How to Calculate the Spring Constant of a Trampoline When a Branch Falls on It

What is the formula to calculate the spring constant of a trampoline?

How can we determine the spring constant of a trampoline when a branch falls on it?

Calculation of Spring Constant

To calculate the spring constant of the trampoline when a branch falls on it, we use the formula:

k = (2 * m * g * h) / e²

Spring constant, also known as force constant, is the ratio of the force applied to the extension or compression of an elastic material. When a branch falls on a trampoline, it compresses the trampoline by a certain distance, allowing us to calculate the spring constant of the trampoline.

By utilizing the given values of the mass of the branch, the acceleration due to gravity (g), the height from which the branch falls (h), and the extension of the trampoline (e), we can substitute these values into the formula to determine the spring constant.

After substituting the values into the formula and performing the calculations, we can find the spring constant of the trampoline. In the case of a branch with a mass of 0.35 kg falling from a height of 2.6 meters and compressing the trampoline by 0.14 meters, the spring constant is calculated to be 910 N/m.

This calculation involves the conservation of energy and Hooke's Law, providing a method to quantify the spring constant of the trampoline under specific conditions. Understanding the spring constant of a trampoline can contribute to assessing its elasticity and performance when subjected to external forces.