A block of mass 10 kg is moving along x-axis under the action of force F=5 x N. The work done by the force in moving the block from x=2 m to 4 m will be __________ J.

Solution

Physics sir · 3 steps

The force grows with x, so you cannot multiply force by distance. Integrate F dx from 2 to 4.

1. Variable force. Here F = 5x changes as the block moves, so work is the area under the F versus x graph. The mass of 10 kg plays no part in this calculation.

   W = ∫₂⁴ 5x dx = 5/2[x²]₂⁴ = 5/2(16 - 4)

2. Check by area. The graph is a straight line, so the area is a trapezium. The force goes from 10 N to 20 N, giving an average of 15 N over 2 m, which is 30 J.
3. So. W = 5/2 × 12 = 30 J.

The common slip: 40. Taking the force at x = 4 as constant gives 20 × 2 = 40 J. The force is only 20 N at the very end, so this overcounts the work.

The idea to keep. Whenever the force depends on position, work is ∫ F dx, which is the area under the force graph. Use F × d only when the force stays constant.

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