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Chapter 1: Problem 1

You are pushing a child on a playground swing. If you exert a \(50-N\) ( 11 -lbf) force on him as he is swinging away from you, how much force will he exert back on you?

Short Answer

Expert verified
The child will exert a 50 N force back on you.

Step by step solution

01

Identify the Forces

When pushing a child on a swing, the force you exert on him is given as 50 N.
02

Apply Newton's Third Law

According to Newton's Third Law, for every action force, there is an equal and opposite reaction force. Therefore, the force the child exerts back on you will be equal in magnitude and opposite in direction to the force you exerted.
03

Determine the Reaction Force

As per Newton's Third Law, the child will exert a force of 50 N back on you.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Action and Reaction Forces
In Newton's Third Law, the core idea is that forces come in pairs. When you push a child on a swing with a force of 50 N, this force acts upon the child. This is called the action force. Despite acting in different directions, the reaction force is always equal in magnitude to the action force. This principle is easier to understand through practical examples like pushing on a swing. When such a push occurs, it sets off both action and reaction forces simultaneously.

A visual way to grasp this would be to consider the moment of contact between your hands and the child.
  • The moment you apply force on the child through your hands, you have created an action force.
  • The child's body will naturally respond with an equal force pushing back on you.
Both of these forces together form the foundational concept of action and reaction forces.
Force Interactions
Force interactions are the mutual forces two objects exert on each other. These interactions are essential in understanding Newton's Third Law. When you exert a force on another object, that object simultaneously exerts a force back on you.

Let's break this down using the swing example:
  • You (Object A) push the child (Object B) with 50 N.
  • Object B (the child) exerts an equal force back on Object A (you).
These forces occur at the same time and are the result of their interaction. Within any type of force interaction:
  • The action force and the reaction force are components.
  • These are never isolated but always tied to their interacting counterparts.
This simultaneous occurrence of force interactions is crucial for understanding how objects influence each other.
Equal and Opposite Forces
Newton's Third Law states that action and reaction forces are equal in magnitude and opposite in direction. This concept is fundamental to ensuring that forces are balanced within an interaction. In the example of pushing a child on a swing:
  • If you push the child with 50 N, this force is applied in a forward direction.
  • According to Newton's Third Law, the child pushes back with an equal force of 50 N, but in the opposite direction.
This balance of forces is important to comprehend because it is not limited to swings but applies universally:
  • Rockets launching into space also follow this principle; the exhaust gases push down, and the rocket moves up.
  • Walking involves equal and opposite forces between your foot and the ground.
Understanding that these forces must always be equal and opposite helps explain why objects behave the way they do under various interactions.

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