Question

explain what happens to the potential energy of a rock as it falls off the side of a cliff. the potential energy decreases as the kinetic energy increases. the kinetic energy decreases as the potential energy decreases. the kinetic energy decreases as the potential energy increases. the potential energy decreases as the kinetic energy decreases.

Explanation:

To solve this, we recall the principle of conservation of mechanical energy (potential + kinetic) in a system with no non - conservative forces (like air resistance, which we can ignore here for a falling rock). Potential energy (PE) is given by \(PE = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, and \(h\) is height). Kinetic energy (KE) is given by \(KE=\frac{1}{2}mv^{2}\) (where \(v\) is velocity). As the rock falls off the cliff, its height \(h\) decreases, so \(PE\) (which depends on height) decreases. At the same time, the rock speeds up (velocity \(v\) increases) because of gravity, so \(KE\) (which depends on velocity squared) increases. So we need to find the option that correctly states the relationship between the decreasing potential energy and the increasing kinetic energy.

Let's analyze each option:

• Option 1: "The potential energy decreases as the kinetic energy increases." This matches our analysis. As the rock falls, \(h\) (for PE) decreases and \(v\) (for KE) increases, so PE decreases and KE increases.
• Option 2: "The kinetic energy decreases as the potential energy decreases." This is incorrect. When PE decreases (rock falls), KE should increase (rock speeds up), not decrease.
• Option 3: "The kinetic energy decreases as the potential energy increases." This is incorrect. If PE were to increase (which it doesn't as the rock falls down), KE would decrease, but in our case, PE is decreasing and KE is increasing.
• Option 4: "The potential energy decreases as the kinetic energy decreases." This is incorrect. Both can't decrease as the rock falls; PE decreases and KE increases.

Answer:

A. The potential energy decreases as the kinetic energy increases.