A body of mass 5 kg is moving with a momentum of 10 kg ms⁻¹. Now a force of 2 N acts on the body in the direction of its motion for 5 s. The increase in the Kinetic energy of the body is ___________ J.

Solution

Physics sir · 3 steps

The force adds an impulse to the momentum. Find the new momentum, then use K = p²/2m before and after.

1. Impulse adds momentum. The force acts along the motion, so the impulse adds directly to the momentum: Δ p = F t = 2 × 5 = 10 kg m s⁻¹. The new momentum is p₂ = 10 + 10 = 20 kg m s⁻¹.

   K = p²/2m

2. Kinetic energy each time. Before: K₁ = 10²/(2 × 5) = 10 J. After: K₂ = 20²/(2 × 5) = 40 J.
3. So. The increase in kinetic energy is K₂ - K₁ = 40 - 10 = 30 J.

The common slip: 10. Putting the change in momentum straight into the formula, (Δ p)²/2m = 100/10, gives 10 J. Kinetic energy depends on p², so you must subtract p₁² from p₂², not square Δ p.

The idea to keep. When a force acts for a given time, think impulse first: F t changes the momentum. Kinetic energy goes as p², so find it at the start and at the end, then subtract.

Answer from the NTA final answer key. Solution by PrepWiser.