Question

The force exerted on an object is F=fo(x/a-1)
Find the work done in moving the object from x =
O to x = 3a.​

Answer 1

Explanation: W=Fdx

so f= fo(xdx)1/a-1

f= fo(x^2/2)1/a-1

use limit get your answer

Answer 2

Answer:

$f_0(\frac{3a}{2})$

Explanation:

We are given that force exterted  on an object  is

$F=f_0(\frac{x}{a}-1)$

We have to find the work done in moving the object from x=0 to x=3a

We know that w=fdx

$Work done=\int_{0}^{3a}f_0(\frac{x}{a}-1)dx$

$\int_{a}^{b}fdx=F(b)-F(a)$

$w=f_0[\frac{x^2}{2a}-x]^{3a}_0$

$w=f_0(\frac{(3a)^2}{2a}-(3a)-0-0)=f_0(\frac{9a}{2}-3a)=f_0\frac{9a-6a}{2}=f_0(\frac{3a}{2})$

$\int_{a}^{b}fdx=F(b)-F(a)$

Hence, work done in moving the object from x=0 to x=3a is given by =$f_0(\frac{3a}{2})$