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 m ahead.

Explanation / Answer

here,

The acceleration would be just that of the rock since that is the only thing on the y - axis. So g or gravity is the only acceleration.

So you get the force which is 30kg * G. You then know this equals the force.

F = 30 * 9.8 = 294 N

Then just use this as the force on the sled, and use the mass of sled to solve for a,
where,

Force = mass of sled * aacceleration
solving for acceleration

a = F / M
a= 294 / 140 = 2.1 m/s^2

acceleration of the sled is 1.2 m/s^2

b.)
F = mass of sled * acceleration
F = 140 * 1.2

the force that the rope exerts on the sled and on the rock is 168N

C.) time interva
Solving by suing second equation of motion

S = u*t + 0.5*a*t^2

10 = 0 + 0.5 * 1.2 * t^2

0.6 t^2 = 10

t = 4.08 s

the time interval during which the person can jump off the sled before it reaches the cliff 10 m ahead is 4.08s

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