Work Done by a Variable Force?

📌 CONCEPT: The work done by a variable force is calculated using the graphical method or by integrating the expression of force with respect to displacement.

📐 RULE / FORMULA: The work done (W) is given by the integral of force (F) with respect to displacement (x), i.e., W = ∫F dx. For a uniformly varying force, we can find the average force (F_avg) and multiply it by the displacement (d) to get the work done, i.e., W = F_avg * d.

💡 WORKED EXAMPLE: Consider a body moved from x = 0 to x = 2 m by a force varying uniformly from 0 N to 2000 N. The average force (F_avg) is (0 + 2000) / 2 = 1000 N. Therefore, the work done (W) is W = F_avg * d = 1000 N * 2 m = 2000 J.

⚠️ COMMON MISTAKE: Students often forget to take the average force into account when calculating work done by a variable force, which can lead to incorrect results.