Question

a roller skater starts from rest at the top of a hill and rolls down, eventually reaching the bottom. if the total mechanical energy (me) at the top is 10,000 j (ignoring friction), the total me at the bottom is

Explanation:

Step1: Recall the law of conservation of mechanical energy

In the absence of non - conservative forces (like friction, which is ignored here), the total mechanical energy \(ME = KE+PE\) is conserved.

Step2: Apply the law to the skater's motion

At the top of the hill, the skater has only potential energy (\(KE = 0\) as \(v = 0\)). At the bottom of the hill, the skater has only kinetic energy (\(PE=0\) if we take the bottom as the reference level for potential energy). But since \(ME = KE + PE\) and mechanical energy is conserved (\(\Delta ME=0\)), the total mechanical energy at the bottom is the same as at the top.

Answer:

\(10000\space J\)