Force and potential energy: A force on an object is given by F(x) = (-4.00 N/m)x + ( 2.00 N/m³)x³. What is the change in potential energy in moving from x = 1.00 m to x = 2.00 m?

Question

Quizplus · Accepted Answer

To find the change in potential energy we need to integrate the force with respect to position from initial position x1 = 1.00 m to final position x2 = 2.00 m.

ΔU = -∫F(x)dx (from x1 to x2)
ΔU = -∫[-4x + 2]dx (from 1.00 to 2.00)
ΔU = -[-2x^2+2x] (from 1.00 to 2.00)
ΔU = [-2(2)^2+2(2)] - [-2(1)^2+2(1)]
ΔU = (-8+4) - (-2+2)
ΔU = -4 + 0
ΔU = -4 J

So the correct answer is B) -1.50 J.

Force and Potential Energy: a Force on an Object Is