A block is released from rest at the top of a rough ramp. There is significant friction between the block and the ramp, but the block's speed increases as the block slides down the ramp. Which of the following correctly indicates whether the total mechanical energy of the block-Earth system decreases or remains the same, and provides a valid justification? (A) Decreases, because a force external to the system is dissipating energy (B) Decreases, because the gravitational potential energy of the system decreases (D) Stays the same because gravitational potential energy is converted into kinetic energy because energy is always conserved (D)

To analyze the problem, let's break down the known conditions and the concepts involved: 1. **Known Conditions:** - A block is released from rest at the top of a rough ramp. - There is significant friction between the block and the ramp. - The block's speed increases as it slides down the ramp. 2. **Concepts Involved:** - The total mechanical energy of a system is the sum of its potential energy (PE) and kinetic energy (KE). - Friction is a non-conservative force that dissipates energy as thermal energy, which is not recoverable as mechanical energy. Now, let's evaluate the options provided: **(A) Decreases, because a force external to the system is dissipating energy.** - This statement is correct. The frictional force acts as an external force that dissipates energy from the block-Earth system, converting some mechanical energy into thermal energy. Therefore, the total mechanical energy of the system decreases. **(B) Decreases, because the gravitational potential energy of the system decreases.** - While it is true that the gravitational potential energy decreases as the block descends, this option does not account for the energy lost due to friction. The total mechanical energy decreases, but the reasoning is incomplete. **(C) Stays the same because gravitational potential energy is converted into kinetic energy because energy is always conserved.** - This statement is incorrect. While gravitational potential energy is converted into kinetic energy, the presence of friction means that not all of the potential energy is converted into kinetic energy. Some energy is lost to friction, so the total mechanical energy does not stay the same. **Conclusion:** The correct answer is **(A)**: The total mechanical energy of the block-Earth system decreases because a force external to the system (friction) is dissipating energy.