A spring has a force constant of 500.0 N/m. Show that the potential energy stored in the spring is as follows: a. 0.400 J when the spring is stretched 4.00 cm from equilibrium b. 0.225 J when the spring is compressed 3.00 cm from equilibrium c. zero when the spring is unstretched

(a) Hence, the potential energy = 0.400 J.

(b) Hence the potential Energy = 0.225 J.

(c) Hence the potential energy = 0 J

Explanation:

Potential Energy; This is the energy of a body, by virtue of its position in the gravitational field. The unit of potential energy is Joules (J)

the potential energy stored in a spring is

Ep = 1/2ke² ... Equation 1

Where Ep = potential Energy, k = force constant, e = extension.

a.

When spring is stretched 4.00 cm, e = 4.00 cm = 4/100 = 0.04 m, and k = 500 N/m.

Substituting into equation 1

Ep = 1/2 (500) (0.04) ²

Ep = 0.4 J.

Hence, the potential energy = 0.400 J.

(b)

When the spring is compressed 3.00 cm, e = 3.00 cm = 3/100 = 0.03 m, and k = 500 N/m.

Substitute into equation 1,

Ep = 1/2 (500) (0.03) ²

Ep = 250 (0.0009)

Ep = 0.225 J.

Hence the potential Energy = 0.225 J.

(c) When the spring is unstretched, e = 0 cm = 0 m and k = 500 N/m.

Substituting into equation 1

Ep = 1/2 (500) (0) ²

Ep = 250 (0)

Ep = 0.

Hence the potential energy = 0 J