Physics Chapter 6 - Work and Energy

1) What is the correct unit of work expressed in SI units? A) kg m/s2 B) kg m2/s C) kg m2/s2 D) kg2 m/s2

C) kg m2/s2

A 20-kg cart is pushed up the inclined plane shown by a force F to a height of 3 m. What is the potential energy of the cart when it reaches the top of the inclined plane? use g = 10 m/s2 (A) 1500 J (B) 630 J (C) 600 J (D) 300 J (E) 150 J

(C) 600 J The potential energy is equal to the work done against gravity: Work = mgh (20 X 10 X 3)

A car traveling at a velocity v can stop in a minimum distance d. What would be the car's minimum stopping distance if it were traveling at a velocity of 2v? * (a) d. (b) square root of 2d (c) 2d. (d) 4d. (e) 8d.

(d) 4d.

A ball is thrown straight up. At what point does the ball have the most energy? Ignore air resistance. * (a) At the highest point of its path. (b) When it is first thrown. (c) Just before it hits the ground. (d) When the ball is halfway to the highest point of its path. (e) Everywhere; the energy of the ball is the same at all of these points.

(e) Everywhere; the energy of the ball is the same at all of these points.

A skier starts from rest at the top of each of the hills shown in Fig. 6-34. On which hill will the skier have the highest speed at the bottom if we ignore friction: (a), (b), (c), (d), or (e) c and d equally? * (a) (b) (c) (d) (e) c and d (See pic in answer card)

(e) c and d The tallest hills, no matter how steep

Which of the following energy forms is associated with an object due to its position? a. potential c. total b. positional d. kinetic

a. potential

A force does work on an object if a component of the force a. is perpendicular to the displacement of the object. b. is parallel to the displacement of the object. c. perpendicular to the displacement of the object moves the object along a path that returns the object to its starting position. d. parallel to the displacement of the object moves the object along a path that returns the object to its starting position.

b. is parallel to the displacement of the object.

What is the kinetic energy of a 0.135 kg baseball thrown at 40.0 m/s? a.54.0 J b.87.0 J c.108 J d.216 J

c.108 J

Drew lifts a 60-kg crate onto a truck bed 1 meter high in 3 seconds. Connor lifts sixty 1-kg boxes onto the same truck in a time of 2 minutes. Which of the following statements is true? (A) Drew does more work than Connor does. (B) Connor does more work than Drew does. (C) They do the same amount of work, but Drew operates at a higher power level. (D) They do the same amount of work, but Connor operates at a higher power level. (E) Drew and Connor do the same amount of work and operate at the same power level

(C) They do the same amount of work, but Drew operates at a higher power level.

Which of the following is NOT true of work? (A) It is the scalar product of force and displacement. (B) It is measured in joules. (C) It has the same units as energy. (D) It is a vector which is always in the same direction as the displacement. (E) It takes energy to perform work

(D) It is a vector which is always in the same direction as the displacement. Work is not a vector!

A 4-kg box is pushed across a level floor with a force of 60 N for a displacement of 20 m, then lifted to a height of 2 m. What is the total work done on the box? (A) 200 J (B) 400 J (C) 1120 J (D) 1200 J (E) 1280 J

(E) 1280 J Work total =

You push a heavy crate down a ramp at a constant velocity. Only four forces act on the crate. Which force does the greatest magnitude of work on the crate? * 1 point (a) The force of friction. (b) The force of gravity. (c) The normal force. (d) The force of you pushing. (e) The net force.

(a) The force of friction. The speed of the crate is constant, so the net (total) work done on the crate is zero. The normal force is perpendicular to the direction of motion, so it does no work. Your applied force and a component of gravity are in the direction of motion, so both do positive work. The force of friction opposes the direction of motion and does negative work. For the total work to be zero, the work done by friction must equal the sum of the work done by gravity and by you.

Two balls are thrown off a building with the same speed, one straight up and one at a 45° angle. Which statement is true if air resistance can be ignored? * (a) Both hit the ground at the same time. (b) Both hit the ground with the same speed. (c) The one thrown at an angle hits the ground with a lower speed. (d) The one thrown at an angle hits the ground with a higher speed. (e) Both (a) and (b).

(b) Both hit the ground with the same speed

You push very hard on a heavy desk, trying to move it. You do work on the desk: * (a) whether or not it moves, as long as you are exerting a force. (b) only if it starts moving. (c) only if it doesn't move. (d) never—it does work on you. (e) None of the above.

(b) only if it starts moving

Answer Question 10 assuming a small amount of friction. * 1 point (a) (b) (c) (d) (e) c and d

(c) The tallest hill with the steepest slope

When the speed of your car is doubled, by what factor does its kinetic energy increase? * (a) square root of 2 . (b) 2. (c) 4. (d) 8.

(c) 4.

A man pushes a block up an incline at a constant speed. As the block moves up the incline, * (a) its kinetic energy and potential energy both increase. (b) its kinetic energy increases and its potential energy remains the same. (c) its potential energy increases and its kinetic energy remains the same. (d) its potential energy increases and its kinetic energy decreases by the same amount.

(c) its potential energy increases and its kinetic energy remains the same. The kinetic energy depends on the speed and not the position of the block. Since the block moves with constant speed, the kinetic energy remains constant. As the block moves up the incline its elevation increases, so its potential energy also increases.

Is it possible for the kinetic energy of an object to be negative? A. Yes B. No

B. No The kinetic energy is 1/2 mv2. The mass and the velocity squared will always be positive, so KE must always be positive.

A satellite in circular orbit around the Earth moves at constant speed. This orbit is maintained by the force of gravity between the Earth and the satellite, yet no work is done on the satellite. A. No work is done because there is no gravity in space. B. No work is done if objects move in a circle. C. No work is done if the direction of motion is perpendicular to the force. D. No work is done if there is no contact between objects.

C. No work is done if the direction of motion is perpendicular to the force.

2) Can work be done on a system if there is no motion? A) Yes, if an outside force is provided. B) Yes, since motion is only relative. C) No, since a system which is not moving has no energy. D) No, because of the way work is defined.

D) No, because of the way work is defined.

3) If you push twice as hard against a stationary brick wall, the amount of work you do A) doubles. B) is cut in half. C) remains constant but non-zero. D) remains constant at zero.

D) remains constant at zero.

A ball falls from a height h from a tower. Which of the following statements is true? (A) The potential energy of the ball is conserved as it falls. (B) The kinetic energy of the ball is conserved as it falls. (C) The difference between the potential energy and kinetic energy is a constant as the ball falls. (D) The sum of the kinetic and potential energies of the ball is a constant. (E) The velocity of the ball is constant as the ball falls.

D. The sum of the kinetic and potential energies of the ball is a constant. As the ball falls, the potential energy decreases and the kinetic energy increases, but the sum of the two remains constant.

You see a leaf falling to the ground with constant speed. When you first notice it, the leaf has initial total energy PEi + KEi. You watch the leaf until just before it hits the ground, at which point it has final total energy PEf + KEf. How do these total energies compare? a) PEi + KEi > PEf + KEf b) PEi + KEi = PEf + KEf c) PEi + KEi < PEf + KEf d) impossible to tell from the information provided

a) PEi + KEi > PEf + KEf As the leaf falls, air resistance exerts a force on it opposite to its direction of motion. This force does negative work, which prevents the leaf from accelerating. This frictional force is a non-conservative force, so the leaf loses energy as it falls, and its final total energy is less than its initial total energy.

When you pay the electric company by the kilowatt-hour, what are you actually paying for? a) energy b) power c) current d) voltage e) none of the above

a) energy We have defined: Power = energy / time So we see that: Energy = power x time This means that the unit of power x time (watt-hour) is a unit of energy !!

Two paths lead to the top of a big hill. One is steep and direct, while the other is twice as long but less steep. How much more potential energy would you gain if you take the longer path? a) the same b) twice as much c) four times as much d) half as much e) you gain no PE in either case

a) the same Since your vertical position (height) changes by the same amount in each case, the gain in potential energy is the same.

A child moving at constant velocity carries a 2 N ice-cream cone 1 m across a level surface. What is the net work done on the ice-cream cone? a. 0 J c. 2 J b. 0.5 J d. 20 J

a. 0 J

A ball is thrown straight up. Neglecting air resistance, which statement is not true regarding the energy of the ball? * 1 point (a) The potential energy decreases while the ball is going up. (b) The kinetic energy decreases while the ball is going up. (c) The sum of the kinetic energy and potential energy is constant. (d) The potential energy decreases when the ball is coming down. (e) The kinetic energy increases when the ball is coming down.

a. The potential energy decreases while the ball is going up.

Can friction ever do positive work? a. Yes b. No

a. Yes Consider the case of a box on the back of a pickup truck. If the box moves along with the truck, then it is actually the force of friction that is making the box move.

Is it possible for the gravitational potential energy of an object to be negative? A. Yes B. No

a. Yes Gravitational PE is mgh, where height h is measured relative to some arbitrary reference level where PE = 0. For example, a book on a table has positive PE if the zero reference level is chosen to be the floor. However, if the ceiling is the zero level, then the book has negative PE on the table. It is only differences (or changes) in PE that have any physical meaning.

A child on a skateboard is moving at a speed of 2 m/s. After a force acts on the child, her speed is 3 m/s. What can you say about the work done by the external force on the child? a) positive work was done b) negative work was done c) zero work was done

a. positive work was done The kinetic energy of the child increased because her speed increased. This increase in KE was the result of positive work being done. Or, from the definition of work, since W = ΔKE = KEf - KEi and we know that KEf > KEi in this case, then the work W must be positive.

Work is done when a. the displacement is not zero. b. the displacement is zero. c. the force is zero. d. the force and displacement are perpendicular.

a. the displacement is not zero.

Energy transferred as heat always moves from an object a.at high temperature to an object at low temperature. b.at low temperature to an object at high temperature. c.at low kinetic energy to an object at high kinetic energy. d.of higher mass to an object of lower mass.

a.at high temperature to an object at low temperature.

Which of the following energy forms is associated with an object due to its position? a.potential b.positional c.total d.kinetic

a.potential

Work is done when a.the displacement is not zero. b.the displacement is zero. c.the force is zero. d.the force and displacement are perpendicular

a.the displacement is not zero.

A car starts from rest and accelerates to 30 mph. Later, it gets on a highway and accelerates to 60 mph. Which takes more energy, the 0→30 mph, or the 30→60 mph? a) 0 → 30 mph b) 30 → 60 mph c) both the same

b) 30 → 60 mph The change in KE (1/2 mv2 ) involves the velocity squared. So in the first case, we have: 1/2 m (302 - 02) = 1/2 m (900) In the second case, we have: 1/2 m (602 - 302) = 1/2 m (2700) Thus, the bigger energy change occurs in the second case.

A cart starting from rest rolls down a hill and at the bottom has a speed of 4 m/s. If the cart were given an initial push, so its initial speed at the top of the hill was 3 m/s, what would be its speed at the bottom? a) 4 m/s b) 5 m/s c) 6 m/s d) 7 m/s e) 25 m/s

b) 5 m/s When starting from rest, the cart's PE is changed into KE: ΔPE = ΔKE = 1/2 m(4)2 When starting from 3 m/s, the final KE is: KEf = KEi + ΔKE = 1/2 m(3)2 + 1/2 m(4)2 = 1/2 m(25) = 1/2 m(5)2

Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power? a) Mike produced more power b) Joe produced more power c) both produced the same amount of power

b) Joe produced more power Since power = work / time, we see that Mike produced 0.5 W and Joe produced 0.6 W of power. Thus, even though Mike did more work, he required twice the time to do the work, and therefore his power output was lower.

A mass attached to a vertical spring causes the spring to stretch and the mass to move downwards. What can you say about the spring's potential energy (PEs) and the gravitational potential energy (PEg) of the mass? a) both PEs and PEg decrease b) PEs increases and PEg decreases c) both PEs and PEg increase d) PEs decreases and PEg increases e) PEs increases and PEg is constant

b) PEs increases and PEg decreases he spring is stretched, so its elastic PE increases, since PEs = 1/2 kx2. The mass moves down to a lower position, so its gravitational PE decreases, since PEg = mgh.

In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by the catcher on the ball? a) catcher has done positive work b) catcher has done negative work c) catcher has done zero work

b) catcher has done negative work The force exerted by the catcher is opposite in direction to the displacement of the ball, so the work is negative. Or using the definition of work (W = F d cos θ ), since θ = 180o, then W < 0. Note that because the work done on the ball is negative, its speed decreases.

A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction? a) friction does no work at all b) friction does negative work c) friction does positive work

b) friction does negative work Friction acts in the opposite direction to the displacement, so the work is negative. Or using the definition of work: W = F d cos θ since θ = 180o, then W < 0.

Two blocks of mass m1 and m2 (m1 > m2) slide on a frictionless floor and have the same kinetic energy when they hit a long rough stretch (μ > 0), which slows them down to a stop. Which one goes farther? a) m1 b) m2 c) they will go the same distance

b) m2 With the same ΔKE, both blocks must have the same work done to them by friction. The friction force is less for m2 so stopping distance must be greater.

A hill is 100 m long and makes an angle of 12 degrees with the horizontal. As a 50 kg jogger runs up the hill, how much work does gravity do on the jogger? a. 50 000 J c. -10 000 J b. 10 000 J d. 0.0 J

b. 10 000 J

The magnitude of the component of the force that does the work is 43.0 N. How much work is done on a bookshelf being pulled 5.00 m at an angle of 37.0 from the horizontal? a. 172 J c. 129 J b. 215 J d. 792 J

b. 215 J

A car accelerates from rest to 30 km/h. Later, on a highway it accelerates from 30 km/h to 60 km/h. Which takes more energy, going from 0 to 30, or from 30 to 60? * (a) 0 to 30 km/h. (b) 30 to 60 km/h. (c) Both are the same.

b. 30 to 60 km/h.

Is it possible to do work on an object that remains at rest? a. Yes b. no

b. No Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done.

As an object is lowered into a deep hole in the ground, which of the following assumptions must be made in regard to the object's potential energy? a. The potential energy increases. b. The potential energy decreases. c. The potential energy remains constant. d. The potential energy increases and then decreases.

b. The potential energy decrease

The main difference between kinetic energy and potential energy is that a. kinetic energy involves position and potential energy involves motion. b. kinetic energy involves motion and potential energy involves position. c. although both energies involve motion, only kinetic involves position. d. although both energies involve position, only potential involves motion.

b. kinetic energy involves motion and potential energy involves position.

Engine #1 produces twice the power of engine #2. Can we conclude that engine #1 does twice as much work as engine #2? a) yes b) no

b. no No!! We cannot conclude anything about how much work each engine does. Given the power output, the work will depend upon how much time is used. For example, engine #1 may do the same amount of work as engine #2, but in half the time.

The more powerful the motor is, a. the longer the time interval for doing the work is. b. the shorter the time interval for doing the work is. c. the greater the ability to do the work is. d. the shorter the workload is.

b. the shorter the time interval for doing the work is

What is the average power supplied by a 60.0 kg secretary running up a flight of stairs rising vertically 4.0 m in 4.2 s? a.380 W b.560 W c.610 W d.670 W

b.560 W m= weight g=9.8 (gravity) h=height PE = m * g * h PE = 60 * 9.8 * 4 PE = 2352 J Power = E/t Power = PE/t Power = 2352/4.2 Power = 560 Watt

Which of the following energy forms is stored in any compressed or stretched object? a.nonmechanical energy c.gravitational potential energy b.elastic potential energy d.kinetic energy

b.elastic potential energy

A force does work on an object if a component of the force a.is perpendicular to the displacement of the object. b.is parallel to the displacement of the object. c.perpendicular to the displacement of the object moves the object along a path that returns the object to its starting position. d.parallel to the displacement of the object moves the object along a path that returns the object to its starting position.

b.is parallel to the displacement of the object.

The more powerful the motor is, a.the longer the time interval for doing the work is. b.the shorter the time interval for doing the work is. c.the greater the ability to do the work is. d.the shorter the workload is

b.the shorter the time interval for doing the work is.

How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? a) same amount of work b) twice the work c) 4 times the work d) 8 times the work

c) 4 times the work The elastic potential energy is 1/2 kx2. So in the second case, the elastic PE is 4 times greater than in the first case. Thus, the work required to stretch the spring is also 4 times greater.

Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work? a) Mike b) Joe c) both did the same work

c) both did the same work Both exerted the same force over the same displacement. Therefore, both did the same amount of work. Time does not matter for determining the work done.

Paul and Corinne start from rest at the same time on frictionless water slides with different shapes. At the bottom, whose velocity is greater? a) Paul b) Corinne c) both the same

c) both the same

You throw a ball straight up into the air. In addition to gravity, the ball feels a force due to air resistance. Compared to the time it takes the ball to go up, the time it takes to come back down is: a) smaller b) the same c) greater

c) greater Due to air friction, the ball is continuously losing mechanical energy. Therefore it has less KE (and consequently a lower speed) on the way down. This means it will take more time on the way down !!

In the previous question, just before hitting the ground, what is the final speed of the heavy stone compared to the light one? a) quarter as much b) half as much c) the same d) twice as much e) four times as much

c) the same

A construction worker pushes a wheelbarrow 5.0 m with a horizontal force of 50.0 N. How much work is done by the worker on the wheelbarrow? a. 10 J c. 250 J b. 1250 J d. 55 J

c. 250 J

A worker pushes a wheelbarrow with a horizontal force of 50.0 N over a level distance of 5.0 m. If a frictional force of 43 N acts on the wheelbarrow in a direction opposite to that of the worker, what net work is done on the wheelbarrow? a. 250 J c. 35 J b. 0.0 J d. 10.0 J

c. 35 J

A 1.00 X 10^3 kg sports car accelerates from rest to 25.0 m/s in 7.50 s. What is the average power output of the automobile engine? a. 20.8 kW c. 41.7 kW b. 30.3 kW d. 52.4 kW

c. 41.7 kW

A bowling ball is dropped from a height h onto the center of a trampoline, which launches the ball back up into the air. How high will the ball rise? * (a) Significantly less than h. (b) More than h. The exact amount depends on the mass of the ball and the springiness of the trampoline. (c) No more than h—probably a little less. (d) Cannot tell without knowing the characteristics of the trampoline.

c. No more than h-probably a little less.

Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. but different steepness. Which ball has the greater speed at the bottom of its ramp? a. The ball from steepest ramp b. The ball from the least steep ramp c. They will all have the same speed since the ramps are all the same height

c. They will all have the same speed since the ramps are all the same height

By what factor does the kinetic energy of a car change when its speed is tripled? a) no change at all b) factor of 3 c) factor of 6 d) factor of 9 e) factor of 12

d) factor of 9 Since the kinetic energy is 1/2 mv2, if the speed increases by a factor of 3, then the KE will increase by a factor of 9.

A box sliding on a frictionless flat surface runs into a fixed spring, which compresses a distance x to stop the box. If the initial speed of the box were doubled, how much would the spring compress in this case? a) half as much b) the same amount c) √ 2 times as much d) twice as much e) four times as much

d) twice as much

You lift a book with your hand in such a way that it moves up at constant speed. While it is moving, what is the total work done on the book? a) mg × Δr b) FHAND × Δr c) (FHAND + mg) × Δr d) zero e) none of the above

d) zero The total work is zero since the net force acting on the book is zero. The work done by the hand is positive, while the work done by gravity is negative. The sum of the two is zero. Note that the kinetic energy of the book does not change, either!

Engines, including car engines, are rated in horsepower. What is horsepower? * (a) The force needed to start the engine. (b) The force needed to keep the engine running at a steady rate. (c) The energy the engine needs to obtain from gasoline or some other source. (d) The rate at which the engine can do work. (e) The amount of work the engine can perform

d. The rate at which the engine can do work. P=w/t

Which of the following energy forms is associated with an object in motion? a. potential energy c. nonmechanical energy b. elastic potential energy d. kinetic energy

d. kinetic energy

Which of the following is the rate at which energy is transferred? a. potential energy c. mechanical energy b. kinetic energy d. power

d. power

Two stones, one twice the mass of the other, are dropped from a cliff. Just before hitting the ground, what is the kinetic energy of the heavy stone compared to the light one? a) quarter as much b) half as much c) the same d) twice as much e) four times as much

d. twice as much Consider the work done by gravity to make the stone fall distance d: ΔKE = Wnet = F d cosθ ΔKE = mg d Thus, the stone with the greater mass has the greater KE, which is twice as big for the heavy stone.

If both the mass and the velocity of a ball are tripled, the kinetic energy of the ball is increased by a factor of a.3. b.6. c.9 d.27

d.27 3X3X3

Which of the following energy forms is involved in winding a pocket watch? a.electrical energy b.nonmechanical energy c.gravitational potential energy d.elastic potential energy

d.elastic potential energy

Which of the following energy forms is associated with an object in motion? a.potential energy b.elastic potential energy c.nonmechanical energy d.kinetic energy

d.kinetic energy

Which contributes more to the cost of your electric bill each month, a 1500-Watt hair dryer or a 600-Watt microwave oven? a) hair dryer b) microwave oven c) both contribute equally d) depends upon what you cook in the oven e) depends upon how long each one is on

e) depends upon how long each one is on

You and your friend both solve a problem involving a skier going down a slope, starting from rest. The two of you have chosen different levels for y = 0 in this problem. Which of the following quantities will you and your friend agree on? A) skier's PE B) skier's change in PE C) skier's final KE a) only B b) only C c) A, B, and C d) only A and C e) only B and C

e) only B and C The gravitational PE depends upon the reference level, but the difference ΔPE does not! The work done by gravity must be the same in the two solutions, so ΔPE and ΔKE should be the same.