Review for Exam 2 S 2019

Transcription

1 Review for Exam 2 S 2019

2 R1. Work W = F.d (in N m =Joules = J If we know the angle between vectors, q F.d = F d cos q F = (1, 2, 3) F =sqrt(1+4+9)=~4 d = (4, 5, 6) d =sqrt( )~9 q=10; W=F d cos(60) ~36* 0.9 ~ 32 q F x If we know just the components: F.d =1*4+2*5 +3*6 = 32. Also, we can find q=> cos(q)=32/36 => q=~10 If q=0, or F and d are in the same direction, W=Fx (3 possible questions)

3 R1. Horse pulls car A horse pulls a broken down car on the level with an energy of 14,000 J. The force of the horse s pull is 700 N. How far, in m, did she pull the car? a. Need to know friction b. 20 c. 0.5 d. 70 e. 200

4 R1. Horse pulls car A horse pulls a broken down car with an energy of 14,000 J. The force of the horse s pull is 700 N. How far, in m, did she pull the car? a. Need to know friction b. 20 c. 0.5 d. 70 e. 200

5 R2. Work and friction Wf=Ff d = µ N d Pushing a suitcase: N = weight + vertical component of force. Ef mg Wf=Ff d=µ N d = µ {m 1 +mj}g d (6 possible questions.) Work on part of box depends only on N for that part.

6 R2. Friction on 2 suitcases An airline steward is pushing 2 identical suitcases horizontally (one pushing the other) on rollers with a force of 280 N. The coefficient of friction is 0.3. What is the mass, in kg, of the 1 st suitcase? a. 47 b. 93 c. 280 d. 852 e. 0.02

7 R2. Friction on 2 suitcases An airline steward is pushing 2 identical suitcases (one pushing the other) on rollers with a force of 280 N. The coefficient of friction is 0.3. What is the mass, in kg, of the 1 st suitcase? a. 47 b. 93 c. 280 d. 852 e. 0.02

8 R3. Work at an angler W = F d cos(q) Pushing a suitcase: F Ef mg F d cos(q) W=F d cos(q) (4 possible questions.)

9 R3. Pulling a suitcase A woman pulls a suitcase with a handle up at 20 degrees along a level floor at a constant speed. She pulls the suitcase 6 m and does 85 J of work. What is her force, in N? a. 3.1 b. 14 c. 12 d. 15 e. 10

10 R3. Pulling a suitcase A woman pulls a suitcase with a handle up at 20 degrees along a level floor at a constant speed. She pulls the suitcase 6 m and does 85 J of work. What is her force, in N? a. 3.1 b. 14 c. 12 d. 15 e. 10

11 R4. Work and friction Work due to friction = Wf=Ff d = µ N d N = weight + vertical component of force.5 Ef mg F If q=0, Wf=µ N d = µ mg d (5 possible questions)

12 R4. Friction on a planet A block of mass 7.1 kg sits on a planet surface with a coefficient of friction of 0.2. A force of 14 N is just able to move the block parallel to the surface. What is the gravitational field on the planet? a. 9.8 b. 20 c. 5 d. 2 e. 1

13 R4. Friction on a planet A block of mass 7.1 kg sits on a planet surface with a coefficient of friction of 0.2. A force of 14 N is just able to move the block parallel to the surface. What is the gravitational field on the planet? a. 9.8 b. 20 c. 5 d. 2 e. 1

14 R5. Work and gravity W = F.d If we know the vector components F = (1, 2, 3) F =sqrt(1+4+9)=~4 d = (4, 5, 6) d =sqrt( )~9 F.d = = 32 => cos(q)=32/36 => q=~10 q F x If F=mg, it s vector is (0, 0, -mg). W= F. z (3 possible questions)

15 R5. Throwing a ball A baseball player throws a ball from a starting point to a point (20 i, 3 j, 15 k ), where i, j, and k are unit vectors with k upward. The work done by gravity is What is the mass of the ball? a. 2.0 b. 20 c. 1.5 d. 10 e. 0.8

16 R5. Throwing a ball A baseball player throws a ball from a starting point to a point (20 i, 3 j, 15 k ), where i, j, and k are unit vectors with k upward. The work done by gravity is What is the mass of the ball? a. 2.0 b. 20 c. 1.5 d. 10 e. 0.8

17 R6. Work and Kinetic energy: 2 ax = v^2-vo^2 Force is ma, 2 ma x= m v^2 m vo^2 Define work as F.x: 2 F.x = m v^2 m vo^2 F.x = ½ mv^2 ½ mvo^2 Move the 2: Work = increase in Kinetic energy Units are N m **If F = gravity = (0, 0, -mg), then increased KE depends only on vertical component of d.

18 R6. 3 fire persons Three workers in a fire house respond to an alarm by going down from the second floor to the first where the truck is parked. The 1 st slides down a pole, the 2 nd goes down the back stairs and then up to the truck and the third jumps to the top of the truck and then up the side and down to the floor. There is friction, but pretend there wasn t, and then in what order would their kinetic energies be (small to large) at the bottom? a. Need the distances b. Tied c. 1,2,3 d. 3,2,1 e. 2,3,1

19 R6. 3 fire persons Three workers in a fire house respond to an alarm by going down from the second floor to the first where the truck is parked. The 1 st slides down a pole, the 2 nd goes down the back stairs and then up to the truck and the third jumps to the top of the truck and then up the side and down to the floor. There is friction, but pretend there wasn t, and then in what order would their kinetic energies be (small to large) at the bottom? a. Need the distances b. Tied c. 1,2,3 d. 3,2,1 e. 2,3,1

20 R7. Spring Spring Constant: K = Force of spring times distance moved for rest. F = -K x F increases with x, so Energy in spring = ½ K x 2 (3 possible questions.)

21 R7. Spring constant A student places a mass of 4 kg on a (light weight) spring. Starting from rest, the spring lengthens by 0.14 m. What is the spring constant of the spring, in N/m? a. 290 b. 29 c. 800 d. 40 e. 35

22 R7. Spring constant A student places a mass of 4 kg on a (light weight) spring. Starting from rest, the spring lengthens by 0.14 m. What is the spring constant of the spring, in N/m? a. 290 b. 29 c. 800 d. 40 e. 35

23 R8.Spring energy and Kinetic energy: Spring Energy = ½ K x 2 = ½ mv^2 ½ mvo^2 Work = increase in Kinetic energy Units are N m **If F & x in same dir and x is distance from equilibrium, vo=0, ½ k x 2 = ½ mv 2

24 R8. Energy of a spring A spring with very small mass has a spring constant of 800 N/m. A student hangs a mass of 2 kg on the spring, and then another student gives the mass a push down and it moves for 0.14 m. What speed was the push (v 0 ), in m/s? a. 1.4 b. 2.0 c. 2.8 d. 3.6 e. 56

25 R8. Energy of a spring A spring with very small mass has a spring constant of 800 N/m. A student hangs a mass of 2 kg on the spring, and then another student gives the mass a push down and it moves for 0.14 m. What speed was the push (v 0 ), in m/s? a. 1.4 b. 2.0 c. 2.8 d. 3.6 e. 56

26 R9. Potential energy and Kinetic energy: mgh = ½ mv^2 ½ mvo^2 Work = increase in Kinetic energy Units are N m **If F = gravity = (0, 0, -mg), then increased KE depends only on vertical component of d.

27 R9. sliding skiers Two skiers start together and ski down a hill. The first is 1.5 times heavier than the skinny one. There is essentially no friction. After going down for a height of 50 m, how many times the kinetic energy of the skinny skier the heavy one have? a b. 1.0 c. 2.0 d. 1.5 e. 0.75

28 R9. sliding skiers Two skiers start together and ski down a hill. The first is 1.5 times heavier than the skinny one. There is essentially no friction. After going down for a height of 50 m, how many times the kinetic energy of the skinny skier the heavy one have? a b. 1.0 c. 2.0 d. 1.5 e. 0.75

29 R10. Energies on ramp: At start: F g. d = mgh h d At end: K = ½ m v 2 + E f (Ef = W f =F f. d ) mgh =½ m v 2 For different hills, mgh 2 = ½ m v 2 2

30 R10. sliding car A car skids down a hill on ice (no friction) and hits the bottom at a speed v. The driver thinks he will be all right on a hill that is not as steep. But he slides down a hill 1/3 as steep and crashes at a speed N times v. What is N? a. 1.0 b. 3.0 c d. 1.7 e. 0.58

31 R10. sliding car A car skids down a hill on ice (no friction) and hits the bottom at a speed v. The driver thinks he will be all right on a hill that is not as steep. But he slides down a hill 1/3 as steep and crashes at a speed N times v. What is N? a. 1.0 b. 3.0 c d. 1.7 e. 0.58

32 More complex problems

33 R10. Power and Energies on ramp: At start: F g. d = mgh h P=energy/t d At end: K = ½ m v 2 + E f (Ef = W f =F f. d ) mgh =½ m v 2 (3 different questions.) For different hills, different v at bottom

34 R11 Biking up a hill A woman of mass 56 kg bikes up a hill that is 12 m long and at an angle of 25 degrees. The minimum average power that she could expend is 925 W. How long, in s, does it take? a. 30 b. 60 c. 45 d. 20 e. 3

35 R11 Biking up a hill A woman of mass 56 kg bikes up a hill that is 12 m long and at an angle of 25 degrees. The minimum average power that she could expend is 925 W. How long, in s, does it take? a. 30 b. 60 c. 45 d. 20 e. 3

36 R6. Work and Kinetic energy: 2 ax = v^2-vo^2 Force is ma, 2 ma x= m v^2 m vo^2 Define work as F.x: 2 F.x = m v^2 m vo^2 Move the 2: m (gravitation force mass)gh = ½ m (inertial mass) v^2 ½ m (i.m.) vo^2 Work = increase in Kinetic energy Units are N m **If F = gravity = (0, 0, -mg), then increased KE depends only on vertical component of d. **Inertial mass is all the mass that s moving.

37 R12. Work and inertial mass Two masses m1 = 3 kg over the side and M2 = 7 kg on top are attached by a string as shown. They start from rest with no friction. m1 falls down for 6 m. What s the speed when it hits? a. 3.3 b. 2 c. 6 d. 10 e. 20 M2 g Table m1 g

38 R12. Work and inertial mass Two masses m1 = 3 kg over the side and M2 = 7 kg on top are attached by a string as shown. They start from rest with no friction. m1 falls down for 6 m. What s the speed when it hits? a. 3.3 b. 2 c. 6 d. 10 e. 20 M2 g Table m1 g

39 R6. Two types of work and Kinetic energy: m(g.m.) gh - Ef = ½ m (i.m.) v^2 ½ m (i.m.) vo^2 Work = increase in Kinetic energy Units are N m **If F = gravity = (0, 0, -mg), then increased KE depends only on vertical component of d. **Inertial mass is all the mass that s moving.

40 R12. Friction and inertial mass on another planet Two masses, m1=8 kg and m2 are connected by a cable so that m1 is a height h from the bottom of a cliff. m2 is on a flat plateau above the cliff with a coefficient of friction is 0.5. The friction just allows m1 to keep from falling. What is the mass m2 in kg. a. 4 b. 8 c. 16 d. Can t tell without h e. Can t tell without g

41 R13 Two skiers A fat skier is on a slope of 8 degrees and just about to slide. A thin skier with half the mass tries out different slopes with the same friction. What will happen? a. The thin skier will slide at 8 degrees. b. The thin skier will slide at 7 degrees c. The thin skier will slide at 10 degrees d. Need to know the friction coefficient e. Need to know the masses

42 R14. raising a bucket A person does 250 J of work raising a bucket from the bottom of a well to the surface of the water through a distance of 10 m. The work done by friction was -80 J. What was the mass of the bucket in kg? a. 170 b. 1.0 c. 2.5 d. 37 e. 1.7

43 R15. Work and friction Wf=Ff d = µ N d Pushing a suitcase: N = weight + vertical component of force. Ef mg F sin(q) Wf=Ff d=µ N d = µ {mg + Fsin(q)} d (6 possible questions.) Work on part depends only on N for that part.

44 R15 Pushing a box A force of 140 N at a downward angle of 40 degrees pushes a 26 kg box for 8 m with a frictional energy of -800 J. How fast does it go at the end? a. 2.1 b c. 22 d. 37 e. 1.2

45 R16. Weighing with a spring A spring is calibrated by hanging a mass = 10 kg and measuring the distance to which it moves, say 3 cm. If an unknown weight, Mg, is hung from the spring, what is the work, in J, that M does in extending the spring 17 cm? a b. 700 c d. 48 e. 4770