A 2.1 kg pendulum bob hangs from a 2 meter string. It is pulled to the side, position A, so that the bob is 79 cm (h on the sketch) above the lowest position, position C. The bob is released and begins to swing. See below.

Question

A 2.1 kg pendulum bob hangs from a 2 meter string. It is pulled to the side, position A, so that the bob is 79 cm (h on the sketch) above the lowest position, position C. The bob is released and begins to swing. See below.

Answer 1

To find the answer to your question, we need to determine the potential energy and the kinetic energy at positions A and C.

Let's start by calculating the potential energy at position A. The potential energy is given by the formula:

Potential Energy = mass * acceleration due to gravity * height

In this case, the mass of the pendulum bob is 2.1 kg, and the height above the lowest position is 79 cm, which is equal to 0.79 meters. The acceleration due to gravity is approximately 9.8 m/s². Plugging these values into the formula, we get:

Potential Energy at A = 2.1 kg * 9.8 m/s² * 0.79 m

Now, let's calculate the potential energy at position C. At the lowest position, the height is zero, so the potential energy is also zero.

Now, let's move on to calculating the kinetic energy at positions A and C. The kinetic energy is given by the formula:

Kinetic Energy = (1/2) * mass * velocity²

We know that the velocity at position A is zero, as the pendulum bob is momentarily at rest. Therefore, the kinetic energy at A is also zero.

At position C, the pendulum bob is at its maximum speed. To find the velocity at this position, we can use the conservation of energy principle, which states that the total mechanical energy (the sum of potential energy and kinetic energy) remains constant throughout the motion.

Since the potential energy at position C is zero, the total mechanical energy at position C is equal to the kinetic energy. Therefore, we can set up the equation:

Potential Energy at A = Kinetic Energy at C

Plugging in the values we know, we get:

2.1 kg * 9.8 m/s² * 0.79 m = (1/2) * 2.1 kg * velocity²

Simplifying the equation, we can solve for the velocity:

velocity² = (2.1 kg * 9.8 m/s² * 0.79 m) / (1/2 * 2.1 kg)

velocity² = 9.8 m/s² * 0.79 m

Finally, we take the square root of both sides to find the velocity:

velocity = √(9.8 m/s² * 0.79 m)

Now, you can use this velocity to analyze the motion of the pendulum bob at positions A and C.