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

The work done by a force is given by the formula W = ∫Fdx, where the integral is evaluated between the limits of initial and final positions. In this case, the force varies with position, so we need to evaluate the integral as follows:

W = ∫F(x)dx from x = 2 m to x = 8 m

= ∫(10 - x)dx from x = 2 m to x = 8 m

= [10x - 0.5x^2] from x = 2 m to x = 8 m

= (10(8) - 0.5(8)^2) - (10(2) - 0.5(2)^2)

= 80 - 10 - 20 + 1

= +51 J

Since the work done is positive, it means that the force is doing work on the object, which is in the direction of the displacement. The correct option is C) +30 J, which is the closest to the calculated value.

An Object Moving Along the X Axis Is Acted Upon