Determining the Final Extension of a Spring

How can we calculate the final extension of a spring with given elastic energy and spring constant?

20 J of energy was used to stretch a spring with a spring constant of 445 N/m. What is the final extension of the spring?

Answer:

The final extension of the spring is 0.3 meters.

When calculating the final extension of a spring using the given parameters of elastic energy and spring constant, we use the formula for elastic potential energy. The elastic potential energy (EP) of a stretched spring can be determined using the expression:

EP = 0.5 * k * e²

Where:
- EP is the elastic potential energy
- k is the spring constant
- e is the extension of the spring

Given parameters:
- Elastic energy = 20 J
- Spring constant = 445 N/m
- Unknown final extension of the spring = ?

Solution:
Substitute the known values into the formula:
20 = 0.5 * 445 * e²
Multiply both sides by 2:
40 = 445e²
Divide by 445:
e² = 40 / 445
e = √0.09
e = 0.3 meters