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Chapter 2: Problem 22

How is Newton's third law of motion involved when you jump straight upward?

Short Answer

Expert verified
Answer: Newton's third law of motion applies when someone jumps straight upward by showing that the action force a person exerts on the ground is met with an equal and opposite reaction force by the ground on the person, allowing them to move against gravity and jump.

Step by step solution

01

Recall Newton's third law of motion

Newton's third law of motion states that for every action, there is an equal and opposite reaction. In other words, when an object A exerts a force on object B, object B exerts an equal force in the opposite direction on object A. Mathematically, it can be represented as: F_AB = -F_BA
02

Identify the action force

When a person jumps straight upward, they exert a force on the ground beneath them. This force is the action force. The person has to apply a force on the ground equal to their body weight (which is the force due to gravity) but in the opposite direction, to overcome gravity and jump off the ground. Mathematically, this force can be represented as the following for the person (P) and the ground (G): F_PG = -mP * g, where mP is the mass of the person, and g is the acceleration due to gravity.
03

Identify the reaction force

According to Newton's third law of motion, the ground must exert an equal and opposite force on the person. This force is known as the reaction force. This force is what enables the person to move upward against gravity. Mathematically, this force can be represented as: F_GP = mP * g
04

Apply Newton's third law of motion to the jump

During the jump, the person's action force (F_PG) is equal and opposite to the ground's reaction force (F_GP): F_PG = -F_GP. This relationship demonstrates how Newton's third law of motion is involved in jumping straight upward. The person exerts a force on the ground to overcome gravity (action force), and the ground provides an equal and opposite force on the person (reaction force) to push them upward. In conclusion, Newton's third law of motion is involved in jumping straight upward, as the action force a person exerts on the ground is met with an equal and opposite reaction force by the ground on the person, allowing them to move against gravity and jump.

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