Question

the diagram shows a ball resting at the top of a hill. which statement best describes the energy in this system? the potential energy in the system is greatest at x. the kinetic energy in the system is greatest at x. total energy in the system decreases as the ball moves from x to y. total energy in the system increases as the ball moves from x to y.

Explanation:

Step1: Analyze potential energy

Potential energy \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, \(h\) is height). At the top of the hill (\(X\)), height \(h\) is maximum. So potential energy is maximum at \(X\).

Step2: Analyze kinetic energy

Kinetic energy \(K=\frac{1}{2}mv^{2}\). At \(X\), the ball is at rest (\(v = 0\)), so \(K=0\) at \(X\).

Step3: Analyze total energy

According to the law of conservation of energy, in the absence of non - conservative forces (assuming no air resistance, friction etc. for simplicity), total mechanical energy \(E=K + U\) is conserved. So total energy does not increase or decrease as the ball moves from \(X\) to \(Y\).

Answer:

The potential energy in the system is greatest at \(X\).