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Work Energy Theorem

A block of ma...

Question

A block of mass $10 k g$ is moving in $x -$ direction with a constant speed $10 m s^{- 1}$ . It is subjected to retarding force $F = - 0.1 x J / m$ during its travel from $x = 20$ m to $x = 30$ m. Find the final kinetic energy.

475 J

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450 J

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275 J

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250 J

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Solution

The correct option is A 475 J
As a retarding force is applied, the speed of the body decreases so is the kinetic energy.
This change in KE is the amount of work done by the force.
$W = K E_{i} - K E_{f}$
$K E_{f} = K E_{i} - W$
$K E_{f} = K E_{i} - \int_{20}^{30} F \cdot d x$
$K E_{f} = 0.5 (10) (10^{2}) - \int_{20}^{30} 0.1 x \cdot d x$
$K E_{f} = 500 - 0.1 [\frac{x^{2}}{2}]_{20}^{30} = 500 - 0.1 [\frac{30^{2}}{2} - \frac{20^{2}}{2}]$
$K E_{f} = 500 - 25 = 475 J$
Option A is correct.

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A block of mass 10 kg is moving in x−direction with a constant speed 10 ms−1. It is subjected to retarding force F=−0.1x J/m during its travel from x=20 m to x=30 m. Find the final kinetic energy.

A block of mass $10 k g$ is moving in $x -$ direction with a constant speed $10 m s^{- 1}$ . It is subjected to retarding force $F = - 0.1 x J / m$ during its travel from $x = 20$ m to $x = 30$ m. Find the final kinetic energy.