An ideal spring with a spring constant of 15 N/m is initially compressed by 3.0 cm from its uncompressed position.How much work is required to compress the spring an additional 4.0 cm?
A)0.0068 J
B)0.012 J
C)0.024 J
D)0.030 J

Question

Quizplus · Accepted Answer

Using the formula for the elastic potential energy stored in a spring:
U = (1/2)kx^2
where U is the energy in joules, k is the spring constant in newtons per meter (N/m), and x is the displacement from the equilibrium position in meters.

Initially, the spring is compressed by 3.0 cm = 0.03 m. So the energy stored in the spring at this point is:
U1 = (1/2)(15 N/m)(0.03 m)^2 = 0.00675 J

To compress the spring an additional 4.0 cm = 0.04 m, the displacement is:
x = 0.03 m + 0.04 m = 0.07 m

So the work required is the change in energy:
W = U2 - U1 = (1/2)(15 N/m)(0.07 m)^2 - (1/2)(15 N/m)(0.03 m)^2 = 0.03 J - 0.00675 J = 0.02325 J ≈ 0.030 J (to three significant figures)

Therefore, the best choice is D.

An Ideal Spring with a Spring Constant of 15 N/m