Question

The P.E. of a certain spring certain when stretched from natural length through a distance $0.3m$ is $10J$ . The amount of work in joule that must be done on this spring to stretch it through an additional distance $0.15m$ will be :

• A. $10J$
• B. $20J$
• C. $7.5J$
• D. $12.5J$

Answer 1

The correct option is D $12.5J$

The initial potential energy of the spring is given as,

$U_i=\frac{1}{2}k{x}^2$

$10=\frac{1}{2}k{\left(0.3\right)}^2$

$k=\frac{20}{0.09}$

The final potential energy of the spring is given as,

$U_f=\frac{1}{2}k{x_1}^2$

$=\frac{1}{2}\times \frac{20}{0.09}{\left(0.45\right)}^2$

$=22.5J$

The amount of work done is given as,

$W=U_f-U_i$

$=22.5-10$

$=12.5J$

Thus, the amount of work done is $12.5J$.