The center of a 2.00 kg mass is released from rest at point A and slides a dista

Question

The center of a 2.00 kg mass is released from rest at point A and slides a distance of L = 14.0 m down a 60.0 degree frictionless slope to point B. It then slides on a short horizontal frictionless segment to point C. (See the figure.) The mass then slides up a 30.0 degree rough slope whose coefficient of kinetic friction is mu_k = 0.200, a distance of Delta = 4.00 m to point D. When it comes to rest it has compressed the spring by amount Delta x = 0.750 m. b) Calculate the work done by the fractional force and by the gravity force as the mass moves up 30.0 degree slope from point C to point D. c) Use the Work-Energy theorem to determine the work done by the spring. d) What is the value of the spring constant, k?

Explanation / Answer

a)

conserving energy between A and C

mg ( L sin 60 ) = 0.5 mV^2

Vc = 15.41 m/s

b)

work fone by gravity from C to D

Wg = - mg (4sin30)

Wg = -39.2 J

work done by friction

Wf = - umg( 4cos 30)

Wf = -13.579 J

c)

Wg+ Wf +Ws = change in kinetic energy

-39.2 J -13.579 J + Ws = 0- 0.5 mVc^2

Ws = -184.6891 J

d)

we know that

0.5 kx^2 = -Ws

x = 0.75 m

substituting we get

k = 656.67 N/m

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