Question
What is work and also give examples of the following :(i) Zero work(ii) Positive work(iii) Negative work
✓
Answer
Suppose a constant force F is acting on an object of mass $m$ due to which the displacement of the
object in the positive $x$-direction is $\overrightarrow{ S }$, as shown in the figure.
Therefore the work done by a force is defined as 'the product of the magnitude of displacement and component of force along the direction of displacment. Therefore,
$
W=(F \cos \theta) s=\overrightarrow{F} \cdot \overrightarrow{S} \ \ldots(1)
$
(i) Zero work : It is clear from equation (1) that if the displacement of the object is zero then no matter how great is the magnitude of force, the work done by the object is zero. No work is considered completed if
(a) the displacement is zero
(b) force is zero
(c) force and displacement are perpendicular to each other. Since $\theta=\frac{\pi}{2}$ and $\cos \frac{\pi}{2}=0$ is always zero.
The centripetal force on an object moving in a circular path with constant speed is perpendicular to the displacement hence the work done by the centripetal force is zero.
(ii) Positive work : If $\theta \geq 0^{\circ}$ and $\theta<90^{\circ}$ then the value of $\cos \theta$ is positive. In such a situation the work is positive. For example, when a man pulls a roller, the value of work is positive.
(iii) Negative work: When $90^{\circ}<\theta \leq 180^{\circ}$ then the value of $\cos \theta$ is negative. Hence the work is negative.
For example, when a roller is pulled on a rough surface, the friction force and displacement are in opposite directions hence the work done by the friction force is negative.
object in the positive $x$-direction is $\overrightarrow{ S }$, as shown in the figure.
Therefore the work done by a force is defined as 'the product of the magnitude of displacement and component of force along the direction of displacment. Therefore,
$
W=(F \cos \theta) s=\overrightarrow{F} \cdot \overrightarrow{S} \ \ldots(1)
$
(i) Zero work : It is clear from equation (1) that if the displacement of the object is zero then no matter how great is the magnitude of force, the work done by the object is zero. No work is considered completed if
(a) the displacement is zero
(b) force is zero
(c) force and displacement are perpendicular to each other. Since $\theta=\frac{\pi}{2}$ and $\cos \frac{\pi}{2}=0$ is always zero.
The centripetal force on an object moving in a circular path with constant speed is perpendicular to the displacement hence the work done by the centripetal force is zero.
(ii) Positive work : If $\theta \geq 0^{\circ}$ and $\theta<90^{\circ}$ then the value of $\cos \theta$ is positive. In such a situation the work is positive. For example, when a man pulls a roller, the value of work is positive.
(iii) Negative work: When $90^{\circ}<\theta \leq 180^{\circ}$ then the value of $\cos \theta$ is negative. Hence the work is negative.
For example, when a roller is pulled on a rough surface, the friction force and displacement are in opposite directions hence the work done by the friction force is negative.
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