Question

law of conservation of energy (developing)
practice it!
select the statement(s) that accurately describe what happens to the ball as it rolls down the hill.
when the ball reaches the bottom of the hill, it will not have any more gravitational potential energy.
potential and kinetic energy transform into other forms of energy as the ball rolls down the hill.
kinetic energy increases as potential energy decreases.
potential energy is stored in the ball at the top of the hill until it is acted upon by another force and starts rolling, transforming the potential energy into kinetic energy.
the ball sitting on the top of the hill has the greatest amount of kinetic energy.

Explanation:

• Gravitational potential energy depends on height. At the bottom of the hill (height = 0 relative to the bottom), gravitational potential energy is 0. So, "When the ball reaches the bottom of the hill, it will not have any more gravitational potential energy" is correct.
• As the ball rolls down, due to friction (a non - conservative force), some potential and kinetic energy is transformed into other forms like heat (thermal energy) and sound. So, "Potential and kinetic energy transform into other forms of energy as the ball rolls down the hill" is correct.
• By the law of conservation of mechanical energy (neglecting non - conservative forces initially, but even with them, the general trend holds), as the ball rolls down (height decreases, so potential energy \(U = mgh\) decreases) and speed increases (kinetic energy \(K=\frac{1}{2}mv^{2}\) increases). So, "Kinetic energy increases as potential energy decreases" is correct.
• At the top of the hill, the ball is at rest (assuming it starts from rest), so kinetic energy is 0. The potential energy is stored as gravitational potential energy. When a force (like the component of gravitational force along the slope) acts on it and it starts moving, potential energy is transformed into kinetic energy. So, "Potential energy is stored in the ball at the top of the hill until it is acted upon by another force and starts rolling, transforming the potential energy into kinetic energy" is correct.
• At the top of the hill (assuming it starts from rest), kinetic energy \(K = 0\) (since \(v = 0\)), so "The ball sitting on the top of the hill has the greatest amount of kinetic energy" is incorrect.

Answer:

• When the ball reaches the bottom of the hill, it will not have any more gravitational potential energy.
• Potential and kinetic energy transform into other forms of energy as the ball rolls down the hill.
• Kinetic energy increases as potential energy decreases.
• Potential energy is stored in the ball at the top of the hill until it is acted upon by another force and starts rolling, transforming the potential energy into kinetic energy.