Question

Your daredovil 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 Another person attaches a 30 kg rock at the end of the rope after it passes over the tree trunk and then releases the rock the rope is initially lout. There is no friction between the rope and the tree trunk Determine the acceleration of the sled Express your answer to two significant figures and include the appropriate units. Determine the force that the rope exerts on the sled and on the rock Express your answer to two significant figures and include the appropriate units. Determine the time interval during which the person can jump off the sled before it reaches the Express your answer to two significant figures and include the appropriate units.

Answer 1

Part A:

Here, use Newton's second law to find the acceleration of the sled.

We have -

ma = mg - T

And, ma = mg - Ma

So, from the above two euations -

a = mg / (m+M) = (30*9.81) / (30+140) = 1.73 m/s^2

Part B:

The force exerted on the sled and on the rock -

T = Ma = 140*1.73 = 242.4 N

Part C:

For the time interval -

s = ut + (1/2)*at^2

=> 10 = 0 + 0.5*1.73*t^2

=> t = sqrt(10/(0.5*1.73)) = 3.40 s.