics

Exhaust gas from a rocket ship is released at a speed of 1,000 m / s so that the craft accelerates from 100 m / s to 200 m / s. How much fuel is necessary to complete this acceleration if the mass of the ship was originally 10,000 kg?

Select one:

a. 951.6 kg

b. 9048.4 kg

c. 5657 kg

d. 1813 kg

Question 2

Three pool balls of equal mass are resting on a horizontal frictionless surface. The cue ball (Ball 1) of mass 700 g is rolled into a stationary pool ball (Ball 2) and rebounds at 1.00 m / s in the direction from which it came. Ball 2 does not move, but it is touching another pool ball (Ball 3), which rolls away at 4.00 m / s. Which of the following is the initial speed of the cue ball, v1i? Also, given that the encounter between the cue ball and cue stick lasts for only 0.0500 s, which of the following is the average force delivered F to the cue ball by the stick?

Select one:

a. v1i  = 5.00 m / s
F = 56.0 N

b. v1i  = 3.00 m / s
F = 42.0 N

c. v1i  = 3.00 m / s
F = 2.80 N

d. v1i  = 5.00 m / s
F = 2.80 N

Question 3

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A force is applied to an object as shown. What is the direction of the torque vector?

Select one:

a. the same as the direction of the force vector

b. the same as the direction of the position vector

c. out of the screen

d. into the screen

Question 4

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The work done by a variable force F of the form F = kx where x varies from x0 to x1 where x0 = 0 is given by which of the following?

Select one:

a. kx12

b. kx1

c. (1/2) kx12

d. 0.5kx03

Question 5

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Select one:

a. (3.3, 1.5, −3.8)

b. (6.15, 0.25, 0.30)

c. (2.04, 0.70, −2.0)

d. (1.65, 0.75, −1.9)

Question 6

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It requires 1000 J of work to stretch a spring 3.00 cm. Which of the following is the change in potential energy and the spring constant of the spring?

Select one:

a. increase in potential energy = 1.50×103 J
spring constant = 333 N/m

b. increase in potential energy = 15.0 J
spring constant = 3.33×104 N/m

c. increase in potential energy = 1000 J
spring constant = 2.22×106 N/m

d. increase in potential energy = 30.0 J
spring constant = 6.67×106 N/m

Question 7

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A 200 g plastic ball is at rest on a frictionless incline 0.658 m above the surface of a table. The ball then rolls down the incline and across the table, coming to rest after a distance of 2.45 m. Which of the following the average friction on the ball while rolling across the table.

Select one:

a. 7.30 N

b. 0.527 N

c. 1.96 N

d. 1.29 N

Question 8

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A 0.200 kg dart is fired horizontally at a speed of 2.75 m / s when it hits a 0.700 kg block of wood suspended by a string. The nose of the dart sticks into 0.00210 m the wood. Together the dart and block swing upwards from a height of 0.0500 m above a table to 0.128 m above the table. Which of the following is the average force the dart applies to the block during impact?

Select one:

a. 32.4 N

b. 15.1 N

c. 1.36 N

d. 0.872 N

Question 9

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The motor of a toy train quits when the train reaches the top of the far left hill in the diagram. When the train of mass of 7.62 kg gets to the top of this hill, it is moving at a speed of 0.100 m/s. When the train finally makes it up the last hill, it uses all of its available mechanical energy to compress the spring. Which of the following is the distance the spring compresses if the spring constant is 1.00 × 105 N/m.

Select one:

a. 0.0271 m

b. 0.000 m

c. 0.0119 m

d. 0.0192 m

Question 10

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Two tops have the exact same shape, mass, and mass distribution, but one is 2.5 times larger than the other. If the two tops are spun with the same angular velocity and they are tipped from vertical at the same angle, what is the ratio of the precessional angular velocity of the smaller top to that of the larger top?

Select one:

a. 1:1

b. 1:2.5

c. 2.5:1

d. 6.25:1

Question 11

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The distance between the front and rear wheels of a 2280 kg car is 3.15 m. The car’s center of gravity lies in the middle of the car, 1.05 m behind the front wheels. When the car is at rest, what is the ratio of the force exerted by the ground on the front wheels to that exerted on the rear wheels?

Select one:

a. 3.0

b. 0.50

c. 0.33

d. 2.0

Question 12

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A pendulum bob has mass of 0.750 kg and is on a pendulum arm of length 1.00 m. The pendulum is pulled back so that the arm makes an angle of 60.0° from the vertical and is then released. Which of the following is the speed of the mass when it reaches its lowest point?

Select one:

a. 3.68 m/s

b. 3.13 m/s

c. 4.43 m/s

d. 4.12 m/s

Question 13

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A 1,450 kg car moves with a speed of 25.0 m / s when it collides with a stationary car having a mass of 1,550 kg. The two vehicles lock bumpers on impact. The two cars then collide with a stationary third car of mass 1,250 kg. During this second impact, the third vehicle becomes attached to the second but the first car is breaks free and moves at 0.125 m / s in the opposite direction. Which of the following is the final velocity of the second and third cars after the final collision?

Select one:

a. 12.88 m / s

b. 12.14 m / s

c. 14.42 m / s

d. 13.01 m / s

Question 14

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Select one:

a. 50.0 N

b. 42.3 N

c. 38.3 N

d. 32.1 N

Question 15

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An empty freight train car of mass 10,000 kg is rolling along a level section of track at 2.00 m / s. It collides with a loaded car of weight 1.96 × 105 N, which is at rest. The cars couple upon collision. Which of the following is the speed of the train after the collision?

Select one:

a. 1.02 m / s

b. 0.667 m / s

c. 2.00 m / s

d. 3.02 m / s

Question 16

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Which of the following is not a unit of power?

Select one:

a. Joule / second

b. Watt / second

c. ft ⋅ lb / s

d. horsepower

Question 17

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A 0.500 kg steel ball is dropped from a height of 4.00 m onto a horizontal steel slab. The collision appears elastic in that the ball rebounds to its original height. If the collision lasts for 2.00 × 10−3 s, which of the following is the impulse imparted to the ball and the average force applied to the ball during the collision?

Select one:

a. I = 8.49 kg•m / s
F = 4.25 × 103 N

b. I = 8.85 kg•m / s
F = 4.43 × 103 N

c. I = 8.00 kg•m / s
F = 4.00 × 103 N

d. I = 8.86 kg•m / s
F = 2.22 × 103 N

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Question 18

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Why are gyroscopes useful?

Select one:

a. They do not flip over so you always know which way is up.

b. They always precess in the same direction.

c. They respond differently depending on their position on the Earth.

d. They respond differently at different altitudes.

Question 19

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A spaceship is in space and currently at rest. The directive is given to accelerate from rest to a speed of 2.90 &times 103 m / s. If the fuel budgeted for this action is 400 kg, which of the following is velocity of the exhaust gas required if the ship mass is 7.38 &times 103 kg?

Select one:

a. 955 [m / s]

b. −955 [m / s]

c. –5.5 × 104 [m / s]

d. −1.01 × 103 [m / s]

Question 20

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True or false?
Clockwise rotations are always positive.

Select one:

a. false

b. true

Question 21

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A roller coaster has 8 cars, each of mass of 95.0 kg. The first hill of the ride is 24.8 m above the ground. Which of the following is the gravitational potential energy of the train once the last car had reached the top of the hill?

Select one:

a. 2.31×104 J

b. 1.85×105 J

c. -2.31×104 J

d. -1.85×105 J

Question 22

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A hanging mass m is connected to another mass M free to slide horizontally over a frictionless surface, as shown. The pulley has a radius R and a moment of inertia I. If the system is released from rest, what is its angular momentum about the center of the pulley 5 seconds later?

Select one:

a. mg

b. 5mg

c. mgR

d. 5mgR

Question 23

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A centrifuge is a device that spins small containers of substances at high speeds. A certain centrifuge can be modeled by four masses connected by massless rods to a rotating pivot, as shown.

Suppose that the masses are each 0.035 kg and that the rods are 8.0 cm long. How much energy does it take to accelerate the centrifuge up to 8,000 rotations per minute (from rest)?

Select one:

a. 310 J

b. 3800 J

c. 3900 J

d. 29,000 J

Question 24

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The work done to accelerate a car from 0 m / s to 40 m / s is _____ times greater than the work done to accelerate it from 0 m / s to 20 m / s?

Select one:

a. two

b. three

c. four

d. eight

Question 25

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In a game of marbles, a 60 g marble is rolling at 8.00 cm / s when it collides with a stationary marble. the 60 g marble takes off at a 27° angle at a reduced speed of 4.89 cm / s. The second marble moves at a rate of 3.21 cm / s at a 31.7° angle. Which of the following is the mass of the second marble?

Select one:

a. 58.1 kg

b. 0.0581 kg

c. 0.0800 kg

d. 80.0 kg

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