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 $\vec F = 6\hat i + 2\hat j - 3\hat k$ acts on a particle,causing a displacement $\vec d = 2\hat i - 3\hat j + c\hat k$. If the work done during this process is zero,find the value of $c$.

$A$ man starts walking from a point on the surface of the Earth (assumed smooth) and reaches the diagonally opposite point. What is the work done by him?

$A$ body of mass $m$ starts from rest and acquires a velocity $v$ in time $t_1$. The work done in time $t$ is proportional to:

Difficult
View Solution

Consider a particle on which constant forces $F_{1}=\hat{i}+2 \hat{j}+3 \hat{k} \text{ N}$ and $F_{2}=4 \hat{i}-5 \hat{j}-2 \hat{k} \text{ N}$ act together, resulting in a displacement from position $r_{1}=20 \hat{i}+15 \hat{j} \text{ cm}$ to $r_{2}=7 \hat{k} \text{ cm}$. The total work done on the particle is:

$A$ force $F = (5\hat i + 3\hat j) \, N$ is applied to a particle,which displaces it from its origin to the point $r = (2\hat i - 1\hat j) \, m$. The work done on the particle is:

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