The elastic potential energy is stored in a certain spring is 14 J when it is compressed 0.240m. the spring is now cut into three equal pieces. once of the pieces is then compressed by 0.150m.
How much elastic potential energy is stored in the compressed piece?

The elastic potential energy stored in the compressed piece is 5.47 J

Explanation:

Given;

elastic potential energy stored, E = 14 J

initial compression, x =  0.240m

The elastic potential energy stored in a spring is given as;

E = ¹/₂Kx²

where;

E is elastic potential energy

K is the spring constant

x is the compression

K = 2E / x²

K = (2*14) / (0.24²)

K = 486.11 N/m

When the spring is cut into three equal pieces, and one of pieces is then compressed by 0.150m, the energy stored in this piece is calculated as;

E = ¹/₂Kx²

E = ¹/₂(486.11)(0.15²)

E = 5.47 J

Therefore, the energy stored in one of the cut pieces compressed by 0.150m is 5.47 J

5.47 J

Explanation:

From Hook's law,

Energy stored in a elastic material = 1/2ke²

E = 1/2ke² Equation 1

Where k = spring constant of the material, e = extension.

make k the subject of the equation

k = 2E/e² Equation 2

Given: E = 14 J, e = 0.24 m

Substitute into equation 2

k = 2(14)/0.24²

k = 28/0.0576

k = 486.11 N/m.

The elastic potential energy stored in the compressed piece is

Given: e = 0.15 m

E = 1/2(466.11)(0.15²)

E = 5.47 J