Work is expressed as force times distance. There is a gain in energy when work is done. In terms of energy, what happens to the work done in pushing an object across a level floor with a constant force?
A 50-kg meteor is moving in outer space. If a 12-N force is applied opposite the direction of motion, what is its deceleration?
The Correct Answer and Explanation is :
Explanation of Work Done on an Object Across a Level Floor
Work is defined as the product of force and displacement in the direction of the force:
[
W = F \cdot d \cdot \cos\theta
]
where:
- ( W ) is the work done,
- ( F ) is the applied force,
- ( d ) is the displacement,
- ( \theta ) is the angle between force and displacement.
When an object is pushed across a level floor at a constant force and velocity, the work done on the object is converted into kinetic energy and dissipated as thermal energy due to friction. Since velocity is constant, there is no net increase in kinetic energy (per Newton’s First Law). The energy input (work done) is balanced by the energy dissipated as heat due to frictional forces between the object and the floor.
Deceleration of a Meteor in Space
Newton’s Second Law states that force equals mass times acceleration:
[
F = ma
]
Rearranging for acceleration (or deceleration when force opposes motion):
[
a = \frac{F}{m}
]
Given:
- ( F = 12 ) N (acting opposite to motion),
- ( m = 50 ) kg,
[
a = \frac{12}{50}
]
[
a = 0.24 \text{ m/s}^2
]
Since the force opposes motion, this is a deceleration of 0.24 m/s².
Conclusion
The work done in pushing an object at constant velocity is converted into heat energy due to friction. In the case of the meteor, the force applied in the opposite direction causes it to decelerate at 0.24 m/s², slowing it down over time.