Suggested E.7 In the figure, a block of mass m = 3 kg slides head on into a spri

Question

Suggested E.7 In the figure, a block of mass m = 3 kg slides head on into a spring of spring constant k = 320 N/m, when the block stops, it has compressed the spring by 4.5 cm. A kinetic frictional force with a magnitude of 4.4 N acts on the block as it slides. a. While the block slides, does mechanical energy increase, decrease, or remain the same? While the block is in contact with the spring and being brought to rest, what is the change in elastic potential energy of the block-spring system? 0.324 J b. While the block is in contact with the spring and being brought to rest, what is the work done by friction. -0.198J c. d. What is the block's kinetic energy just as it reaches the spring? 0.522 J 0

Explanation / Answer

a] While the block slides, the mechanical energy decreases due to the friction present between the spring and the horizontal surface.

b] Change in elastic potential energy =

U = (1/2)kx2 = (1/2)(320)(0.045)2 = 0.324 J

c] Work Done by friction =

W = FScos(180) = - FS = - 4.4 x 0.045 = - 0.198 J

d] By conservation of energy, the kinetic energy just as the block reaches the spring will be:

K.E = 0.324 - (- 0.198) = 0.522 J.

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