Question

At a certain instant, a particle-like object is acted on by a force F=(4i - 2j + 9k) (N) while having a velocity v=(-4i + 4k) (m/s). What is the instantaneous rate (in W) at which the force does work on the object?

Answer 1

Given:

At a certain instant, a particle-like object is acted on by a force F=(4i - 2j + 9k) (N) while having a velocity v=(-4i + 4k) (m/s).

To find:

Power delivered by the force

Calculation:

Power is described as the instantaneous rate of work done on an object by a force.

Mathematically , it can be calculated by the scalar product between force and velocity vector.

$\therefore \: P = \vec{ F} \: . \: \vec{v}$

$= > \: P = \bigg(4 \hat{i} - 2 \hat{j} + 9 \hat{k} \bigg) . \bigg( - 4 \hat{i} + 4 \hat{k} \bigg)$

$= > \: P = - 16 + 0 + 36$

$= > \: P = 20 \: watt$

So, final answer is:

$\boxed{ \sf{ \: P = 20 \: watt}}$