Question

A force which pushes the object in the x direction is given by F = (3x+2) . Find the work done by this force as it pushes the object from x= 0 to x = 4 m​

Answer 1

Answer :

=case 1)

=Force =3x+2

=distance=0

=work done =Force*displacement

=work done =(3x+2)*0

=work done = 0

=case 1)

=Force =3x+2

=distance=1

=work done =Force*displacement

=work done =(3x+2)*1

=work done = (3x+2)

=case 3)

=Force =3x+2

=distance=2

=work done =Force*displacement

=work done =(3x+2)*2

=work done = (6x+4)

=case 4)

=Force =3x+2

=distance=3

=work done =Force*displacement

=work done =(3x+2)*3

=work done = (9x+6)

=case 5)

=Force =3x+2

=distance=4

=work done =Force*displacement

=work done =(3x+2)*4

=work done = (12x+8)

Answer 2

Given : Force which pushes the object in the x direction is given by F = (3x+2)

To Find : Work done by the force as it pushes the object from x= 0 to x = 4 m​.

Solution :

As the force is variable, we shall find the work done in a small displacement from x to x + dx and then integrate it to find the total work. The work done in this small displacement is

$\[dW = Fdx = (3x + 2)dx\]$

Then, on integration from x = 0 to x = 4m is

$\[W = \int\limits_0^4 {dW} = \int\limits_0^4 {(3x + } 2)dx\]$

$\[W = {\left[ {\frac{{3{x^2}}}{2} + 2x} \right]_0}^4\]$

W= 24J

Hence ,work done by this force as it pushes the object from x= 0 to x = 4 m​ is 24 J.