Question

A body is desplaced from origin to (2m, 4m) under the following two forces: (a) F=(2^hati + 6^hatj)N, a constant force (b) F(2x^hati + 3y^(2)hatj)N Find word done by the given forces in both cases.

Answer 1

Here,the force and displacement are given.

We know, work done is the dot product of force and displacement.

Therefore,in case a) we put the values of displacemeny and force and find the dot product, we get the value for work done.

In case b) as well, we find it in a similar way as that of case a) with the given values of force and displacement.

The displacement d=2i+4j

a) F=2i+6j

Work done in this vase will be

W=force.displacement

=(2i+6j).(2i+4j)

=4+24=28Joules

b) F=2xi+3y^2j

Work done in this case will be

W=force.displacement

=(2xi+3y^2j).(2i+4j)

=4x+12y^2 joules