An object moving along the x axis is acted upon by a force F_x that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m? A) −10 J B) +10 J C) +30 J D) −30 J E) +40 J

Question

Quizplus · Accepted Answer

To find the work done by this force, we need to integrate the force with respect to x over the distance the object travels. ∫F_x dx from x = 2 m to x = 8 m = ∫(2x - 5) dx from x = 2 m to x = 8 m = [(x^2 - 5x)] from x = 2 m to x = 8 m = ((8^2 - 5(8)) - (2^2 - 5(2))) = (40 - (-5)) = +45 J The work done by the force is positive (+45 J), which means that the force is doing work on the object and increasing its kinetic energy. Therefore, the correct answer is (C) +30 J.

An Object Moving Along the X Axis Is Acted Upon