Question

The elastic potential energy stored in a spring,
having a compression 10 cm, is 20 J. The
potential energy stored in spring, when it is given
an extension of 10 cm from its natural length, is
(1) 40 J
(2) 20 J
(3) 10 J
(4) 5 J​

Answer 1

Answer:(2) 20J

Explanation:

The potential energy when a spring is compressed increases. When you stretch or compress a spring you work against the restoring force of the spring. This work is stored as elastic potential energy in the spring. So ,potential energy = 20J

Answer 2

Answer:

The elastic potential energy stored in a spring,  having a compression 10cm, is 20J. The  potential energy stored in spring, when it is given

an extension of 10 cm from its natural length is 20J

Explanation:

• The elastic potential energy is the energy stored when a force applied to deform an elastic object

• A spring with elastic constant K compressed or expanded at a distance x from its mean position, then the potential energy stored is

        $PE=\frac{1}{2}Kx^{2}$

From the question, we have

compressed distance $x=10cm=0.1m$

the potential energy stored is $PE_{1}=20J$

⇒

$PE_{1} =\frac{1}{2} (K*(0.1)^{2} )=20J\\K=40/0.01=4000N/m$

new extension from natural length is $x=10cm=0.1m$

new potential energy $PE_{2}=\frac{1}{2}(4000*0.1^{2} ) =20J$