Final answer:
The elastic potential energy of a compressed spring can be calculated using the formula (1/2)kx^2, where k is the spring constant and x is the displacement of the spring. The change in gravitational potential energy can be calculated using the formula mgh, where m is the mass, g is the acceleration due to gravity, and h is the change in height. The distance along the incline can be calculated using trigonometry.
Step-by-step explanation:
The elastic potential energy of a compressed spring is given by the formula:
PEelastic = (1/2)kx2
Where PEelastic is the elastic potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
To determine the change in gravitational potential energy of the block-Earth system, we need to calculate the change in height of the block as it moves from the release point to its highest point on the incline. The formula to calculate this change in potential energy is:
PEgravitational = mgh
Where PEgravitational is the change in gravitational potential energy, m is the mass of the block, g is the acceleration due to gravity, and h is the change in height.
The distance from the release point to the highest point on the incline can be calculated using trigonometry. If we know the height of the incline and the angle of the incline, we can use the trigonometric functions to find the distance along the incline.