An ideal spring hangs vertically from the ceiling. When 1.0 kg mass hangs from the spring it is extended 5.0 cm from its relaxed length. A downward external force is now applied to the mass to extend the spring an additional 10 cm. While the spring is being extended by the force, what is the work done by the spring?

To calculate the work done by the spring, we need to find the change in potential energy of the spring. The potential energy stored in a spring can be calculated using the formula:

U = (1/2) * k * x^2

Where U is the potential energy, k is the spring constant, and x is the displacement from the relaxed position.

1. First, we need to find the spring constant, k. The spring constant is a measure of how stiff the spring is. It can be calculated using Hooke's Law:

F = -k * x

Where F is the force applied, k is the spring constant, and x is the displacement from the relaxed position.

In this case, we know that when a 1.0 kg mass hangs from the spring, it is extended 5.0 cm from its relaxed length. Therefore, the force applied would be:

F = m * g

Where m is the mass and g is the acceleration due to gravity.

2. Calculate the force applied:
m = 1.0 kg
g = 9.8 m/s^2
F = m * g

3. Calculate the spring constant:
k = -F / x

4. Calculate the change in potential energy:
ΔU = (1/2) * k * x^2

5. Finally, the work done by the spring is equal to the change in potential energy:

Work = ΔU

By following these steps, you can calculate the work done by the spring.

work done=finalenergy-initialenergy

= 1/2 k (.15)^2-1/2 k(.05^2)
= 1/2 k (.0225-.0025)