The Physics Behind Trampoline Bounce: Exploring Hooke's Law

How can we determine the spring constant of a trampoline using Hooke's Law?

Given the scenario of a 35-kg child standing on a trampoline, how does the displacement affect the calculation of the spring constant?

Understanding Hooke's Law and the Spring Constant

The spring constant of the trampoline is approximately 3118.18 N/m. To solve this problem, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. Mathematically, it can be expressed as:

F = -k * x

Where:

F is the force exerted by the spring,

k is the spring constant, and

x is the displacement from the equilibrium position.

In this case, we know the child's mass (m = 35 kg) and the displacement of the trampoline center (x = 0.11 m). We can calculate the force exerted by the spring using the child's weight:

Weight = mass * acceleration due to gravity

Let's substitute the values and solve for the force exerted by the spring:

F = 35 kg * 9.8 m/s²

F = 343 N

Since the displacement is downward, we can take the negative sign in Hooke's Law equation:

-343 N = -k * 0.11 m

Now we can solve for the spring constant (k):

k = (-343 N) / (-0.11 m)

k ≈ 3118.18 N/m

Therefore, the spring constant of the trampoline is approximately 3118.18 N/m.