# b) A horizontal rope pulls a 10kg wood sled across frictionless snow. A 5kg wood box rides on top of the sled. What is the largest tension force for which the box doesnt slip.

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### 1 Answer

*Let us assume the friction coeeficient as 0.44 for the question.*

When the wood sled start to travel due to the pull the small wooden box also start to travel. If we assume that tension force of rope is T then by the Newtons second law of motion ;

T = (5+10)*a where a is the acceleration.

When T increases acceleration will also increase. But initially the wooden box travel with the wood sled due to friction force between wood sled and wood box. When T increases maximum friction force the wooden box will start to slip.

Using F = ma to the whole system

Since the small box travel together with the wood sled before it slips it has the same acceleration as the whole system.

Using F = ma to the small box at slip

friction force = m*a

*So the maximum tension of the rope is 64.746N*

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