A mass m = 13 kg is pulled along a horizontal floor with NO friction for a dista

Question

A mass m = 13 kg is pulled along a horizontal floor with NO friction for a distance d =8 m. Then the mass is pulled up an incline that makes an angle = 37° with the horizontal and has a coefficient of kinetic friction k = 0.35. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of = 37° (thus on the incline it is parallel to the surface) and has a tension T =52 N.

5)

How far up the incline does the block travel before coming to rest? (Measured along the incline.)

Explanation / Answer

The kinetic energy at the bottom was computed in 1) above as 350 J. The block will come to rest when the sum of frictional, tension gravitational energy equals that amount. The gravitational energy change moving up the block is m*g*h, where h is the vertical altitude change. Let L be the distance the block moves: h = L*sin28

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