1. Module 5, Recitation 1 Concept Problems

2. Is it possible to do work on an object that remains at rest? 1) yes 2) no ConcepTest To Work or Not to Work

3. Is it possible to do work on an object that remains at rest? 1) yes 2) no force acts over a distance no displacementno work done 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. ConcepTest To Work or Not to Work

4. ConcepTest Friction and Work I 1) friction does no work at all 2) friction does negative work 3) friction does positive work A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?

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

6. Can friction ever do positive work? 1) yes 2) no ConcepTest Friction and Work II

7. Can friction ever do positive work? 1) yes 2) no moves along with the truck force of friction that is making the box move 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. ConcepTest Friction and Work II

8. ConcepTest Tension and Work 1) tension does no work at all 2) tension does negative work 3) tension does positive work A ball tied to a string is being whirled around at a constant speed in a circle. What can you say about the work done by tension?

9. ConcepTest 6.2d Tension and Work 1) tension does no work at all 2) tension does negative work 3) tension does positive work A ball tied to a string is being whirled around at a constant speed in a circle. What can you say about the work done by tension? v T perpendicular W = F d cos   = 90 o W = 0 No work is done because the force acts in a perpendicular direction to the displacement. Or using the definition of work: W = F d cos  since  = 90 o, then W = 0

10. ConcepTest Force and Work 1) one force 2) two forces 3) three forces 4) four forces 5) no forces are doing work A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?

11. ConcepTest Force and Work N f T mg displacement Any force not perpendicular to the motion will do work: no work N does no work positive T does positive work f does negative work mg does negative work 1) one force 2) two forces 3) three forces 4) four forces 5) no forces are doing work A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?

12. 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 ConcepTest Kinetic Energy I

13. 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 1/2 mv 2 speed increases by a factor of 3KE will increase by a factor of 9 Since the kinetic energy is 1/2 mv 2, if the speed increases by a factor of 3, then the KE will increase by a factor of 9. ConcepTest Kinetic Energy I

14. Car #1 has twice the mass of car #2, but they both have the same kinetic energy. How do their speeds compare? ConcepTest Kinetic Energy II 1) 2 v 1 = v 2 2)  2 v 1 = v 2 3) 4 v 1 = v 2 4) v 1 = v 2 5) 8 v 1 = v 2

15. Car #1 has twice the mass of car #2, but they both have the same kinetic energy. How do their speeds compare? 1/2 mv 2 If the ratio of m 1 /m 2 is 2, then the ratio of v 2 values must also be 2 ratio of v 2 /v 1 must be the square root of 2 Since the kinetic energy is 1/2 mv 2, and the mass of car #1 is greater, then car #2 must be moving faster. If the ratio of m 1 /m 2 is 2, then the ratio of v 2 values must also be 2. This means that the ratio of v 2 /v 1 must be the square root of 2. ConcepTest Kinetic Energy II 1) 2 v 1 = v 2 2)  2 v 1 = v 2 3) 4 v 1 = v 2 4) v 1 = v 2 5) 8 v 1 = v 2

16. ConcepTest Slowing Down 1) 20 m 2) 30 m 3) 40 m 4) 60 m 5) 80 m 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. 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.

17. F d = W net =  KE = 0 – 1/2 mv 2 |F| d = 1/2 mv 2 thus: |F| d = 1/2 mv 2 doubles Therefore, if the speed doubles, four times larger the stopping distance gets four times larger. ConcepTest Slowing Down 1) 20 m 2) 30 m 3) 40 m 4) 60 m 5) 80 m 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. 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.

18. ConcepTest Speeding Up I 1) 0  30 mph 2) 30  60 mph 3) both the same 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?

19. 1/2 mv 2 velocity squared The change in KE (1/2 mv 2 ) involves the velocity squared. 1/2 m (30 2 - 0 2 ) = 1/2 m (900) So in the first case, we have: 1/2 m (30 2 - 0 2 ) = 1/2 m (900) 1/2 m (60 2 - 30 2 ) = 1/2 m (2700) In the second case, we have: 1/2 m (60 2 - 30 2 ) = 1/2 m (2700) bigger energy changesecond case Thus, the bigger energy change occurs in the second case. ConcepTest Speeding Up I 1) 0  30 mph 2) 30  60 mph 3) both the same 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?

20. The work W 0 accelerates a car from 0 to 50 km/hr. How much work is needed to accelerate the car from 50 km/hr to 150 km/hr? ConcepTest Speeding Up II 1) 2 W 0 2) 3 W 0 3) 6 W 0 4) 8 W 0 5) 9 W 0

21. The work W 0 accelerates a car from 0 to 50 km/hr. How much work is needed to accelerate the car from 50 km/hr to 150 km/hr? 1) 2 W 0 2) 3 W 0 3) 6 W 0 4) 8 W 0 5) 9 W 0 Let’s call the two speeds v and 3v, for simplicity. We know that the work is given by: W =  KE = KE f – KE i v 2 0 2 v 2 Case #1: W 0 = ½ m(v 2 – 0 2 ) = ½ m(v 2 ) 3vv 2 9v 2 v 2 8v 2 Case #2: W = ½ m((3v) 2 – v 2 ) = ½ m(9v 2 – v 2 ) = ½ m(8v 2 ) = 8W 0 ConcepTest Speeding Up II

22. 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 ConcepTest Work and Energy II

23. 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 4 times the distance4 times the workinitial KE must be 4 times greater increase in the initial speed by a factor of 2KE = 1/2 mv 2 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, since KE = 1/2 mv 2. ConcepTest Work and Energy II Follow-up: What speed do you need to hit the ball at from where it is at to get it into the hole?

24. Numerically finding areas of graphs What area are we interested in?

25. Numerically finding areas of graphs Area = ½bh 1 (Triangle) h1h1 Area = ½b(h 1 +h 2 ) (Trapezoid) h2h2 Area = ½b(h 2 +h 3 ) (Trapezoid) h3h3 h4h4 Area = ½b(h 3 +h 4 ) (Trapezoid)

26. Trapezoid Rule A 1 =½b(h 0 +h 1 ) h1h1 A 2 =½b(h 1 +h 2 ) h2h2 A 3 =½b(h 2 +h 3 ) h3h3 h4h4 A 4 =½b(h 3 +h 4 ) Area = b(0.5h 0 +h 1 +h 2 +h 3 +0.5h 4 )