Question

A body constrainedto move along the z-axis of a co-ordinate system is subjected to a constant force `vec(F)` given by `vec(F)=-hat(i)+2hat(j)+3hat(k)` newton where `hat(i),hat(j)`and `hat(k)` represent unit vectors along x-,y-,and z-axes of the system, respectively.Calculate the work done by this force in displacing the body through a distance of `4m`along the z-axis.

Answer 1

Displacement=`4hat(k)`,Force: `vec(F)=-hat(i)+2hat(j)+3hat(k)`
Since work W is the scalar product of force and displacement,
`:.W=(-hat(i)+2hat(j)+3hat(k)).4hat(k)`
`= -4(hat(i).hat(k))+8(hat(j).hat(k))+12(hat(k).hat(k))=12J`
`[Because hat(i).hat(k)=0=hat(j).hat(k)` and `hat(k).hat(k)=1]`