Questions: Conservation of Mechanical Energy

Question 1

A 3 kg ball is released from rest at a height of 5 m (g = 10 m/s²). Assuming no air resistance, what is its speed just before it hits the ground?

• A. 5 m/s
• B. 10 m/s
• C. 15 m/s
• D. 50 m/s

Answer: (B)

Setting PE_i = KE_f: mgh = ½mv². The mass cancels, giving v = sqrt(2gh) = sqrt(2 × 10 × 5) = sqrt(100) = 10 m/s. Note that the mass does not matter — all objects dropped from the same height reach the same speed in the absence of air resistance.

Question 2

When a block slides down a ramp with friction, the total mechanical energy (KE + PE) of the block is conserved.

• T. True
• F. False

Answer: False

Friction is a nonconservative force that converts mechanical energy into thermal energy. The block's KE + PE decreases as it slides. The correct statement is that the *total energy* of the system (mechanical + thermal) is conserved — but mechanical energy alone is not.

Question 3

A roller coaster car starts from rest at a height of 20 m. Using energy conservation (no friction), explain why its speed at the bottom does not depend on its mass.

Model answer: Setting initial PE equal to final KE: mgh = ½mv². When you solve for v, the mass m appears on both sides and cancels, giving v = sqrt(2gh). Speed at the bottom depends only on the height drop and gravitational acceleration, not on the mass of the car.

This is a direct consequence of both kinetic energy (½mv²) and gravitational potential energy (mgh) being proportional to mass. The mass factor cancels algebraically, so energy conservation predicts the same final speed for any mass dropped from the same height — consistent with Galileo's observation that objects of different mass fall at the same rate.