Question

Force constants k1 and k2 of two springs are in the ratio 5:4 .They are stretched by same length .If potential energy stored in one spring is 25 J then potential energy stored in second spring is

Answer 1

here both springs suffers same elongation so we could have approached. directly that ratio of pe stored is directly proptional to ratio os spring constants

Answer 2

Given:

• The ratio of spring constants are 5:4
• The springs are stretched by the same length.
• Potential energy stored in the first string is 25 Joule.

To find:

• Potential energy in the 2nd string ?

Calculation:

Let the spring constants be 5x and 4x, where 'x' is the constant of proportionality.

Now, let the length stretched be y.

So, for the 1st spring :

$\dfrac{1}{2} (5x) {y}^{2} = 25$

Now, for the 2nd spring :

$PE = \dfrac{1}{2} (4x) {y}^{2}$

• Multiplying numerator and denominator by 5:

$\implies PE = \dfrac{1}{2} (5x) {y}^{2} \times \dfrac{4}{5}$

$\implies PE = 25 \times \dfrac{4}{5}$

$\implies PE = 20 \: joule$

So, the potential energy of the second spring will be 20 Joules