A wooden block with a mass of 1.35 kg is placed against a compressed spring at t

Question

A wooden block with a mass of 1.35 kg is placed against a compressed spring at the bottom of a slope inclined at an angle of 29.00 with the horizontal (refer to this as location A). When the spring is released, it projects the block up the incline. At location B, a distance of 7.10 m up the incline from A, the block is observed to be moving up the incline at a measured speed of 6.60 m/s and is no longer in contact with the spring. The coefficient of kinetic friction between the block and incline is 0.55. The mass of the spring is negligible.

A. What is the change in gravitational potential energy for the system of the block and the Earth as the block moves from point Ato point B?

B. How much thermal energy will have been produced in the block and the slope as the block moves from point A to point B?

C. Calculate the amount of potential energy that was initially stored in the spring. Assume that the spring potential energy is zero when the spring is relaxed.

Explanation / Answer

A. change in G.P.E. = mgh = 1.35 x 9.8 x 7.10sin29 = 45.54 J

B. thermal energy = work done by friction

magnitude of friction = u.mgcos29 = 6.36 N

Work done = F.d

E = 6.36 x 7.10 = 45.19 J

C. Spring potential energy = G.p>E. gain + K.E. + thermal energy release

= 45.54 + 45.19 + 1.35 x 6.6^2/2 =120.13 J

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