AP Physics 1 Exam Question:

A block of mass 2 kg is released from rest at the top of a frictionless inclined plane. The angle of inclination of the plane is 30 degrees with the horizontal. The block slides down the plane and reaches a horizontal surface at the bottom. The height of the inclined plane is 4 meters.

a) Calculate the gravitational potential energy of the block when it is at the top of the inclined plane. b) Calculate the kinetic energy of the block when it reaches the horizontal surface at the bottom. c) In this scenario, does the total mechanical energy (kinetic energy + potential energy) of the block change? Justify your answer.

Answer:

a) To calculate the gravitational potential energy of the block when it is at the top of the inclined plane, we can use the formula:

Gravitational Potential Energy = mass × gravity × height

Given: mass (m) = 2 kg gravity (g) = 9.8 m/s^2 (approximate value) height (h) = 4 m

Gravitational Potential Energy = 2 kg × 9.8 m/s^2 × 4 m = 78.4 J (Joules)

Therefore, the gravitational potential energy of the block when it is at the top of the inclined plane is 78.4 Joules.

b) To calculate the kinetic energy of the block when it reaches the horizontal surface at the bottom, we need to use the conservation of energy principle. Since there is no friction, the total mechanical energy of the system should remain constant.

Initial energy (top of inclined plane) = Final energy (bottom of inclined plane)

The initial energy is the gravitational potential energy calculated in part (a).

Initial energy = 78.4 J

The final energy at the bottom of the inclined plane is the sum of kinetic energy and potential energy.

Final energy = kinetic energy + potential energy

Since the block is at the bottom of the inclined plane, the potential energy is zero.

Final energy = kinetic energy + 0

Therefore, the kinetic energy of the block when it reaches the horizontal surface at the bottom is 78.4 Joules (same as the initial energy).

c) In this scenario, the total mechanical energy of the block remains constant. This is because there is no non-conservative force (like friction) acting on the block, and the only change in energy is due to the conversion between potential energy and kinetic energy. The block's initial gravitational potential energy is converted to kinetic energy as it slides down the inclined plane, and this kinetic energy is maintained when it reaches the bottom. Therefore, the total mechanical energy of the block does not change.