Final answer:
To find the spring potential energy before the ball is released when a spring is fully compressed, use the formula U = 1/2kx². For a 100 N/m spring compressed by 12 cm, the energy stored is 0.72 J.
Step-by-step explanation:
The spring potential energy of a ball just before it is released, when the spring is fully compressed, can be calculated using the formula PE = (1/2)kx^2, where PE is the potential energy, k is the spring constant, and x is the displacement of the spring.
To calculate the amount of spring potential energy stored in a compressed spring just before it is released, we can use the formula U = 1/2kx², where U is the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position. For a spring with a spring constant of 100 N/m compressed by 12 cm (0.12 m), the potential energy is calculated as:
U = 1/2 (100 N/m) (0.12 m)²
U = 0.5 × 100 × (0.12)²
U = 0.5 × 100 × 0.0144
U = 0.5 × 1.44
U = 0.72 Joules
Therefore, the spring potential energy is 0.72 J just before the ball is released.