An object moving along the x axis is acted upon by a force Fx 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

An object moving along the x axis is acted upon by a force Fx 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

Quizplus · Accepted Answer

To find the work done by a force that varies along a path, we need to integrate the force with respect to position. In this case, we can use the formula: W = integral of Fx dx from x = 2 to x = 8.

Breaking up the integral into two parts, we have:

W = integral of Fx dx from x = 2 to x = 4 + integral of Fx dx from x = 4 to x = 8.

The first integral evaluates to 3 J (the area of the rectangle with base 2 and height 1.5), and the second integral evaluates to 27 J (the area of the trapezoid with bases 2 and 4 and height 4.5).

Adding them together, we get W = 30 J, which is positive because the force is in the same direction as the displacement. Therefore, the answer is (C) +30 J.

An Object Moving Along the X Axis Is Acted Upon