A sled is tied to a tree on a frictionless, snow-covered hill. The
sled weighs 77 N.
(a) Draw a free body diagram for the sled.
(b) Find the magnitude of the tension T exerted by the rope on
the sled.
(c) Find the magnitude of the normal force N exerted by the hill
on the sled.
To answer these questions, we need to analyze the forces acting on the sled. Let's go step by step:
(a) Drawing a free body diagram for the sled:
A free body diagram is a visual representation of all the forces acting on an object. In this case, the sled is tied to a tree, so we need to consider the forces at play.
Since the hill is frictionless, the only forces acting on the sled are the tension T exerted by the rope and the weight W of the sled itself. The weight of the sled can be represented as a downwards force of magnitude 77 N.
Here is a free body diagram for the sled:
T (upward)
/
/
\
\
W (downward)
(b) Finding the magnitude of the tension T exerted by the rope on the sled:
To find the magnitude of the tension T, we need to consider the vertical equilibrium of forces. Since the sled is not accelerating vertically, the sum of the vertical forces must be zero.
The only vertical force present is the weight W of the sled, which is equal to 77 N. Therefore, the magnitude of the tension T exerted by the rope on the sled is also 77 N, acting upward to balance the weight.
(c) Finding the magnitude of the normal force N exerted by the hill on the sled:
The normal force N is the force exerted by a surface perpendicular to an object resting on it. In this case, the hill is the surface on which the sled rests.
Since the hill is frictionless and there is no vertical acceleration, the normal force N must equal the weight W of the sled. Therefore, the magnitude of the normal force N is also 77 N, acting perpendicular to the hill.