Question

10.) what happens to the total (mechanical) energy of the skater as time passes?

Explanation:

In a real - world scenario (like on a skate - park ramp), the skater experiences non - conservative forces such as friction and air resistance. Mechanical energy is the sum of kinetic energy ($KE=\frac{1}{2}mv^{2}$) and potential energy ($PE = mgh$ for gravitational potential energy). As time passes, the work done by non - conservative forces (friction and air resistance) is negative. According to the work - energy theorem, the work done by non - conservative forces ($W_{nc}$) is equal to the change in mechanical energy ($\Delta E_{mech}$), i.e., $W_{nc}=\Delta E_{mech}=E_{mech,final}-E_{mech,initial}$. Since $W_{nc}<0$ (because friction and air resistance oppose the motion), the total mechanical energy of the skater decreases over time. However, if we consider an ideal situation with no friction or air resistance (a theoretical case), the mechanical energy would remain constant because only conservative forces (gravity in the case of a skate - park) would be doing work, and for conservative forces, the mechanical energy is conserved. But in most practical cases with a skater, we have to account for non - conservative forces, so the total mechanical energy decreases as time passes.

Answer:

In a practical (real - world) situation with friction and air resistance, the total mechanical energy of the skater decreases as time passes. In an ideal (frictionless, no air resistance) situation, the total mechanical energy remains constant.