AP Physics 1 Exam Question:

A pendulum with a length of 2.0 meters swings back and forth. The pendulum bob is released from rest at point A as shown in the diagram below.

1. At point A, what is the total mechanical energy of the pendulum?

(A) Zero (B) Negative (C) Positive (D) Cannot be determined without additional information

Answer:

The correct answer is (C) Positive.

Step-by-step Explanation:

In a simple pendulum motion, the total mechanical energy of the system remains constant. The mechanical energy is given by the sum of the potential energy and the kinetic energy.

At point A, the pendulum bob is released from rest, which means it has maximum potential energy and zero kinetic energy.

1. Potential Energy: The potential energy of the pendulum bob is given by the formula: PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height above a reference point. At point A, the height h is at its maximum value, which is equal to the length of the pendulum L. Therefore, the potential energy at point A is PE = mgh = mgL.

2. Kinetic Energy: At point A, the pendulum bob is at its lowest point, so its velocity is at a maximum. Kinetic energy is given by the formula: KE = (1/2)mv^2, where m is the mass and v is the velocity. At point A, the velocity v is at its maximum value, so the kinetic energy at point A is KE = (1/2)mv^2.

Since the pendulum is released from rest, the velocity at point A is equal to zero. Therefore, the kinetic energy at point A is KE = (1/2)m(0)^2 = 0.

3. Total Mechanical Energy: As mentioned earlier, the total mechanical energy is the sum of the potential energy and the kinetic energy. Therefore, at point A, the total mechanical energy is given by: Total Energy = Potential Energy + Kinetic Energy = mgL + 0 = mgL.

Since the potential energy mgL is positive (as the height h is positive), the total mechanical energy at point A is positive.

Hence, the correct answer is (C) Positive.