Question

A sled is tied to a tree on a frictionless, snow-covered hill, as shown in Figure. If the sled weighs 77.0 N, find the magnitude of the tension force T exerted by the rope on the sled and that of the normal force n exerted by the hill on the sled.

Answer 1

The magnitude of the tension force T exerted by the rope on the sled is 77.0 N, equal to the weight of the sled. The magnitude of the normal force n exerted by the hill on the sled is also 77.0 N, perpendicular to the surface.

Step-by-step explanation:

In this scenario, the sled on a frictionless, snow-covered hill experiences forces solely due to gravity and the tension in the rope. As the sled is at rest, the forces in the vertical direction must balance out. The tension force T exerted by the rope vertically upward is equal in magnitude to the weight of the sled, which is 77.0 N (given). This relationship holds true because the sled is stationary on the hill.

Regarding the normal force exerted by the hill on the sled, since there's no acceleration in the direction perpendicular to the surface, the normal force and the component of the weight perpendicular to the hill's surface must cancel each other out. Therefore, the normal force n equals the weight of the sled, which is 77.0 N, as both forces are in opposite directions.

Considering Newton's laws and equilibrium, the forces acting on the sled must balance out in both the vertical and perpendicular-to-the-surface directions for it to remain stationary. Hence, both the tension force exerted by the rope and the normal force exerted by the hill on the sled are equal in magnitude to the weight of the sled, which is 77.0 N each.