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 Question:
The question describes a cyclist moving up a hill without pedaling, and we must consider the situation under the assumption of "no loss of energy" (i.e., no friction or air resistance). We need to determine what happens to the cyclist's energy.
Step 2: Key Formula or Approach:
The Principle of Conservation of Mechanical Energy states that if there are no non-conservative forces (like friction or air resistance) doing work, the total mechanical energy of a system remains constant.
Total Mechanical Energy (TME) = Kinetic Energy (KE) + Potential Energy (PE).
\[ TME = KE + PE = \text{constant} \] \[ KE = \frac{1}{2}mv^2 \] \[ PE = mgh \] Step 3: Detailed Explanation:
The problem explicitly states to assume "no loss of energy". This means we can apply the Principle of Conservation of Mechanical Energy.
As the cyclist moves up the hilly track, his height (h) above the starting point increases.
- Because height (h) increases, his potential energy (\(PE = mgh\)) increases.
- Since the total mechanical energy (\(TME = KE + PE\)) must remain constant, and PE is increasing, his kinetic energy (\(KE = \frac{1}{2}mv^2\)) must decrease. This means his speed (v) decreases.
- Let's analyze the options:
(A) his kinetic energy remains constant: Incorrect. It decreases as he goes up.
(B) his potential energy remains constant: Incorrect. It increases as he goes up.
(C) his total mechanical energy continuously increases: Incorrect. It is conserved (remains constant).
(D) his total mechanical energy remains constant: Correct. This is the direct consequence of the conservation of energy principle.
Step 4: Final Answer:
According to the law of conservation of energy, with no energy loss, the total mechanical energy of the cyclist remains constant. The energy transforms from kinetic to potential energy as he moves uphill.