A pendulum is swinging back and forth. At its lowest point it has a speed of 4 m/s. It has a mass of 1 kg.

a. How much KE does it have at it's lowest point? I got 8 Joules.
b. At its highest point it is not moving. How much potential energy does it have there?

To calculate the kinetic energy (KE) at the lowest point of a swinging pendulum, we can use the formula:

KE = 1/2 * m * v^2,

where m is the mass of the pendulum (1 kg) and v is the velocity at its lowest point (4 m/s).

a. Plugging in the given values into the formula:

KE = 1/2 * 1 kg * (4 m/s)^2,
= 1/2 * 1 kg * 16 m^2/s^2,
= 8 Joules.

So, you are correct. The kinetic energy at the lowest point of the pendulum is indeed 8 Joules.

b. At its highest point, the pendulum has zero velocity, which means it is not moving. At this point, the potential energy (PE) of the pendulum is at its maximum. The potential energy is given by the formula:

PE = m * g * h,

where m is the mass of the pendulum (1 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the pendulum at its highest point.

Since the pendulum is at its highest point, its height h is its maximum displacement from the equilibrium position. Hence, h is equal to the length of the pendulum.

In this case, let's assume the length of the pendulum is L meters. Therefore, the height at its highest point is also L meters.

PE = 1 kg * 9.8 m/s^2 * L meters,
= 9.8 L Joules.

Hence, the potential energy at the highest point of the pendulum is 9.8 times the length L of the pendulum in Joules.