Question

2. An engine exerts a force F = (20 – 3j + 5k) N and moves with velocity = (6î + 20 - 3k) ms 1.
The power of the engine (in watt) is​

Answer 1

Answer:

• Power of engine = 45 W

Explanation:

Given:-

Given force exerted by the engine,

$\rm{\vec{F} = (20\vec{i} - 3\vec{j} + 5\vec{k})\;\;N}$

the velocity of the body,

$\rm{\vec{v} = (6\vec{i} + 20\vec{j} - 3\vec{k})\;\;ms^{-1}}$

To find:-

Power of the engine (in watt), P =?

Formula required:-

Power of the body is given by the dot product of the force applied and velocity of the body.

$\rm{P = \vec{F}\;.\;\vec{v}}$

Solution:-

Using formula

$\implies \rm{P = \vec{F}\;.\;\vec{v}}$

$\implies \rm{P = (20\vec{i} - 3\vec{j} + 5\vec{k})\;.\;(6\vec{i} + 20\vec{j} - 3\vec{k})}$

$\implies \rm{P = (20\;.\;6)(\vec{i}\;.\;\vec{i}) + (-3\;.\;20)(\vec{j}\;.\;\vec{j}) +(5\;.\;-3) (\vec{k}\;.\;\vec{k})}$

[ since the dot product of an orthogonal vector with itself is 1 therefore,]

$\implies \rm{P = 120-60 -15 = 45\;}$

Therefore,

• Power of engine is 45 Watt.