Question

A body of mass 10 kg is displaced from point a(2,1,3)to point b(3,3,4) under the effect of force of magnitude 20N in the direction of 6i+8j . calculate W.D by the force?

Answer 1

The work is `=44J`

Explanation:

The work done is the dot product of the Force and the Distance.

The vector `vec(ba)= ((3),(3),(4))-((2),(1),(3))=((1),(2),(1))`

The magnitude of the force is

`||vecF||=20N`

The unit vector in the direction of the force is

`hatf=1/sqrt(6^2+8^2+0^2)((6),(8),(0))=((6/10),(8/10),(0))`

Therefore,

the force is `vecF= ||vecf|| * hatf = 20*((6/10),(8/10),(0))=((12),(16),(0))`

The work done is

`W=vecF.vec(ba)=((12),(16),(0)).((1),(2),(1))=(12*1+16*2+0*1)=44J`