Final answer:
The spring will stretch approximately 12.96 cm when the mass is increased to 530.0 g.
Step-by-step explanation:
To find how much the spring will stretch when a new mass is added, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement. The formula is given by F = kx, where F is the force, k is the force constant of the spring, and x is the displacement.
We can rearrange the formula to solve for x: x = F/k. Using the given values, the original force F is 250.0 g times the acceleration due to gravity (9.8 m/s^2), and the original displacement x is 6.00 cm. Therefore, the original force is (250.0 g) * (9.8 m/s^2) = 2450.0 g m/s^2, and the force constant k is given by k = F/x = (2450.0 g m/s^2)/(6.00 cm). Now we can plug in the new mass and solve for the new displacement.
Calculating the new force F' = (530.0 g) * (9.8 m/s^2) = 5194.0 g m/s^2, and using the formula x = F'/k, we find the new displacement to be x = (5194.0 g m/s^2)/(2450.0 g m/s^2 / 6.00 cm) = 12.96 cm. Therefore, the spring will stretch by approximately 12.96 cm when the mass is increased to 530.0 g.