Review. Kinetic Energy Work Hooke s s Law Potential Energy Conservation of Energy Power 1/91

Review Kinetic Energy Work Hooke s s Law Potential Energy Conservation of Energy Power 1/91

The unit of work is the A. Newton B. Watt C. Joule D. Meter E. Second 2/91

The unit of work is the A. Newton B. Watt C. Joule D. Meter E. Second 3/91

If you push an object with 3 times the force and 3 times the distance, you do A. The same amount of work B. 3 times the work C. 6 times the work D. 9 times the work E. 27 times the work 4/91

If you push an object with 3 times the force and 3 times the distance, you do A. The same amount of work B. 3 times the work C. 6 times the work D. 9 times the work E. 27 times the work W = Fx cosθ 5/91

Kinetic Energy = A. B. C. D. E. mv ma 2 m v 1 mv 2 2 mc 2 6/91

Kinetic Energy = A. B. C. D. E. mv ma 2 m v 1 mv 2 2 mc 2 7/91

An object that has kinetic energy must be A. at rest B. falling C. moving D. accelerating E. elevated 8/91

An object that has kinetic energy must be A. at rest B. falling C. moving D. accelerating E. elevated 9/91

Which has greater kinetic energy, a car moving at 30km/h or a half-as as- massive car moving at 60 km/h? A. The 30km/h car B. The 60km/h car C. They both have the same kinetic energy 10/91

Which has greater kinetic energy, a car moving at 30km/h or a half-as as- massive car moving at 60 km/h? A. The 30km/h car B. The 60km/h car C. They both have the same kinetic energy K K K 1 2 2 = = = 1 2 1 2 2 m v ( ) 1 2 m v 2 1 m 2 2 1 1 1 2 1 ( ) ( 1 2v = m )( 4) 1 1 2 1 2 v 2 1 11/91

In which of the diagrams below is non-zero work being done? A B C Force Displacement A. A B. B C. C D. A and B E. A and C F. A, B, and C 12/91

In which of the diagrams below is non-zero work being done? A B C Force Displacement A. A B. B C. C D. A and B E. A and C F. A, B, and C 13/91

Is it possible to do work if there is no motion? A. Yes, as long as a force is present. B. Yes, since motion is relative. C. No, because an object that is not moving has no energy. D. No, because of how work is defined. 14/91

In which case is work being done by gravity? A. A meteor heading towards earth B. A spaceship lifting off the earth C. A satellite in orbit around the earth D. A and B E. All of the above F. None of the above 16/91

If there is only one non-zero force acting on an object then which is possible for the Kinetic Energy? I. Increase II. Decrease III. Stay constant A. I B. I and II C. II and III D. I and III E. I, II, and III 18/91

In both cases a 5N force is applied to a moving object. In which case is more work being done by this force? A B Force Displacement A. A B. B C. Same for both cases 20/91

In both cases a 5N force is applied to a moving object. In which case is more work being done by this force? A B Force Displacement A. A B. B C. Same for both cases W = Fd cosθ 21/91

A spring, attached to a wall, has an unstretched length of 1m and a spring constant of 10N/m. The spring is pulled with a force of 10N. The length of the spring is now A. 1.1 m B. 2.0 m C. 10.0 m D. 11.0 m 22/91

Hooke s s Law applies to A. Springs B. Most solid materials C. Most solid materials but only up to the elastic limit of the material 24/91

Hooke s s Law applies to A. Springs B. Most solid materials C. Most solid materials but only up to the elastic limit of the material 25/91

How much work is done by the force when the object moves from 0.0m to 5.0m? A. 15.0J B. 12.5J C. 10.5J D. 4.5J Force (N) 3.5 3 2.5 2 1.5 1 0.5 0 0 1 2 3 4 5 6 Position (m) 26/91

How much work is done by the force when the object moves from 0.0m to 5.0m? A. 15.0J B. 12.5J C. 10.5J D. 4.5J Force (N) 3.5 3 2.5 2 1.5 1 0.5 0 6 4.5 0 1 2 3 4 5 6 Position (m) 27/91

Power is A. Work / distance B. Work / time C. Work X distance D. Work X time 28/91

Power is A. Work / distance B. Work / time C. Work X distance D. Work X time 29/91

Which of the paths below requires more work? A B A. A B. B C. Both the same 30/91

Which of the paths below requires more work? A B A. A B. B C. Both the same 31/91

The net work is the sum of the work from all forces. If the net work done on an object is positive then the KE must A. Increase B. Decrease C. Stay constant D. Not enough information to tell 32/91

The net work is the sum of the work from all forces. If the net work done on an object is positive then the KE must A. Increase B. Decrease C. Stay constant D. Not enough information to tell 33/91

As a planet orbits the sun, when is its kinetic energy the largest? A. Near the sun B. Far from the sun C. Its kinetic energy does not change 34/91

As a planet orbits the sun, when is its kinetic energy the largest? A. Near the sun B. Far from the sun C. Its kinetic energy does not change 35/91

The unit for power is the A. Joule B. Watt C. Newton Kg D. Kg E. S 36/91

The unit for power is the A. Joule B. Watt C. Newton Kg D. Kg E. S 37/91

The gravitational potential energy of an object depends on I. Mass II. Height III. Speed A. I B. II C. III D. I and II E. I and III F. All of the above 38/91

The gravitational potential energy of an object depends on I. Mass II. Height III. Speed A. I B. II C. III D. I and II E. I and III F. All of the above 39/91

Potential energy can be negative A. True B. False 40/91

Potential energy can be negative A. True B. False You can always add an arbitrary constant to any PE for convenience. For gravitational PE, you can always choose the height at which the gravitational PE=0. 41/91

What is the gravitational potential energy of the block? m=2 kg h=1 m A. 2 J B. 20 J C. 4 J D. You need more information before you can tell 42/91

What is the gravitational potential energy of the block? m=2 kg h=1 m A. 2 J B. 20 J C. 4 J The zero for potential energy is arbitrary. D. You need more information before you can tell 43/91

If you double the spring constant then the work necessary to compress the spring by the same amount will A. Stay constant B. Double C. Quadruple 44/91

If you double the spring constant then the work necessary to compress the spring by the same amount will A. Stay constant B. Double C. Quadruple U = 1 kx 2 2 45/91

An object is dragged at a speed of 10m/s along a rough surface with a force of 5N for 4m. How A. 10W B. 20W C. 50W D. 100W much power is exerted? 46/91

An object is dragged at a speed of 10m/s along a rough surface with a force of 5N for 4m. How A. 10W B. 20W C. 50W D. 100W much power is exerted? P= Fv 47/91

Assuming the gravitational potential energy of a pendulum is zero at the bottom, when is its PE = KE? A. At the top of the swing B. At the point half way up C. At the bottom of the swing D. In the lower half of the swing E. In the upper half of the swing 48/91

You shoot a rocket across the football field. At the highest point the energy is A. Purely KE B. Purely PE C. A combination of PE and KE D. Zero 50/91

You shoot a rocket across the football field. At the highest point the energy is A. Purely KE B. Purely PE C. A combination of PE and KE D. Zero 51/91

ConcepTest 6.2b Friction and Work II Can friction ever do positive work? 1) yes 2) no 52/91

ConcepTest 6.2b Friction and Work II Can friction ever do positive work? 1) yes 2) no Static Friction Can! 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. 53/91

ConcepTest 6.2c Play Ball! 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? 1) catcher has done positive work 2) catcher has done negative work 3) catcher has done zero work 54/91

ConcepTest 6.2c Play Ball! In a baseball game, the catcher stops a 90-mph pitch. What can you say about the work done by 1) catcher has done positive work 2) catcher has done negative work 3) catcher has done zero work the catcher on the ball? 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 cosθ), since θ = 180 o, then W < 0. Note that because the work done on the ball is negative, its speed decreases. Follow-up: What about the work done by the ball on the catcher? 55/91

ConcepTest 6.2d Tension and Work A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension? 1) tension does no work at all 2) tension does negative work 3) tension does positive work No work is done because the force acts in a perpendicular direction to the displacement. Or using the definition of work: W = F d cosθ since θ = 90 o, then W = 0. T v Follow-up: Is there a force in the direction of the velocity? 57/91

ConcepTest 6.5a Kinetic Energy I By what factor does the kinetic energy of a car change when its speed is tripled? 1) no change at all 2) factor of 3 3) factor of 6 4) factor of 9 5) factor of 12 Since the kinetic energy is 1/2 mv 2, if the speed increases by a factor of 3, 3 then the KE will increase by a factor of 9. 9 Follow-up: How would you achieve a KE increase of a factor of 2? 59/91

ConcepTest 6.7 Work and KE 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? 1) positive work was done 2) negative work was done 3) zero 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 = KE = KE f KE i and we know that KE f > KE in i this case, then the work W must be positive. Follow-up: up: What does it mean for negative work to be done on the 61/91 child?

ConcepTest 6.8a Slowing Down If a car traveling 60 km/hr can brake to a stop within 20 m, what is its stopping distance if it is traveling 120 km/hr? Assume that the braking force is the same in both cases. 1) 20 m 2) 30 m 3) 40 m 4) 60 m 5) 80 m W friction = fd F d = W net = KE = 0 1/2 mv 2 thus: F d = 1/2 mv 2 Therefore, if the speed doubles, the stopping distance gets four times larger. 63/91

ConcepTest 6.8b Speeding Up I 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? 1) 0 30 mph 2) 30 60 mph 3) both the same The change in KE (1/2 mv 2 ) involves the velocity squared. So in the first case, we have: 1/2 m (30 2-0 2 ) = 1/2 m (900) In the second case, we have: 1/2 m (60 2-30 2 ) = 1/2 m (2700) Thus, the bigger energy change occurs in the second case. Follow-up: How much energy is required to stop the 60 How much energy is required to stop the 60-mph 65/91 car?

ConcepTest 6.9b Work and Energy II A golfer making a putt gives the ball an initial velocity of v 0, but he has badly misjudged the putt, and the ball only travels one-quarter of the distance to the hole. If the resistance force due to the grass is constant, what speed should he have given the ball (from its original position) in order to make it into the hole? 1) 2 v 0 2) 3 v 0 3) 4 v 0 4) 8 v 0 5) 16 v 0 In traveling 4 times the distance, the resistive force will do 4 times the work. Thus, the ball s initial KE must be 4 times greater in order to just reach the hole this requires an increase in the initial speed by a factor of 2, 2 since KE = 1/2 mv 2. 67/91

ConcepTest 6.2a Friction and Work I A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction? 1) friction does no work at all 2) friction does negative work 3) friction does positive work Friction acts in the opposite direction to the displacement, so the work is negative. Or using the f N displacement Pull definition of work: W = F d cosθ since θ = 180 o, then W < 0. mg 69/91

ConcepTest 6.6a Free Fall I 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? 1) quarter as much 2) half as much 3) the same 4) twice as much 5) four times as much Consider the work done by gravity to make the stone fall distance d: KE = W net = F d cosθ KE = mg d Thus, the stone with the greater mass has the greater KE, which is twice as big for the heavy stone. Follow-up: up: How do the initial values of gravitational PE compare? 71/91

ConcepTest 6.10 Sign of the Energy I Is it possible for the kinetic energy of an object to be negative? 1) yes 2) no 74/91

ConcepTest 6.10 Sign of the Energy I Is it possible for the kinetic energy of an object to be negative? 1) yes 2) no The kinetic energy is 1/2 mv 2. The mass and the velocity squared will always be positive, so KE must always be positive. 75/91

ConcepTest 6.12 KE and PE 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? 1) only B 2) only C 3) A, B, and C 4) only A and C 5) only B and C A) skier s s PE B) skier s s change in PE C) skier s s final KE The gravitational PE depends upon the reference level, but the difference PE does not! The work done by gravity must be the same in the two solutions, so PE and KE should be the same. 77/91 Follow-up: Does anything change physically by the choice of y = 0?

ConcepTest 6.13 Up the Hill 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? 1) the same 2) twice as much 3) four times as much 4) half as much 5) you gain no PE in either case Since your vertical position (height) changes by the same amount in each case, the gain in potential energy is the same. Follow-up: How much more work do you do in taking the steeper path? Follow-up: Which path would you rather take? Why? 79/91

ConcepTest 6.14 Elastic Potential Energy How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm? 1) same amount of work 2) twice the work 3) 4 times the work 4) 8 times the work The elastic potential energy is 1/2 kx 2. 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. 81/91

ConcepTest 6.15 Springs and Gravity 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 (PE s ) and the gravitational potential energy (PE g ) of the mass? 1) both PE s and PE g decrease 2) PE s increases and PE g decreases 3) both PE s and PE g increase 4) PE s decreases and PE g increases 5) PE s increases and PE g is constant 82/91

ConcepTest 6.16 Down the Hill Three balls of equal mass start from rest and roll down different ramps. All ramps have the same height. Which ball has the greater speed at the bottom of its ramp? 1 2 3 4) same speed for all balls All of the balls have the same initial gravitational PE, since they are all at the same height (PE = mgh). Thus, when they get to the bottom, they all have the same final KE, and hence the same speed (KE = 1/2 mv 2 ). Follow-up: Which ball takes longer to get down the ramp? 85/91

ConcepTest 6.17a Runaway Truck A truck, initially at rest, rolls down a frictionless hill and attains a speed of 20 m/s at the bottom. To achieve a speed of 40 m/s at the bottom, how many times higher must the hill be? 1) half the height 2) the same height 3) 2 times the height 4) twice the height 5) four times the height Use energy conservation: initial energy: E i = PE g = mgh final energy: E f = KE = 1/2 mv 2 Conservation of Energy: E i = mgh = E f = 1/2 mv 2 therefore: gh = 1/2 v 2 So if v doubles, H quadruples! 87/91

ConcepTest 6.21a Time for Work I 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? 1) Mike 2) Joe 3) 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. 89/91

ConcepTest 6.21b Time for Work II Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power? 1) Mike produced more power 2) Joe produced more power 3) both produced the same amount of 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. 91/91