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A solid sphere of mass m is placed on a rough incline plane. The coefficient of friction \mu is...

Question:

A solid sphere of mass m is placed on a rough incline plane. The coefficient of friction {eq}\mu {/eq} is insufficient to start pure rolling. The sphere slides length L from rest and its KE becomes K. Find work done by friction.

Kinetic energy :

The kinetic energy is found, when the object is in motion. Kinetic energy is part of the energy, which can be transformed according to our needs. When a body falls from a height, it has kinetic energy.

Answer and Explanation:

Given data

  • The mass of the sphere is: {eq}m {/eq}
  • The coefficient of the friction is: {eq}\mu {/eq}
  • The length on which sphere slides: {eq}L {/eq}
  • The kinetic energy of the system is: {eq}K {/eq}


The free body diagram of the sphere plane system is as follows.

Free body diagram


The work energy theorem of the system is as follows.

{eq}{W_{friction}} + {W_{gravity}} + {W_{normal\;force}} = K {/eq}


Here, Work done by the normal forces will be zero because of motion direction is the perpendicular to the normal forces.


Work done by the gravity is as follows.

{eq}{W_{gravity}} = mgL\sin \theta {/eq}

Here, g is the gravitational acceleration.


Substitute all the value in above equation.

{eq}\begin{align*} {W_{friction}} + mgL\sin \theta + 0 &= K\\ {W_{friction}} &= K - mgL\sin \theta \end{align*} {/eq}


Thus, the work done by the friction is {eq}{W_{friction}} = K - mgL\sin \theta {/eq}


Learn more about this topic:

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Kinetic Energy Lesson for Kids: Definition & Examples

from Physics for Kids

Chapter 1 / Lesson 9
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