Question

an ideal spring of negligible mass is 11.00 cm long when nothing is attached to it. when you hang a 3.75 kg object from it, you measure its length to be 12.50 cm.If you wanted to store 10.0J of potential energy in this spring, what would be its total length? Assume that it continues to obey Hooke's law.Express your answer numerically. If there is more than one answer, enter each answer, separated by a comma.

Answer 1

The total length of the spring when 10 J energy is stored is 20 cm.

How to calculate the total length of the spring?

The extension of the spring is calculated by applying the following formula.

E = ¹/₂kx²

Where;

• k is spring constant
• x is the extension of the spring

E = ¹/₂kx²

kx² = 2E

x² = 2E/k

x = √ (2E/k)

The spring constant k is calculated as follows;

f = kx

k = f / x

(x = 12.5 cm - 11 cm = 1.5 cm)

k = (3.75 kg x 9.8 m/s²) / (0.015 m)

k = 2,450 N/m

The extension of the spring is calculated as;

x = √ (2E/k)

x = √ (2 x 10 J / 2,450 )

x = 0.09 m

x = 9 cm

Total when 10 J is stored = 11 cm + 9 cm = 20 cm