Gravitational Potential Energy: When Is It Present?

Gravitational potential energy is a fundamental concept in physics that describes the energy an object possesses due to its position in a gravitational field. It's the "stored" energy that can be converted into kinetic energy (the energy of motion) when an object is allowed to fall or move closer to a source of gravity. So, when is gravitational potential energy present? It's present whenever an object has the potential to move due to gravity. This means it needs to be elevated above a reference point, or more broadly, at a certain distance from a gravitational source.

Let's break down the scenarios to understand this better. Gravitational potential energy, often denoted as PE or U, is typically calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s² on Earth), and h is the height of the object above a chosen reference point. The key here is the 'height' (h). Without a difference in height (or more generally, a difference in position within a gravitational field), there's no gravitational potential energy to speak of. This energy is relative; we define a 'zero' point for potential energy, and the value depends on the object's position relative to that zero. Often, the ground is chosen as the zero reference point, but it could be any level.

Now, let's consider the given options to see which scenario best illustrates the presence of gravitational potential energy. We're looking for a situation where an object's position allows for the possibility of gravitational influence leading to motion. It's about the stored energy due to its height, not necessarily the energy of motion itself (which is kinetic energy).

A. A rabbit looks out of a hole in the ground.

This scenario directly addresses the concept of height relative to a reference point. Imagine the rabbit is at the bottom of the hole. If the ground level is our reference point (h=0), then the rabbit is at a negative height, meaning it has negative gravitational potential energy relative to the ground. Alternatively, if we consider the ground above the rabbit as the reference point, then the rabbit is at a certain height below that reference, and thus possesses gravitational potential energy. More commonly, if the rabbit is looking out of a hole, it implies the rabbit is below ground level. Therefore, relative to the ground surface, the rabbit is at a certain depth. This depth, if considered as a negative height, means it has negative gravitational potential energy. However, if the rabbit is looking out and up towards ground level, then the rabbit itself is below ground level. If we set the ground level as our zero potential energy reference, the rabbit has negative potential energy because it's below the reference. If the rabbit is at the ground level, looking out, its potential energy relative to that level is zero. The wording is a bit ambiguous, but the core idea is the rabbit's position relative to the ground. Crucially, if the rabbit is below the surface, it has potential energy relative to the surface. This potential energy is stored and could be converted to kinetic energy if the rabbit were to leap upwards out of the hole.

B. A squirrel runs up the trunk of a tree.

This is a classic example of where gravitational potential energy is increased. As the squirrel runs up the trunk of a tree, its height (h) above the ground increases. According to the formula PE = mgh, an increase in h means an increase in gravitational potential energy. The squirrel is doing work against the force of gravity to gain this potential energy. This stored energy is present because the squirrel is now at a higher elevation than it was at the base of the tree. If the squirrel were to fall from a branch, this stored potential energy would be converted into kinetic energy as it accelerates downwards. So, yes, gravitational potential energy is present and is actively being increased as the squirrel ascends. The squirrel's higher position means it has more potential energy than if it were on the ground.

C. A deer runs across a grassy field.

Consider a deer running across a grassy field. While a field might not be perfectly flat, for the most part, the change in height over the distance the deer runs is likely negligible. If we assume the field is relatively flat, then the height (h) of the deer above the ground remains almost constant. Since PE = mgh, and m, g, and h are all approximately constant, the gravitational potential energy of the deer is also approximately constant. It's not gaining or losing significant potential energy as it runs horizontally. The energy being primarily used and converted in this scenario is kinetic energy (the energy of motion), and perhaps some thermal energy due to friction and muscle activity. Therefore, this scenario is not the best illustration of the presence or change of gravitational potential energy.

D. A cat pins a mouse to the ground.

In this scenario, the cat has successfully captured the mouse. The phrase "pins a mouse to the ground" implies that both the cat and the mouse are at ground level, or very close to it. If we consider the ground as our reference point (h=0), then both the cat and the mouse have a height of approximately zero. Consequently, their gravitational potential energy relative to the ground is approximately zero (PE = mg(0) = 0). There is no significant height difference to create a substantial amount of gravitational potential energy in this situation. The energy involved here might be related to forces, pressure, and potentially kinetic energy if the pinning action was rapid, but not gravitational potential energy due to significant elevation.

Conclusion: Which Scenario Best Represents Gravitational Potential Energy?

After analyzing each option, the most fitting scenario for the presence of gravitational potential energy, and importantly, its increase, is B. A squirrel runs up the trunk of a tree.

Gravitational potential energy is defined by an object's position within a gravitational field, specifically its height above a reference point. As the squirrel ascends the tree, it gains height, and therefore gains gravitational potential energy. This stored energy is a direct consequence of its elevated position. Option A involves a rabbit below ground, which has negative potential energy relative to the surface, a valid scenario. However, option B illustrates the gain of potential energy due to elevation, which is often the primary focus when introducing the concept. Options C and D represent situations where the change in height is negligible, meaning the gravitational potential energy remains relatively constant or is near zero.

Understanding gravitational potential energy is crucial in many areas of physics, from simple projectile motion to complex celestial mechanics. It's the energy waiting to be unleashed by gravity. For further reading on physics principles, you can explore resources from NASA or HyperPhysics.