A sled is tied to a tree on a frictionless, snow-covered hill, as shown in Figur

Question

A sled is tied to a tree on a frictionless, snow-covered hill, as shown in Figure (a). If the sled weighs 76.0 N, find the force exerted by the rope on the sled and the magnitude of the force nS exerted by the hill on the sled.

Force exerted by the rope on the sled 38 N

Force exerted by the hill on the sled 66 N

Use the values from PRACTICE IT to help you work this exercise. Suppose a child of weight w climbs onto the sled. If the tension force is measured to be 61.5 N, find the weight of the child and the magnitude of the normal force acting on the sled.

Weight of the child N

Normal force on the sled N

Explanation / Answer

You have already solved for the Tension and the Normal force and got 38 N for the tension and 66 N for the normal from the equations

T = mgsin

Fn = mgcos

We will use those formulas for the second part with the child

The new T is given as 61.5 N

61.5 = mg(sin30)

W = 123 N

Since the sled weighs 76 N, then the child is 123 - 76 = 47 N

The normal force

Fn = (123)(cos 30)

Fn = 106.5 N

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