Question

A bike is hanging from a hook in a garage. Consider the following forces: (a) the force of the Earth pulling down on the bike, (b) the force of the bike pulling up on the Earth, (c) the force of the hook pulling up on the bike, and (d) the force of the hook pulling down on the ceiling. Which two forces are equal and opposite because of Newton's third law? Which two forces are equal and opposite because of Newton's first law?

Short answer

Answer: The forces that follow Newton's third law are (a) and (b), while the forces that follow Newton's first law are (c) and (d).

Step-by-step solution

1. Determine the force pairs according to Newton's third law

By definition, every action force has a corresponding reaction force. These pairs are equal in magnitude and opposite in direction. In this exercise, the force pairs are as follows: (a) the force of the Earth pulling down on the bike (b) the force of the bike pulling up on the Earth (c) the force of the hook pulling up on the bike (d) the force of the hook pulling down on the ceiling Now, let's determine which of these forces follow Newton's third law. The pairs (a) and (b) are following Newton's third law because the Earth pulls the bike down, and the bike pulls the Earth up with equal and opposite forces.

2. Determine the force pairs according to Newton's first law

For an object to remain at rest, all forces acting on the object must balance each other. In this case, the bike is hanging stationary, so we can use Newton's first law to determine which forces are equal and opposite. The only pair of forces that work together to keep the bike in equilibrium are: (c) the force of the hook pulling up on the bike (d) the force of the hook pulling down on the ceiling Since the bike isn't accelerating, the force that the hook pulls up on the bike (c) should be equal to the gravitational force that the Earth exerts on the bike (d). In this scenario, the force pair (c) and (d) follow Newton's first law. In conclusion: - The forces that follow Newton's third law are (a) and (b). - The forces that follow Newton's first law are (c) and (d).