Final answer:
The question relates to the field of Physics, specifically to the interaction between a mass resting on a vertical spring and the forces at play when the system reaches equilibrium.
Step-by-step explanation:
Understanding Mass and Spring Systems in Physics
A 0.530 kg block sits at rest on a vertical spring with a spring constant of 80.0 N/m. In this scenario, the spring provides a restoring force that pushes upwards while gravity pulls the mass downwards. When the block and spring system reaches equilibrium, the spring is compressed by an amount that balances the gravitational force on the block.
The force exerted by the spring can be calculated using Hooke's Law, F = kx, where k is the spring constant and x is the displacement from the spring's resting length. The gravitational force on the block is given by F = mg, where m is the mass of the block and g is the acceleration due to gravity (9.8 m/s2).
At equilibrium, the force of the spring equals the gravitational force, enabling us to solve for the displacement: kx = mg. By plugging in the given values, we can determine the amount the spring is compressed under the mass of the block.