Question

A) At a certain instant, a particle-like object is acted on by a force F = (3.0 N) ihat - (3.0 N) jhat + (9.0 N) khat while the object's velocity is v = - (2.0 m/s) ihat + (4.0 m/s) khat. What is the instantaneous rate at which the force does work on the object?
(b) At some other time, the velocity consists of only a j component. If the force is unchanged, and the instantaneous power is -12 W, what is the velocity of the object just then?

Answer 1

Answer:

a) Instantaneous rate at which the force does work on the object = -6 W

b) $\texttt{Velocity of object,}\vec{v}=4\hat{j}$

Explanation:

a) Given that

             $\vec{F}=3\hat{i}-3\hat{j}$

   and

            $\vec{v}=-2\hat{i}+4\hat{k}$

Instantaneous rate at which the force does work on the object is called power.

          Power is the dot product of force and velocity.

          $P=\vec{F}.\vec{v}=(3\hat{i}-3\hat{j}).(-2\hat{i}+4\hat{k})=-6W$

Instantaneous rate at which the force does work on the object = -6 W

b) Here given that    $\vec{v}=-a\hat{j}$

  Power = -12 W

  $P=\vec{F}.\vec{v}=(3\hat{i}-3\hat{j}).a\hat{j}=-12W\\\\-3a=-12\\\\a=4\\\\\vec{v}=4\hat{j}$

$\texttt{Velocity of object,}\vec{v}=4\hat{j}$