When is the work done by a force positive and when is it negative?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The general formula for work done is $W = \vec{F} \cdot \vec{d} = F d \cos \theta$,where $\theta$ is the angle between the force vector $\vec{F}$ and the displacement vector $\vec{d}$.
$1$. Positive Work: If the angle $\theta$ between the force and displacement is in the range $0^{\circ} \le \theta < 90^{\circ}$,then $\cos \theta$ is positive. Consequently,the work done $W$ is positive. In this case,the force aids the motion of the body.
$2$. Negative Work: If the angle $\theta$ between the force and displacement is in the range $90^{\circ} < \theta \le 180^{\circ}$,then $\cos \theta$ is negative. Consequently,the work done $W$ is negative. In this case,the force opposes the motion of the body.

Explore More

Similar Questions

$A$ force of $(-\,1, \,2, \,3) \,N$ is applied to an object,causing a displacement of $4 \,m$ along the $X$-axis. Calculate the work done by the force on the object. (in $,J$)

$A$ force $F = (5 \hat{i} + 4 \hat{j}) \text{ N}$ acts on a body and produces a displacement $s = (6 \hat{i} - 5 \hat{j} + 3 \hat{k}) \text{ m}$. The work done by the force is: (in $\text{ J}$)

If a force $(3 \hat{i} + 2 \hat{j} + 5 \hat{k}) \text{ N}$ acting on a body displaces it through $(2 \hat{i} + 2 \hat{j} + 1 \hat{k}) \text{ m}$,then the work done by the force on the body is (in $J$)

$A$ heavy object and a light object are placed on the same surface. If the same force is applied to both for the same displacement,on which object is more work done by the force?

$A$ body of mass $8 \ kg$,under the action of a force,is displaced according to the equation $s = \frac{t^2}{4} \ m$,where '$t$' is the time. Find the work done by the force in the first $4 \ s$. (in $J$)

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo