A force (3 x²+2 x-5) N displaces a body from x=2 m to x=4 m. Work done by this force is ________ J.

Solution

Physics sir · 4 steps

The force changes with x, so do not multiply force by distance. Integrate F dx between the limits.

1. Variable force. Here F depends on x, so W = F × d does not work. Add up F dx over every small piece of the path, which means integrating from x = 2 to x = 4.

   W = ∫₂⁴ (3x² + 2x - 5) dx = [ x³ + x² - 5x ]₂⁴

2. Upper limit. At x = 4: 64 + 16 - 20 = 60.
3. Lower limit. At x = 2: 8 + 4 - 10 = 2.
4. So. W = 60 - 2 = 58 J.

The common slip: 60. Evaluating the integral only at the upper limit x = 4 gives 60. Subtract the value at x = 2, which is 2.

The idea to keep. Whenever the force is given as a function of position, work is the area under the F–x curve: W = ∫ F dx between the start and end positions.

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