Final answer:
The wire’s spring constant can be found using Hooke’s Law. The weight's force is converted to Newtons and the stretch to meters, and then the force is divided by the stretch, resulting in a spring constant of 223,929 N/m.
Step-by-step explanation:
To determine the wire's spring constant in N/m, we use Hooke's Law which relates the force exerted on a spring to the distance it stretches. Given that a 25.5 kg weight causes the wire to stretch by 1.12 mm, we can calculate the spring constant (k) with the formula k = F / Δx, where F is the force in Newtons (N) due to the weight, and Δx is the stretch in meters (m).
First, we convert the weight from kilograms to Newtons by multiplying by the acceleration due to gravity (9.8 m/s²): F = 25.5 kg × 9.8 m/s².
The stretch must also be converted from millimeters to meters: Δx = 1.12 mm = 0.00112 m.
Substituting these values into the formula yields the spring constant k:
k = 250.9 N / 0.00112 m = 223,929 N/m.