Question

What work is required to stretch a spring of spring constant 40 N/m from x = 0.20 m to 0.25 m? (Assume the unstretched position is at x = 0.)

A) 0.45 J

B) 0.80 J

C) 1.3 J

D) 0.050 J

Answer 1

The work required to stretch a spring with a spring constant of 40 N/m from 0.20 m to 0.25 m is calculated using the spring work formula, resulting in 0.45 J.

Step-by-step explanation:

The work required to stretch a spring can be calculated using the formula for the work done on a spring: W = 1/2 k (x² - x₀²), where W is the work, k is the spring constant, x is the final stretch, and x₀ is the initial stretch. In this case, with a spring constant of 40 N/m and changing the spring's stretch from 0.20 m to 0.25 m, the work done is:

W = 1/2 × 40 N/m × ((0.25² - 0.20²) m²)

W = 20 × (0.0625 - 0.04)

W = 20 × 0.0225

W = 0.45 J

Therefore, the work required is 0.45 J.