A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension on the string?
a. tension does no work at all
b. tension does negative work
c. tension does positive work
d. tension does maximum work
The correct answer and explanation is :
The correct answer is a. tension does no work at all.
Explanation:
To understand why the tension in the string does no work on the ball, we need to review the definition of work in physics. Work is defined as the product of force and displacement in the direction of the force:
[
\text{Work} = \vec{F} \cdot \vec{d} = Fd \cos(\theta)
]
where:
- ( \vec{F} ) is the force vector,
- ( \vec{d} ) is the displacement vector,
- ( \theta ) is the angle between the force and displacement vectors.
For an object moving in a circle, the tension in the string acts as a centripetal force, always directed towards the center of the circle. The ball, however, is moving tangentially to the circle. In this case, the displacement of the ball is tangential, while the tension force is radial (towards the center of the circle).
Since the tension force and the displacement are perpendicular to each other (the tension force points toward the center, and the displacement of the ball is along the tangent), the angle ( \theta ) between the tension force and the displacement is 90°. This means that the cosine of the angle is:
[
\cos(90^\circ) = 0
]
Thus, the work done by the tension is:
[
\text{Work} = Fd \cos(90^\circ) = 0
]
This demonstrates that no work is done by the tension in this scenario. The tension keeps the ball moving in a circular path, but it does not contribute to changing the ball’s speed (kinetic energy). The ball’s kinetic energy remains constant while it is whirled around the circle, as tension does not cause any change in the speed of the ball.
In summary, the tension force in a circular motion does not perform any work because it acts perpendicular to the direction of the ball’s displacement, and no energy is transferred through this force. Therefore, the correct answer is a. tension does no work at all.