Final answer:
To find the change in length of the spring when a force of 22.0 N is applied to it, we use Hooke's Law (F = kΔx) to get Δx = 0.0978 m or 9.78 cm.
Step-by-step explanation:
We are given a spring of force constant 225 N/m and unstretched length 0.250 m. The spring is stretched until the forces applied on its ends increase to 22.0 N.
To find the change in length, we will use Hooke's Law which states that the force (F) exerted by a spring is directly proportional to the displacement (Δx) from its equilibrium position, where F = kΔx, with k being the force constant of the spring.
First, we solve for Δx using the formula:
F = kΔx
22.0 N = 225 N/m × Δx
Divide both sides of the equation by 225 N/m to solve for Δx:
Δx = 22.0 N / 225 N/m
Δx = 0.0978 m or 9.78 cm
The change in length of the spring is therefore 9.78 cm.