Final answer:
To determine the force constant of the spring, use Hooke's law. The force constant can be calculated using the formula k = -F/x. In this case, the spring stretches 8.00 cm for a 10.0 kg load.
Step-by-step explanation:
To determine the force constant of the spring, we can use Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The formula for Hooke's law is F = -kx, where F is the restoring force, k is the force constant, and x is the displacement.
In this case, we have a 10.0 kg load that stretches the spring 8.00 cm. We need to convert the displacement to meters, so 8.00 cm is equal to 0.08 m. The weight of the load can be calculated using the formula w = mg, where m is the mass and g is the acceleration due to gravity.
Plugging in the values, we have w = (10.0 kg)(9.80 m/s²) = 98 N. Since the restoring force is equal to the weight of the load, we have F = 98 N. We can rearrange Hooke's law to solve for the force constant, so k = -F/x. Substituting the values, we have k = -(98 N)/(0.08 m) = -1225 N/m.