Question

A BODY OF MASS 2 kg IS ACTED UPON BY TWO FORCES 2N AND 5N IN THE DIRECTION OF i^ + j^ AND j^- k^ RESPECTIVELY.IF THE BODY IS DISPLACED FROM [ 3,-2,1 ] TO [-1,2,3 ] , THEN THE WORK DONE IS WHAT ?In this question why have we not added the work done by both forces individually over the displacement(net) over which they act as done in case of telling net work done when 2 forces are given(eg-net work done when a force is applied on block on rough surface then we add the work done by applied force and friction force with their sign to get net work)?Answer to this ques is 5 root2 and not 10 why?

Answer 1

$$\bold{F=F_1+F_2}=2\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},0\right)+5\left(0,\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}\right)$$

$$\bold{F}=\left(\sqrt{2},\frac{7}{\sqrt{2}},\frac{-5}{\sqrt{2}}\right)N$$

$$\bold{\Delta r}=(-1,2,3)-(3,-2,1)=(-4,4,2)m$$

$$W=\bold{F\cdot \Delta r}$$

$$W=(\sqrt{2})(-4)+\left(\frac{7}{\sqrt{2}}\right)(4)-\left(\frac{5}{\sqrt{2}}\right)(2)=5\sqrt{2}\ J$$

We can obtain the same result if we need separate work from two forces.