Question

A fast-moving cyclist stops pedalling on reaching a hilly track. If he continues to move with the acquired energy, then assuming no loss of energy:

• A. his kinetic energy remains constant at all times.
• B. his potential energy remains constant at all times.
• C. his total mechanical energy continuously increases.
• D. his total mechanical energy remains constant.

Hint:

Whenever a problem states "no loss of energy," "smooth surface," or "no friction," immediately think of the Principle of Conservation of Mechanical Energy.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Mechanical energy is the sum of kinetic energy (\( K \)) and potential energy (\( U \)).
Step 2: Key Formula or Approach:
Total Mechanical Energy \( E = K + U \).
Step 3: Detailed Explanation:
The problem states "assuming no loss of energy," which means there is no friction or air resistance (conservative system).
As the cyclist moves up the hill, his velocity decreases (kinetic energy decreases) and his height increases (gravitational potential energy increases).
According to the Law of Conservation of Energy, the energy is merely transformed from kinetic to potential, but the total sum \( E \) stays the same.
Step 4: Final Answer:
The total mechanical energy remains constant.