You take your backpack out of the car, hike to the top of a nearby mountain, and return with your backpack to your car at the bottom. Have you changed the amount of your backpack's mechanical energy?

No. Not when you return to the same elevation.

To determine whether the amount of mechanical energy of the backpack has changed, we need to understand what factors contribute to mechanical energy.

Mechanical energy is the sum of an object's potential energy and kinetic energy. Potential energy is associated with the position or state of an object, while kinetic energy is associated with the object's motion.

In the given scenario, when you take your backpack out of the car and hike to the top of the mountain, the backpack gains gravitational potential energy. As you lift the backpack from the ground, you are doing work against gravity, increasing its potential energy. At this point, the backpack has both gravitational potential energy and zero kinetic energy since it is not in motion.

When you return with your backpack to your car at the bottom of the mountain, the backpack loses some of its gravitational potential energy as it descends. This loss of potential energy is converted into kinetic energy because the backpack starts to move due to the force of gravity. The backpack now has both kinetic energy from its motion and reduced gravitational potential energy.

Therefore, as you hike to the top of the mountain and return to your car, the mechanical energy of the backpack changes. At the top of the mountain, the backpack has high potential energy and no kinetic energy, while at the bottom of the mountain, the backpack has lower potential energy and non-zero kinetic energy.

In conclusion, the mechanical energy of the backpack changes throughout the hiking process due to the conversion between potential and kinetic energy.