The potential energy of a spring when stretched through a distance x is 10 J. What is the amount of work done on the same spring to stretch it through an additional distance x ?

Question

The potential energy of a spring when stretched through a distance x is 10 J. What is the amount of work done on the same spring to stretch it through an additional distance x ? (A) 10 J (B) 20 J (C) 30 J (D) 40 J

Tardigrade Admin · Accepted Answer

Potential energy of the spring when stretched through a distance

x

,

U = \frac{1}{2} k x^{2} = 10 J

When

x

becomes

2 x

, the potential energy will be

U^{'} = \frac{1}{2} k (2 x)^{2} = 4 \times \frac{1}{2} k x^{2}

= 4 \times 10 = 40 J

∴

Work done

= U^{'} - U = 40 - 10 = 30 J

Q. The potential energy of a spring when stretched through a distance $x$ is $10 J$ . What is the amount of work done on the same spring to stretch it through an additional distance $x$ ?

$10 J$

$20 J$

$30 J$

$40 J$

Potential energy of the spring when stretched through a distance $x$ ,
$U = \frac{1}{2} k x^{2} = 10 J$
When $x$ becomes $2 x$ , the potential energy will be
$U^{'} = \frac{1}{2} k (2 x)^{2} = 4 \times \frac{1}{2} k x^{2}$
$= 4 \times 10 = 40 J$
$∴$ Work done $= U^{'} - U = 40 - 10 = 30 J$

Q. The potential energy of a spring when stretched through a distance x is 10J. What is the amount of work done on the same spring to stretch it through an additional distance x ?

10J

20J

30J

40J