# Energy of a Thrill Seeking Cat

A thrill-seeking cat with mass 4.00 (rm kg) is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 (rm m), and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring), the kinetic energy of the cat, the gravitational potential energy of the system relative to the lowest point of the motion, and the sum of these three energies when the cat is at the highest point.

a) Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring) when the cat is at its highest point.

b) Calculate the kinetic energy of the cat when the cat is at its highest point.

c) Calculate the gravitational potential energy of the system relative to the lowest point of the motion when the cat is at its highest point.

d) Calculate the sum of these three energies when the cat is at its highest point.

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#### Solution Preview

a) Energy can be stored in springs. This kind of potential energy is called elastic potential energy. It turns out that the elastic potential energy is:

U = (1/2)*k*x^2

The k is a spring constant, which varies depending on the type of spring used. x is the displacement of the spring from its original position. Now the problem states at it's highest point the spring is at its ...

#### Solution Summary

This solution calculates the elastic potential energy, the kinetic energy, and the gravitational potential energy of the cat at its highest point.