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Chapter 2: Problem 6

When you pull a child back on a playground swing and let go, which way does that child accelerate?

Short Answer

Expert verified
The child accelerates toward the lowest point of the swing’s path.

Step by step solution

01

Understand the Forces

Consider the forces acting on the swing. The main forces here are gravity and the tension in the swing's chains or ropes.
02

Identify the Point of Release

When the swing is pulled back and held, it is at a certain height and possesses potential energy. The moment the swing is let go, it starts converting this potential energy into kinetic energy to move.
03

Determine the Direction

At the point of release, the swing is momentarily stationary but begins to accelerate toward the equilibrium position (the lowest point of the arc) due to gravity. This is because gravity pulls the swing downward.
04

Conclude the Acceleration Direction

Therefore, at the moment of release, the child accelerates towards the equilibrium position or the lowest point of the swing’s path.

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Key Concepts

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

Gravity
Gravity is a force that pulls objects toward the center of the Earth. On a playground swing, gravity is what makes the swing move.
When a swing is pulled back and held, it is lifted to a certain height. This height gives the swing potential energy because it has the potential to move.
As soon as the swing is released, gravity acts on it by pulling it downward. This force causes the swing to accelerate towards the lowest point of its arc.

Gravity ensures that once the swing is let go, it will move back towards the ground. Without gravity, the swing would remain stationary in the air.
Potential Energy
Potential energy is the energy stored in an object because of its position or height. On a playground swing, potential energy is highest when the swing is pulled back and held.
Think of it as energy waiting to be used.
  • When you pull the swing up, you give it energy by doing work against gravity.
  • This stored energy depends on the height of the swing above the ground.
The higher you pull the swing, the more potential energy it has.

The moment you let go of the swing, this potential energy starts converting into kinetic energy as the swing moves downward.
Kinetic Energy
Kinetic energy is the energy an object has due to its motion. As a swing moves, its potential energy changes into kinetic energy.
When the swing is pulled back, its energy is stored as potential energy. Once released, the swing accelerates, and that potential energy gets converted into kinetic energy.
  • At its highest point in motion, the swing has the most potential energy and the least kinetic energy.
  • As it moves toward the lowest point of the arc, potential energy decreases, and kinetic energy increases.
The quickest point of the swing is at its lowest point, where it has the highest kinetic energy.

In summary, the transition from potential to kinetic energy is what drives the motion of the swing. Without this energy conversion, the swing wouldn't move back and forth.

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