Final answer:
The force constant of the spring is calculated using Hooke's Law, which yields a force constant (spring constant) of 1225 N/m when a 10.0 kg load stretches the spring by 8.00 cm.
Step-by-step explanation:
To calculate the force constant of a spring, also known as the spring constant, we use Hooke's Law, which states that the force (F) needed to stretch or compress a spring by some distance (x) is proportional to that distance. The formula for Hooke's Law is given by: F = kx
where F is the force applied, k is the spring constant, and x is the displacement from the spring's equilibrium position.
In this case, we have a 10.0 kg load causing the spring to stretch 8.00 cm. First, we need to convert this stretch to meters (8.00 cm = 0.080 m) to be consistent with SI units. The force (F) applied by the load is the weight of the load, which is the mass (m) multiplied by the acceleration due to gravity (g), given by: F = mg
For a 10.0 kg load, the force in newtons (N) is: F = (10.0 kg)(9.80 m/s²) = 98.0 N
The spring constant k is then calculated by rearranging Hooke's Law: k = F/x
Substituting the values we have: k = 98.0 N / 0.080 m = 1225 N/m
Therefore, the force constant of the spring is 1225 N/m.