You ride your bicycle down a hill, maintaining a constant speed the entire time.
1. As you ride, does the gravitational potential energy of the Earth-bike-rider system increase, decrease, or stay the same?
2. Does the kinetic energy of you and your bike increase, decrease, or stay the same?
3. Has the mechanical energy of this system increased, decreased, or remained the same?
gpe decreases as you go down. It is max at the top of the hill.
To answer these questions, we need to understand the concepts of gravitational potential energy, kinetic energy, and mechanical energy.
1. Gravitational potential energy (GPE) is the energy associated with an object's position in a gravitational field. As you ride your bicycle down a hill, your height above the ground decreases. Since GPE depends on the height, it decreases as you descend. Therefore, the gravitational potential energy of the Earth-bike-rider system decreases.
2. Kinetic energy (KE) is the energy associated with an object's motion. In this case, as you ride down the hill, your speed remains constant. Since KE depends on the square of the velocity, and the velocity is constant, the kinetic energy of you and your bike stays the same.
3. Mechanical energy is the sum of potential energy and kinetic energy for a system. In this case, the gravitational potential energy decreases (as discussed in question 1), but the kinetic energy remains constant (as discussed in question 2). Thus, the mechanical energy of the system decreases due to the decrease in gravitational potential energy alone.
So, to summarize:
1. The gravitational potential energy of the Earth-bike-rider system decreases.
2. The kinetic energy of you and your bike stays the same.
3. The mechanical energy of the system decreases.