# A swing consists of a mass on a rigid rod instead of a chain. The rod swings around a fixed axis...

## Question:

A swing consists of a mass on a rigid rod instead of a chain. The rod swings around a fixed axis and is 2 meters long. What initial horizontal velocity does the mass need to swing over the top?

Pretend the rod is massless.

## Law of energy conversion:

If we talk about the law of energy conversion it relates a fundamental law that energy is not destructible it just changes its state from one form into another, For example if a body is in rest it will be having some potential energy and during the fall of that particular body all the potential energy will be converted into the kinetic energy.

## Answer and Explanation:

Given:

• Length of the rod is {eq}L=2\ m {/eq}

At the highest point of the swing, all the energy will be in the form of potential energy.

Thus, at the highest point of swing potential energy is:

{eq}P.E =mgh {/eq}

Here, the mass on the rigid rod is {eq}m {/eq}

Acceleration due to gravity is {eq}g {/eq}

The distance of the mass from the lowest point of swing is {eq}h=2L {/eq}

At the lowest point all the potential energy will be converted into kinetic energy:

{eq}mg(2L)=\frac{1}{2}mv^2\\ g(2L)=\frac{1}{2}v^2 {/eq}

Now solving for the velocity by which mass need to swing over the top:

{eq}g(4L)=v^2\\ v=\sqrt{g4L} {/eq}

Solving for the velocity:

{eq}v=\sqrt{9.81\times 4\times 2}\\ v=8.85\ m/s {/eq}

Thus, the velcoity by which the mass swing over the top is 8.85 m/s.

#### Learn more about this topic:

What is Energy Conservation? - Definition, Process & Examples

from ICSE Environmental Science: Study Guide & Syllabus

Chapter 1 / Lesson 6
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