Your daredevil friends attach a rope to a 140-kgsled that rests on a frictionles

Question

Your daredevil friends attach a rope to a 140-kgsled that rests on a frictionless icy surface. The rope extends horizontally to a smooth dead tree trunk lying at the edge of a cliff. Another person attaches a 30-kg rock at the end of the rope after it passes over the tree trunk and then releases the rockthe rope is initially taut. There is no friction between the rope and the tree trunk.

A. Determine the acceleration of the sled.

B. Determine the force that the rope exerts on the sled and on the rock

C. Determine the time interval during which the person can jump off the sled before it reaches the cliff 10 mahead.

Please show work

Explanation / Answer

As we know the 30kg rock comes down vertically downwards and the sled will move horizontally.

from free body diagram the equations for rock and sled are

         30g -T = 30a along vertical under gravity

          T = 140a horizontal due to tension

          30g -140a =30a

            30g =170a

   The acceleration of sled is    a =30x9.8/170 =1.73m/s2

   the force on sled is T =140x1.73 =242.2N

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