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:

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What is Energy Conservation? - Definition, Process & Examples

from ICSE Environmental Science: Study Guide & Syllabus

Chapter 1 / Lesson 6
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