A ball of mass 100g falls from a height of 5m onto a concrete floor and rebounds to a height of 3m. Calculate the energy lost. (g = 10$ms^{-2}$)

Analyze the question: A ball falls from 5 m and rebounds to only 3 m. The difference in height means some mechanical energy was lost (as sound, heat and deformation) when it hit the floor.

Concept: Energy lost = loss in gravitational potential energy between the starting height and the rebound height.

Energy lost = mg(h₁ − h₂)

Solution:

• Mass: m = 100 g = 0.1 kg (always convert to kg)
• g = 10 m/s²
• h₁ = 5 m, h₂ = 3 m

Initial PE = mgh₁ = 0.1 × 10 × 5 = 5 J

PE at rebound height = mgh₂ = 0.1 × 10 × 3 = 3 J

Energy lost = 5 − 3 = 2 J

Common mistakes to avoid:

• Forgetting to convert 100 g to 0.1 kg. Using 100 would give 2000 J (option E), which is a trap.
• Using only one height (5 m or 3 m) instead of the difference.

Exam tip: Whenever mass is given in grams, convert to kg first. For bouncing-ball questions, energy lost = mg × (drop height − rebound height). Here that is 1 N × 2 m = 2 J, since the ball's weight is 0.1 × 10 = 1 N.