Final answer:
The force constant of the spring is 122.5 N/m. The total stretched length of the spring when its restoring force is 3F is 2.45 m or 245 cm. The compressed length of the spring when the restoring force is 2F is 1.63 m or 163 cm.
Step-by-step explanation:
To calculate the force constant of the spring, we can use Hooke’s Law: F = kx, where F is the force exerted by the spring, k is the force constant, and x is the displacement from the unstretched length of the spring.
Given that the spring stretches 8.0 cm (0.08 m) for a 10.0 kg load, we can use the formula to find the force constant: F = kx. Rearranging the formula to solve for k, we get k = F / x. Plugging in the values, k = (10.0 kg * 9.8 m/s^2) / 0.08 m = 122.5 N/m.
To find the total stretched length of the spring when its restoring force is 3F, we can equate the force constant and displacement using the formula: F = kx. Rearranging the formula to solve for x, we get x = F / k. Substituting in the values, x = 3F / k = (3 * 10.0 kg * 9.8 m/s^2) / 122.5 N/m = 2.45 m.
Therefore, the total stretched length of the spring is 2.45 m or 245 cm.
To find the compressed length when the restoring force is 2F, we can use the same formula, F = kx. Rearranging the formula to solve for x, we get x = F / k. Substituting in the values, x = 2F / k = (2 * 10.0 kg * 9.8 m/s^2) / 122.5 N/m = 1.63 m.
Therefore, the compressed length of the spring is 1.63 m or 163 cm.