First slide

Work

Question

Three forces $(5 \hat{i} + 4 \hat{j} + 2 \hat{k}) N (- 2 \hat{i} - 2 \hat{j} + 6 \hat{k}) N, (\hat{i} - j - 3 \hat{k}) N$ displaces a particle from (1m,-1m,-1m) to (1m,0,3m) and then to (3m,1m,2m). The total work done by all these forces is

Moderate

A

50J
B

25J
C

15J
D

-10J

Solution

Net force $\vec{F} = \vec{F_{1}} + \vec{F_{2}} + \vec{F_{3}}$
$\vec{F} = 4 \hat{i} + \hat{j} + 5 \hat{k}$
Displacement
$\begin{array}{l} \vec{Δ r} = \vec{r_{3}} - {\vec{r}}_{1} = 3 \hat{i} + \hat{j} + 2 \hat{k} - (\hat{i} - \hat{j} - \hat{k}) \\ \vec{Δ r} = 2 \hat{i} + 2 \hat{j} + 3 \hat{k} \\ W = \vec{F} \cdot \vec{Δ r} = (4 \hat{i} + \hat{j} + 5 \hat{k}) \cdot (2 \hat{i} + 2 \hat{j} + 3 \hat{k}) = 8 + 2 + 15 = 25 J \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App