Final answer:
To find the restoring force of a spring stretched from its natural length, one would use Hooke's Law. The spring constant needed to use this law can be determined from a scenario where the spring's displacement and the force due to a mass are known.
Step-by-step explanation:
The student is asking about the restoring force exerted by a spring when it is stretched from its natural length. To calculate this force, one would typically use Hooke's Law, which states that the force (F) exerted by the spring is equal to the negative spring constant (k) times the displacement (x) from its equilibrium position: F = -kx. However, the value of k is not provided directly in the question, but it can be derived from the given scenario where the spring stretches 8.00 cm for a 10.0 kg load.
The force constant (k) can be calculated using the weight of the load (mg) and the displacement (x) by rearranging Hooke's Law to k = mg/x. For a 10.0 kg mass, the gravitational force (mg) acting on it is 10.0 kg × 9.80 m/s². The displacement (x) is 8.00 cm, which should be converted to meters (0.08 m). Therefore, k = (10 kg × 9.80 m/s²) / 0.08 m. After calculating k, we could then use it to find the restoring force (F) for a different displacement, which in this case is the stretch from 8.0 cm to 9.0 cm.