Question

select all of the following objects that could be described by the free body diagram shown below. note the two forces shown below are a normal force and the force due to gravity.
a ball accelerates downwards as it falls toward the ground
a hockey puck slides across a frictionless ice rink at a constant velocity. assume there is no air resistance.
a semi truck slows down gradually by applying its brakes
a book rests on a desk.

Explanation:

Step1: Analyze the free - body diagram

The free - body diagram shows two vertical forces, the normal force ($F_n$) and the gravitational force ($F_g$), and they seem to be equal in magnitude (since the arrows are of the same length, implying balanced forces). So the object should be in a state of equilibrium (either at rest or moving with a constant velocity) in the vertical direction, and if there are horizontal forces, they should also be balanced.

Step2: Analyze each option

• Option 1: A ball accelerates downwards as it falls toward the ground

When a ball falls downwards, the gravitational force is greater than the air resistance (if we consider air resistance). In the free - body diagram for a falling ball, the gravitational force arrow would be longer than the air resistance arrow. Also, in our given diagram, there are only normal and gravitational forces. For a falling ball, the normal force is not a significant force (unless it's in contact with a surface), so this object does not match the free - body diagram.

• Option 2: A hockey puck slides across a frictionless ice rink at a constant velocity. Assume there is no air resistance

In the vertical direction, the normal force (from the ice) and the gravitational force (weight of the puck) are balanced. In the horizontal direction, since there is no friction and no air resistance, there are no horizontal forces. So the free - body diagram would have two vertical forces (normal and gravitational) of equal magnitude, which matches our given diagram.

• Option 3: A semi - truck slows down gradually by applying its brakes

When a truck applies brakes, there is a net force in the horizontal direction (the braking force) that causes it to slow down. In the vertical direction, normal and gravitational forces are balanced, but the presence of a net horizontal force means that the free - body diagram would have an unbalanced horizontal force. Our given diagram only has two vertical forces, so this object does not match.

• Option 4: A book rests on a desk

When a book rests on a desk, the normal force from the desk (upwards) and the gravitational force (downwards) are balanced. There are no horizontal forces (assuming the book is not moving horizontally). So the free - body diagram would have two vertical forces of equal magnitude, which matches our given diagram.

Answer:

B. A hockey puck slides across a frictionless ice rink at a constant velocity. Assume there is no air resistance.
D. A book rests on a desk.