A bike rider does work to get the top of a mountain How could you use law conservation energy describe his trip down mountain?

When a bike rider reaches the top of a mountain, mechanical energy( in the form of kinetic and potential energy) is transformed into internal energy( primarily due to friction) and sound energy( due to air resistance) during the descent. The bike rider does work in reaching the mountaintop, but the energy is dissipated during the trip down through friction and air resistance, meaning the rider cannot coast down to recover the same amount of energy exerted.

Using the law of conservation energy, we can understand the bike rider's trip down the mountain:

1. Initial Energy at Mountaintop: At the start of the descent, the bike rider possesses maximum potential energy (PE) due to their height above the ground and kinetic energy (KE) from their initial speed gained while pedaling. The total mechanical energy (ME) is the sum of these:

ME = PE + KE

2. Conversion during Descent: As the rider begins coasting down, potential energy is converted into kinetic energy. However, friction between the tires and road, as well as air resistance, causes some of this energy to be lost as internal energy and sound energy:

lost ME = internal energy + sound energy

3. Gradual Loss of Velocity: Due to energy loss, the rider experiences a gradual decrease in velocity as they descend. The mechanical energy decreases, and the energy dissipated increases.

4. Conservation of Energy: According to the law of conservation energy, the total energy in a closed system remains constant. In this case, the closed system is the bike rider and surroundings. The initial mechanical energy (ME) invested to reach the mountaintop is eventually all transformed into internal energy and sound energy, leaving the rider with lower kinetic energy and potential energy at the bottom.

5. Limited Recoverability: While some energy can be recovered by pedaling during the descent, it is impossible to recover all the energy initially invested in reaching the mountaintop. Irrecoverable energy is lost due to friction and air resistance.

In summary, the bike rider's trip down the mountain illustrates the principle of energy conservation. The mechanical energy from the initial ascent is dissipated into various forms of non-recoverable energy, resulting in a gradual loss of velocity during descent.