HW 11: Ch. 10, Problems 7-23 .

7. The speed, v , of the cart when it has reached the top of the hill with a height h1 is:

The person weighs 500 N and puts 1500 J of PE into the trampoline in one bounce. Lowest height is , h = h0 = 0, max. height, h = h2.

8. Gravity, FG = mg, downward, always acts on the person. The trampoline acts upward on the person and has a magnitude greater than mg at the bottom where the person's speed is increased from zero.

9. Net force direction at the high point is down, and at the low point is up, on the person.

10. Trampoline energy is transferred to the person. The person gets to a height h2 = 3 m .

11. Trampoline spring constant is 100 N/cm (104 N/m). The person's lowest distance below the surface of the trampoline is the value of h1 = 0.55 m

12. What is the speed, v , of the person when leaving the surface of the trampoline?

13. What is the highest point the person gets above the surface of the trampoline?

 
 
 A human with mass m , shoes attached to a board, starts with a speed, v0 = 0, and falls from a height, h , to the ground. When reaching the ground (just before hitting the ground) the human has zero gravitational potential energy.  Answer the following questions using only m, h and g, in the answers and ignore air friction.

14. The human, at the initial height, has potential energy =

15. Compared to the answer to problem 14, what is the kinetic energy of the human when reaching the ground?
16. What is the speed, v , of the human when reaching the ground?
When air friction cannot be ignored the magnitude of the frictional force, F , acting on the human grows with speed and becomes equal to, and remains at, the magnitude of the gravitational force at a critical speed vC

17. The two forces acting on the human when the speed reaches vC:

18. The net force, FNet , on the human being when the speed reaches vC is zero (speed has a constant value of vC)

After reaching vC, the human falls an additional distance x.

19. The change in potential energy, DPEG (final - initial), of the human over the distance, x is

20. The change in the kinetic energy DKE of the human over this distance,
21. What is the sum of the kinetic and potential energy changes over this distance
22. The work (non – conservative) done by the frictional force over this distance
23. If all of the frictional force is applied to the bottom of the human’s feet this person feels exactly the same as compared to standing on the ground. Force of gravity is balanced by an opposing force in each case (the compression force of the ground or the air friction)

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