A 2.3 kg pendulum bob hangs from a 2 meter string. It is pulled to the side, position A, so that the bob is 111 cm (h on the sketch) above the lowest position, position C. The bob is released and begins to swing. See below.

What is its potential energy after it has swung to position B, 31.0 cm below the starting point?

And, how fast is it moving at that point?

To determine the potential energy of the pendulum bob at position B, we need to calculate the change in height between positions B and C.

1. Calculate the change in height:
The initial height of the pendulum bob is 111 cm above position C, and position B is 31.0 cm below the starting point. Therefore, the change in height is:
Delta h = h_initial - h_final
= 111 cm - (-31.0 cm)
= 142.0 cm
= 1.42 meters

2. Calculate the potential energy:
The potential energy of an object is given by the equation:
Potential energy = mass x gravity x height
Here, the mass of the pendulum bob is 2.3 kg, gravity is approximately 9.8 m/s^2, and the change in height is 1.42 meters.
Thus, the potential energy at position B can be calculated as:
Potential energy = 2.3 kg x 9.8 m/s^2 x 1.42 m
= 31.1276 Joules (rounded to four decimal places)

To determine the speed of the pendulum bob at position B, we can use the law of conservation of energy. The potential energy at position C will be equal to the kinetic energy at position B.

3. Calculate the speed using conservation of energy:
Kinetic energy = Potential energy at position C
The potential energy at position C is equal to the potential energy at position B, so we can substitute the values:
2.3 kg x 9.8 m/s^2 x 1.42 m = (1/2) x mass x speed^2
Rearranging the equation to solve for speed, we get:
Speed = sqrt((2.3 kg x 9.8 m/s^2 x 1.42 m) / (0.5 x 2.3 kg))
= sqrt(31.1276 J / 2.3 kg)
= sqrt(13.530639130434782608695652173913)
= 3.678 m/s (rounded to three decimal places)

Therefore, the potential energy of the pendulum bob at position B is 31.1276 Joules, and it is moving at a speed of 3.678 m/s at that point.