A simple pendulum consists of a 2 m length of rope and a 3 kg bob. A student not

Question

A simple pendulum consists of a 2 m length of rope and a 3 kg bob. A student notes that at point C the pendulum has 12 J of PE and 3 J of KE.

What is the pendulum’s mechanical energy at point C? (15J)
What is the pendulum’s mechanical energy at point A? (15J)
What is the pendulum’s gravitational potential energy at point A? (0J)
What is the pendulum’s kinetic energy at point A? (15J)

The answers are provided, I just don't know how to arrive at the correct answer. For the first question, I know you just add the potential energy and kinetic energy at that position to get the mechanical energy.

Also, if you could help me out with the formula for Kinetic Energy when the velocity is not available. Thanks.

Explanation / Answer

Because mechanical energy is conserved, if you know it at one point you know it at all points. It is always the sum of U and K so once you added those and got 15J for point C, you know the mechanical energy is also 15J at point A.

There is no diagram, but since you say potential energy is 0 at point A that must be a low point in the pendulum swing; all the energy there is kinetic, which is why the answer to the last question is 15J.

If velocity is not available, you can get kinetic energy by subtracting potential energy from mechanical energy. Kinetic is what is left over.

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