Answer:
Step-by-step explanation:
The potential energy of a spring, U, is given by the equation U = ½k(y - y₀)², where k is the spring constant, y is the displacement from the equilibrium position, and y₀ is the equilibrium position.
1. The equation U = ½k(y - y₀)² represents the potential energy of a spring because it takes into account the displacement of the spring from its equilibrium position. The factor of ½ in front of the equation comes from the integration of the force equation for a spring.
2. The term (y - y₀) represents the displacement of the spring from its equilibrium position. By squaring this term, we ensure that the potential energy is always positive, regardless of the direction of displacement.
3. On the other hand, the expression U = (y² - y₀²) does not accurately represent the potential energy of a spring. This expression does not take into account the displacement of the spring and only considers the squared value of the displacement term. It does not capture the behavior of a spring and does not reflect the physics behind the potential energy stored in a spring.
Regarding the change in kinetic energy, AK = m(v² - v₀²), the equation is correct. The term (v² - v₀²) represents the change in velocity squared, which is proportional to the change in kinetic energy. This equation considers the difference between the final velocity squared (v²) and the initial velocity squared (v₀²) to calculate the change in kinetic energy.
In summary, the potential energy of a spring is given by U = ½k(y - y₀)² because it accurately represents the displacement of the spring from its equilibrium position. The expression U = (y² - y₀²) does not capture the physics of a spring and does not reflect the potential energy stored in it. For the change in kinetic energy, AK = m(v² - v₀²), the equation is correct as it considers the change in velocity squared.