Question

A spring has a natural length of 14 cm. If a 23-N force is required to keep it stretched to a length of 20 cm, how much work W is required to stretch it from 14 cm to 17 cm? (Round your answer to two decimal places.)

Answer 1

1.78 J

Step-by-step explanation:

Find the spring coefficient using Hooke's law:

F = k Δx

23 N = k (0.20 m − 0.14 m)

k = 383.33 N/m

The work is the change in energy:

W = PE₂ − PE₁

W = ½ kx₂² − ½ kx₁²

W = ½ k (x₂² − x₁²)

W = ½ (383.33 N/m) ((0.17 m)² − (0.14 m)²)

W = 1.78 J