Nature of Work Done
Category : JEE Main & Advanced
Positive work
Positive work means that force (or its component) is parallel to displacement
\[{{0}^{o}}\le \theta <{{90}^{o}}\]
The positive work signifies that the external force favours the motion of the body.
Example: (i) When a person lifts a body from the ground, the work done by the (upward) lifting force is positive
(ii) When a lawn roller is pulled by applying a force along the handle at an acute angle, work done by the applied force is positive.
(iii) When a spring is stretched, work done by the external (stretching) force is positive.
Maximum work : \[{{W}_{\max }}=F\,s\]
When \[\cos \theta =\text{maximum}=1\] i.e. \[\theta ={{0}^{o}}\]
It means force does maximum work when angle between force and displacement is zero.
Negative work
Negative work means that force (or its component) is opposite to displacement i.e.
\[{{90}^{o}}<\theta \le {{180}^{o}}\]
The negative work signifies that the external force opposes the motion of the body.
Example: (i) When a person lifts a body from the ground, the work done by the (downward) force of gravity is negative.
(ii) When a body is made to slide over a rough surface, the work done by the frictional force is negative.
Minimum work : \[{{W}_{\min }}=-F\,s\]
When \[\cos \theta =\text{minimum}=-1\] i.e \[\theta ={{180}^{o}}\]
It means force does minimum [maximum negative] work when angle between force and displacement is \[{{180}^{o}}\].
(iii) When a positive charge is moved towards another positive charge. The work done by electrostatic force between them is negative.
| Zero work | |
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Under three condition, work done becomes zero \[W=Fs\cos \theta =0\] |
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(1) If the force is perpendicular to the displacement \[\mathbf{[}\overrightarrow{F}\,\bot \,\overrightarrow{s\,}\mathbf{]}\] Example: (i) When a coolie travels on a horizontal platform with a load on his head, work done against gravity by the coolie is zero. (ii) When a body moves in a circle the work done by the centripetal force is always zero. (iii) In case of motion of a charged particle in a magnetic field as force \[[\overrightarrow{F}=q(\overrightarrow{v\,}\times \overrightarrow{B})]\] is always perpendicular to motion, work done by this force is always zero.
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(2) If there is no displacement [s = 0] Example: (i) When a person tries to displace a wall or heavy stone by applying a force and it does not move, then work done is zero. (ii) A weight lifter does work in lifting the weight off the ground but does not work in holding it up. |
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(3) If there is no force acting on the body [F = 0] Example: Motion of an isolated body in free space. |
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