Deck 7: Work and Energy

Question 1

Work has all of the following characteristics except

A) it is a scalar.
B) it is a vector.
C) it is the cross product of two vectors.
D) it is the product of two scalars.
E) none of the above.

Answer 1

it is a scalar.

Question 2

A girl holds a basketball in a fixed position. The work she does on the ball is

A) dependent on the weight of the ball.
B) dependent on how high above the ground the ball is.
C) positive.
D) zero.
E) negative.

Answer 2

zero.

Question 3

A container of water is lifted vertically 2.0 m and then returned to its original position. If the container's weight is 30 N, the work done during the process is

A) 0 J.
B) 7.5 J.
C) 15 J.
D) 60 J.
E) 1.2 *10² J.

Answer 3

0 J.

Question 4

An apple falls to the ground from a tree. During the fall, the work done by the apple is

A) positive.
B) zero.
C) negative.

Question 5

You want to move a very heavy table across the room, but no matter how hard you push the table, it does not move. As you push harder and harder, the work done by the static friction

A) increases.
B) stays the same and has a positive value.
C) stays the same and is zero.
D) stays the same and has a negative value.
E) decreases.

Question 6

A heavy suitcase is carried by a porter a sizable horizontal distance. The work done on the suitcase by the porter

A) is zero.
B) is positive.
C) is negative.
D) depends on how heavy the suitcase is.
E) is unknown; more information is needed to work out the answer.

Question 7

A heavy suitcase is carried by a porter down a flight of stairs. The work done on the suitcase by the porter is

A) zero.
B) positive.
C) negative.
D) unknown; more information is needed to work out the answer.

Question 8

A heavy suitcase is carried by a porter down a flight of stairs. The work done on the suitcase by the Earth's gravity is

A) zero.
B) positive.
C) negative.
D) unknown; more information is needed to work out the answer.

Question 9

A heavy suitcase is carried by a porter down a flight of stairs. The net work done on the suitcase is

A) zero.
B) positive.
C) negative.
D) unknown; more information is needed to work out the answer.

Question 10

A box is in contact with a surface that makes an angle of 30^o with the horizontal. An applied horizontal force of 10.0 N allows the box to slide along the surface at a constant speed. When the box has moved 2.0 m along the surface, the work done on it by the applied force is

A) 0 J.
B) 17.3 J.
C) 20.0 J.
D) 23.1 J.
E) 40.0 J.

Question 11

A box is in contact with a surface that makes an angle of 30^o with the horizontal. An applied horizontal force of 10.0 N allows the box to slide along the surface at a constant speed. When the box has moved 2.0 m along the surface, the work done on it by the normal force is

A) 0 J.
B) 10.0 J.
C) 20.0 J.
D) 40.0 J.
E) 60.0 J.

Question 12

A box is in contact with a surface that makes an angle of 30^o with the horizontal. An applied horizontal force of 10.0 N allows the box to slide along the surface at a constant speed. When the box has moved 2.0 m along the surface, the net work done on it is

A) 0 J.
B) 10.0 J.
C) 20.0 J.
D) 40.0 J.
E) 60.0 J.

Question 13

A 3.0-kg box is in contact with a surface that makes an angle of 30^o with the horizontal. When the box has moved 2.0 m along the surface, the work done on it by gravity is

A) 0 J.
B) 3.0 J.
C) 5.2 J.
D) 6.0 J.
E) 6.9 J.

Question 14

A 600-kg elevator is pulled upward with a constant force of 6.0 kN for a distance of 30.0 m. The net work done by the elevator is

A) -3.6 * 10⁵ J.
B) -3.6 *10³ J.
C) 0 J.
D) 3.6 * 10³ J.
E) 3.6 * 10⁵ J.

Question 15

A rock, tied at the end of a rope, is swirled at a constant speed in a vertical circle. The net work done on the rock

A) is positive.
B) is zero.
C) is negative.
D) changes from positive to negative and back as the velocity of the rock changes its direction.
E) depends on the weight of the rock.

Question 16

A rock, tied at the end of a rope, is swirled in a vertical circle (the rock's speed changes during the motion). The work done on the rock by the tension in the rope

A) is positive.
B) is zero.
C) is negative.
D) changes from positive to negative and back as the velocity of the rock changes its direction.
E) depends on the weight of the rock.

Question 17

A force of variable magnitude acting on a toy car is represented in a F vs. x graph. The work done by this force on the toy car is

A) the value of F multiplied by the value of x at a certain instant.
B) the area bounded by the curve and the F axis.
C) the slope of the curve.
D) the area bounded by the curve and the x axis.
E) the value of F divided by the value of x at a certain instant.

Question 18

A force of variable magnitude acting on a crate is represented in a F vs. x graph. The work done by this force on the crate is represented by

A) the maximum value of F multiplied by the maximum value of x.
B) the area under the curve.
C) the slope of the curve.
D) the length of the curve.

Question 19

A crate follows a semicircular path of radius 1.0 m. The tangential component of the net force acting on a crate is 10 N, constant in magnitude. The net work done on the crate is

A) 0 J.
B) 3.1 J.
C) 20 J.
D) 31 J.
E) 63 J.

Question 20

In the International System of Units, the unit of energy in base units is

A) kilogram·meter.
B) kilogram·meter/second.
C) kilogram·meter/second².
D) kilogram·meter²/second.
E) kilogram·meter²/second².

Question 21

All of the following statements referring to the kinetic energy of a body are true except

A) its value depends on reference frame.
B) it is energy associated with the motion of the body.
C) it is energy associated with the position of the body.
D) it is positive or zero.
E) it increases if work is done on the body.

Question 22

Car A is three times lighter than car B. Car A moves three times faster than car B. The ratio of the kinetic energy of car A to the kinetic energy of car B is

A) 1/9.
B) 1/3.
C) 1.
D) 3.
E) 9.

Question 23

A projectile is launched at an angle of 30^o above the horizontal. Neglecting air resistance, the ratio of the kinetic energies at the top of the trajectory and the launching point is

A) 1.0.
B) 0.25.
C) 0.50.
D) 0.75.
E) 0.87.

Question 24

All of the following statements referring to the potential energy of a body are true except

A) its value depends on the reference frame.
B) it is energy associated with the motion of the body.
C) it is energy associated with the position of the body.
D) it is negative, positive, or zero.
E) it decreases if positive work is done by gravity on the body.

Question 25

A ball is dropped to the floor from a height h. It strikes the ground and briefly undergoes a change in shape before it bounces back. The height reached by the ball is

A) less than h.
B) h.
C) larger than h.
D) zero.

Question 26

Alex and Kaylee ascend a mountain on two different trails: Alex via a short, steep trail and Kaylee via a long, gentle trail. Which of the following statements is true?

A) To compare gravitational energies one should know the height of the mountain.
B) To compare gravitational energies one should know how the lengths of the two trails compare.
C) Alex gains more gravitational energy than Kaylee.
D) Alex gains the same gravitational energy as Kaylee.
E) Alex gains less gravitational energy than Kaylee.

Question 27

A girl runs up a flight of stairs at a constant speed v, and the gain in her potential gravitational energy is U. When she runs up the same stairs at half that speed, the gain in her potential gravitational energy is

A) 0.
B) U/4.
C) U/2.
D) U.
E) 2U.

Question 28

A spring is stretched 10.0 cm when a 0.200-kg mass is hanging at its end. If another 0.200-kg mass is added to the spring, the elastic potential energy of the spring will be

A) the same.
B) two times larger.
C) three times larger.
D) four times larger.

Question 29

The work-energy theorem is applied to the (frictionless) flight of a projectile (launched from ground level). The following statements are correct except

A) the work done by gravity on the projectile from launch point to highest rise is zero.
B) the direction of the velocity at the highest point is horizontal.
C) the final kinetic energy at impact is equal to the initial kinetic energy at launch.
D) the final speed at impact is equal to the initial speed at launch.

Question 30

An object is initially at rest on the ground. After a series of motions, it ends up at rest on a tower of height h. Which of the following statements is true?

A) Gravity was the only force acting on the body.
B) At least one other force besides gravity must have acted on the body during some steps so that its vertical component was larger than the force of gravity.
C) The magnitude of the net force acting on the body was zero every step of the way.
D) The work done by the net force acting on the body was zero even if the magnitude of the net force acting on the body was not zero every step of the way.
E) The work done by the net force acting on the body was zero, and the magnitude of the net force acting on the body was zero every step of the way.

Question 31

Work done on a body can result in changes in all of the following except

A) the magnitude of the body's velocity.
B) the direction of the body's velocity.
C) the elevation of the object.
D) the internal energy of the object.
E) all of the above are correct.

Question 32

It takes 100 m to stop a car initially moving at 25.0 m/s. The distance required to stop the same car moving at 50.0 m/s under the same conditions is

A) 25.0 m.
B) 50.0 m.
C) 100 m.
D) 200 m.
E) 400 m.

Question 33

The work done to increase the speed of a car from 0.0 m/s to 10.0 m/s is 50.0 kJ. To increase the speed of the same car in the same conditions from 10.0 m/s to 20.0 m/s, the work done will be

A) 50.0 kJ.
B) 100 kJ.
C) 150 kJ.
D) 250 kJ.

Question 34

In a television tube, an electron (mass 9.1 * 10^-31 kg) starting from rest experiences a force of 4.8 *10^-15 N over a distance of 45 cm. Ignoring relativistic effects, the final speed of the electron is

A) 4.7 *10¹⁵ m/s.
B) 2.3 * 10⁷ m/s.
C) 4.9* 10⁷ m/s.
D) 6.9 * 10⁷ m/s.
E) 4.7 * 10^-15 m/s.

Question 35

An 11.0-g bullet traveling at 700 m/s strikes a block of wood fixed in place, penetrates, and travels a distance of 6.0 cm in the block before it stops. The average force exerted by the wooden block on the bullet was

A) 6.4 * 10¹ N.
B) 6.4 * 10² N.
C) 4.5* 10⁴ N.
D) 4.5 * 10⁵ N.
E) 4.5 * 10⁶ N.

Question 36

At a water park, two slides with straight slopes, A and B, start and end at the same elevation. Slide A has a more gradual slope than B. Neglecting friction, your speed at the bottom of the slide is

A) larger for A than for B.
B) larger for B than for A.
C) the same for A and B.
D) unknown; more information is needed to work out the answer.

Question 37

Consider two crates of different masses, A and B, at the top of two frictionless inclined planes. The mass of crate A is larger than the mass of crate B. Both crates slide down the inclines from the same height where they are at rest. Crate A slides on the plane that makes an angle of 30^o with the horizontal, whereas crate B slides on the plane making an angle of 45^o with the horizontal. Which crate has a larger speed at the bottom of its plane?

A) Crate A
B) Crate B
C) Both crates have the same speed.
D) More information is needed to work out the answer.

Question 38

Two stones, A and B, are thrown from a balcony with the same initial speed: stone A horizontally, and stone B at 30^o above the horizontal. Just before their impact with the ground, in the absence of air resistance

A) the velocity of A is larger than the velocity of B.
B) the velocity of A is the same as the velocity of B.
C) the velocity of A is smaller than the velocity of B.
D) both velocities are zero.

Question 39

A 1.0-kg ball is moving at 2.0 m/s, while a 4.0-kg mass is moving at 1.0 m/s. Both are brought to rest by the same constant braking force. The ball that travels the greater distance before stopping is

A) the 1.0-kg ball.
B) the 4.0-kg ball.
C) Both the 1.0-kg and the 4.0-kg ball travel the same distance.
D) More information is needed to work out the answer.

Question 40

If the mechanical energy of a body is conserved,

A) no net work is done on the body.
B) no net work is done by the body.
C) a change in its gravitational potential energy is accompanied by the same change in its kinetic energy.
D) a change in its gravitational potential energy is accompanied by a change in its kinetic energy, equal and opposite in sign.

Question 41

The total mechanical energy of a system

A) is either positive or zero.
B) is mainly due to kinetic energy.
C) is mainly due to potential energy.
D) is equally divided between kinetic energy and potential energy.
E) is divided between kinetic energy and potential energy.

Question 42

A girl runs up a flight of stairs at a constant speed v, and the gain in her potential gravitational energy is U. When she runs up the same stairs at half that speed, her mechanical energy is

A) zero.
B) smaller.
C) the same.
D) larger.

Question 43

A box of mass m and a box of mass 4m are sliding with equal speeds along a level frictionless surface. Then they both slide up the same frictionless hill. Which rises to a greater height?

A) The box of mass m because it is lighter and its inertia is smaller.
B) The box of mass m because it has less kinetic energy and therefore more potential energy.
C) Both boxes slide to the same height.
D) The box of mass 4m because it is heavier.
E) The box of mass 4m because it has a larger kinetic energy and therefore more potential energy.

Question 44

A ball of mass 1.0 kg is tied to a string and allowed to revolve in a vertical circle of radius 1.5 m. If the ball's speed at the top of the trajectory is 2.3 m/s, its speed at the bottom of the trajectory is

A) 0 m/s.
B) 2.3 m/s.
C) 5.9 m/s.
D) 7.7 m/s.
E) 8.0 m/s.

Question 45

A 10-kg toy car moving at 5.0 m/s hits an initially uncompressed horizontal spring with a spring constant of 2.5*10² N/m. Neglecting the mass of the spring, the maximum compression of the spring is

A) 0 m.
B) 0.20 m.
C) 1.0 m.
D) 2.0 m.
E) 50 m.

Question 46

What speed should a roller coaster have at a point 30 m above the bottom of a dip if it is to barely reach the top of the next slope, which is 40 m above the bottom of the dip? Neglect friction.

A) 0 m/s
B) 14 m/s
C) 28 m/s
D) 98 m/s
E) 2.0* 10² m/s

Question 47

As a 1.0-kg ball falls to the ground, its potential and kinetic energies are the same when the ball is 3.0 m above the ground. How fast is the ball moving just before the impact with the ground?

A) 0 m/s
B) 7.7 m/s
C) 11 m/s
D) 59 m/s
E) 1.2 * 10² m/s

Question 48

A flowerpot of mass m, initially at rest, falls a distance h to the ground below. In the absence of air resistance, the graph that best represents the flowerpot's potential gravitational energy as a function of the distance fallen is

A) a straight line with a negative slope.
B) a straight line with a positive slope.
C) a vertical line.
D) a horizontal line.
E) a parabola.

Question 49

A flowerpot of mass m, initially at rest, falls a distance h to the ground below. In the absence of air resistance, the graph that best represents the flowerpot's mechanical energy as a function of the distance fallen is

A) a straight line with a negative slope.
B) a straight line with a positive slope.
C) a vertical line.
D) a horizontal line.
E) a parabola.

Question 50

A ball of mass 0.50 kg is pushed against a horizontal spring of negligible mass and force constant of 450 N/m until the spring is compressed a distance of 0.40 m. When the spring is released, the ball travels along a frictionless, horizontal surface to point B, at the bottom of a vertical circular track of radius R = 1.00 m, and continues to move up the track, where the ball experiences an average friction force of 7.00 N. The speed of the ball at the top of the track

A) is 0 m/s.
B) is 4.1 m/s.
C) is 7.0 m/s.
D) is 12 m/s.
E) cannot be determined because the ball does not reach the top of the track.

Question 51

You need to move a heavy crate by sliding it across a smooth floor-either by pushing it horizontally or by pulling it with a rope that makes a 30^o angle with the floor. If the coefficient of kinetic friction is 0.25, which way should you move the crate so that you do the least amount of work?

A) Pushing it horizontally.
B) Pulling it with a rope that makes a 30^o angle with the floor.
C) Either way the work done will be the same.
D) More information is needed to work out the answer.