Final answer:
No, total mechanical energy is not conserved as the skier accelerates downhill on their skis due to the conversion of potential energy into kinetic energy and presence of non-conservative forces such as air resistance or friction.
Step-by-step explanation:
In the case of a skier accelerating downhill on their skis, the total mechanical energy (TME) is not conserved. This is because as the skier moves downhill, the potential energy decreases while the kinetic energy increases. Additionally, there may be non-conservative forces such as air resistance or friction acting on the skier.
For example, if a skier starts from rest and accelerates downhill, their initial potential energy will be converted into kinetic energy as they gain speed. The opposite is true for a skier moving uphill, where potential energy is converted into kinetic energy as the skier moves against gravity.
Therefore, in the case of a skier accelerating downhill, TME is not conserved due to the conversion of potential energy to kinetic energy and the presence of non-conservative forces.