3.4 Conservation of Energy

E₁ = E₀ Correct. There are no external forces on the system, so the total mechanical energy does not change. The forms of energy change, but not the total amount.

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?

1. Decreases, because a force external to the system is dissipating energy

2. Decreases, because the gravitational potential energy of the system decreases

3. Stays the same because energy is always conserved

4. Stays the same because gravitational potential energy is converted into kinetic energy

Answer one

The frictional force dissipates energy and therefore the total mechanical energy in the block-Earth system decreases.

B

The Earth-block-spring system has both gravitational potential energy and spring potential energy, and the block-spring system only has spring potential energy because the Earth is not part of the system.

A skydiver with an open parachute falls toward the ground at a constant speed. Is the mechanical energy of the skydiver-Earth system constant as the skydiver descends? Why or why not?

1. Yes, because the kinetic energy of the skydiver remains constant.

2. Yes, because the net force on the skydiver-Earth system is zero.

3. No, because the potential energy of the system decreases, and the kinetic energy of the skydiver remains constant.

4. No, because the kinetic energy of the skydiver increases, and the potential energy of the system remains constant.

3. Mechanical energy of a system consists of the potential and kinetic energy of the system. The potential energy decreases as the skydiver descends and the kinetic energy remains constant, therefore the total mechanical energy decreases.

Correct. The asteroid-planet system has no external forces exerted on it, so the total mechanical energy is constant. As the asteroid moves closer to the planet, the kinetic energy of the asteroid increases because the gravitational potential energy of the asteroid-planet system is decreasing.

A block slides to the right across a rough horizontal surface. Which of the following correctly indicates whether the mechanical energy of the block-Earth system decreases or stays the same as the block slides, and provides a valid justification?

1. The mechanical energy decreases because energy is dissipated by the external force of friction.

2. The mechanical energy decreases because kinetic energy is converted to gravitational potential energy.

3. The mechanical energy remains constant because the block remains at the same vertical position throughout.

4. The mechanical energy remains constant because energy is always conserved.

Answer 1: Mechanical energy is only constant when no external forces do work on the system, and when no energy is converted to internal energy.