How to Calculate Stretching Distance of a Spring

What is the stretching distance of a spring with a spring constant of 445 (N)/(m) and elastic potential energy of 111J?

a) 0.707 meters

b) 0.445 meters

c) 1.11 meters

Stretching Distance Calculation

The stretching distance of the spring can be calculated using the formula for elastic potential energy:

Elastic potential energy = (1/2)kx^2

Where:

k = 445 N/m (spring constant)

Elastic potential energy = 111 J

Substitute the values into the equation:

111 = (1/2)(445)(x^2)

Rearrange the equation to solve for x:

x^2 = (2 * 111) / 445

x^2 = 0.5

Take the square root of both sides:

x = √0.5

x ≈ 0.707 meters

When calculating the stretching distance of a spring with a given spring constant and elastic potential energy, we can use the formula for elastic potential energy and substitute the values to find the stretching distance. In this case, with a spring constant of 445 N/m and elastic potential energy of 111 J, the stretching distance is approximately 0.707 meters.

This calculation is essential in understanding the relationship between the spring constant, stretching distance, and elastic potential energy of a spring. By applying the formula correctly, we can determine the exact distance the spring stretches when subjected to a certain force.

Understanding the mechanics of a spring's behavior is crucial in various fields, including physics, engineering, and material science. By grasping the concept of elasticity and spring constant, we can predict and control the behavior of springs in different applications.