Your daredevil friends attach a rope to a 140-kg sled that rests on a frictionle

Question

Your daredevil friends attach a rope to a 140-kg sled 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 rock of unknown mass at the end of the rope after it passes over the tree trunk and then releases the rock - the rope is initially taut. The hanging rock accelerates downward at 2.7 m/s2 and pulls the sled with it. There is no friction between the rope and the tree trunk. 1- Determine the mass of the hanging rock. Express your answer to two significant figures and include the appropriate units. 2- Determine the force that the rope exerts on the sled. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Using the nwtons laws. and free body diagram,

On the rock, T acts upward and mg acts downward. So mg - T = ma

So mg - T = m (2.7) ----------(1)

Also on the sled; we have the only force which is due to tension of rope pulling the sled;

So T = Ma = M(2.7)

M= 140 kg

Substitute eqn 2 in 1 we ger

mg - 140* 2.7 = m ( 2.7)

m ( 2.7 + 9.8) = 140 * 2.7

m = 30.24 kg

Force on sled = T = 140 * 2.7 = 378 N

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