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.
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