How much elastic potential energy did the son add to the trampoline?

What is the scenario involving the son, the trampoline, and his sleeping mother? How can we calculate the elastic potential energy added by the son to the trampoline? The scenario involves a sneaky teenager pulling down a trampoline while his 61-kg mother is sleeping on it. He uses a ring attached to the center of the trampoline to stretch it. When he releases the trampoline, his mother is launched upward with a speed of 2.0 m/s. To calculate the elastic potential energy added by the son, we consider the principles of simple harmonic motion and conservation of energy.

In this scenario, the motion of the trampoline and the mother can be modeled as simple harmonic motion. At the equilibrium position, which is the point where the mother was before the son stretched the trampoline, the velocity is at a maximum. This means that the kinetic energy is maximum at this point, and the potential energy is 0 because the displacement from the equilibrium point is 0.

The total mechanical energy (sum of kinetic energy and potential energy) is constant throughout the motion. Therefore, the initial elastic potential energy added by the son to the trampoline is equal to the kinetic energy at the equilibrium position.

The kinetic energy (K) is given by the formula:
K = 1/2 * m * v^2, where m is the mass and v is the velocity.
Substituting the values:
K = 1/2 * 61 * 2^2 = 122 J

Therefore, the son added 122 J of elastic potential energy to the trampoline by pulling it down.

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