Question

When a falling object impacts the earth and comes to rest, what happens to its kinetic and potential energies?

Short answer

Kinetic and potential energies transform into sound, heat, and deformation energy upon impact.

Step-by-step solution

Understand Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. When the object is falling, it has kinetic energy given by the formula \(KE = \frac{1}{2}mv^2\), where \(m\) is the mass of the object and \(v\) is its velocity.

Understand Potential Energy

Potential energy is the energy an object possesses due to its position in a gravitational field. For a falling object, its potential energy is given by \(PE = mgh\), where \(m\) is the mass, \(g\) is the acceleration due to gravity, and \(h\) is the height.

Impact with the Earth

When the object impacts the Earth and comes to rest, its velocity \(v = 0\), so its kinetic energy becomes zero. At the same time, its height \(h = 0\), so its potential energy also becomes zero.

Energy Transformation

The initial kinetic and potential energies of the object are transformed into other forms of energy, such as sound, heat, deformation energy (as the object may change shape), and sometimes even light (if the impact is sufficiently energetic). Energy is conserved but changes from one form to another.

Key concepts

kinetic energy

Kinetic energy is the energy an object possesses due to its motion. Whenever an object is moving, it has kinetic energy. This energy can be calculated using the formula: \(KE = \frac{1}{2}mv^2\).
Here, \(m\) stands for mass and \(v\) stands for velocity. So, the faster an object moves or the more massive it is, the greater its kinetic energy.
Take a falling object, for example. As it falls, its speed increases, and so does its kinetic energy, until it hits the ground. At the moment immediately before impacting the ground, the object has maximum kinetic energy because it is at its highest speed.

potential energy

Potential energy is the stored energy an object has because of its position. When an object is raised above the ground level, it has gravitational potential energy.
This energy is given by the formula \(PE = mgh\), where \(m\) stands for mass, \(g\) is the acceleration due to gravity (approx. 9.8 m/s² on Earth), and \(h\) is the height above the ground.
For a falling object, this is the energy it has before it starts falling. As the object falls, its height decreases, and so does its potential energy, converting bit by bit into kinetic energy.

energy conservation

Energy conservation is a key principle in physics. It means that energy cannot be created or destroyed, only transformed from one form to another.
In the case of a falling object, its potential energy converts to kinetic energy as it descends. When the object finally hits the ground, its movement stops, so its kinetic energy is zero.
But, the energy doesn't disappear! It has merely transformed into other forms:

• Sound (the noise of the impact)
• Heat (the object and the ground might warm up)
• Deformation energy (the object or the surface might change shape)
• In rare cases, even light (if the impact is very energetic)

impact energy transformation

When an object impacts the ground and comes to rest, its kinetic and potential energies don't just vanish. Instead, they're transformed into other forms of energy.
For example:

• Sound: The sound you hear when the object hits the ground is a result of energy conversion.
• Heat: The energy might make the area of impact slightly warmer.
• Deformation: If the object is soft or the surface is malleable, you might see dents or changes in shape.
• Light: Sometimes, with very powerful impacts, you might see sparks or flashes of light caused by the energy transformation.

This shows how versatile energy transformation can be and how energy conservation works in real-world scenarios.