Question

Follow the evolution of energy exchanges for a wad of clay that you throw high into the air. Describe what is happening as the clay moves upward, as it reaches its apex, as it falls back down, and finally hits the ground with a thud. Where does the initial energy you put into the clay end up?

Short answer

Answer: The three types of energy involved in the trajectory of a wad of clay thrown into the air are kinetic energy (KE), potential energy (PE), and internal energy (IE). The initial energy put into the clay, which starts as kinetic energy, ends up as internal energy within the clay due to the deformation and slight heating when it hits the ground.

Step-by-step solution

Identify the energy types involved in the problem

To follow the energy exchanges in this exercise, we'll need to consider three types of energy: - Kinetic energy (KE): The energy due to the clay's motion - Potential energy (PE): The energy due to the clay's position in the gravitational field - Internal energy (IE): The energy stored within the clay due to molecular bonds and interactions (associated with the clay deformation when it hits the ground)

As the clay moves upward

When the clay is thrown upward, its kinetic energy (KE) is converted into potential energy (PE) due to gravity. The kinetic energy decreases as the clay moves higher, and at the same time, the potential energy increases. The total mechanical energy (TME) of the system (KE + PE) remains the same, as long as we disregard any air resistance.

As the clay reaches its apex

At the apex of the clay's trajectory, its velocity momentarily becomes zero, meaning its kinetic energy (KE) is also zero. At this point, all of the initial kinetic energy has been converted into gravitational potential energy (PE). The total mechanical energy (TME) of the system remains constant (assuming no air resistance).

As the clay falls back down

As the clay falls back to the ground, its potential energy (PE) is converted back into kinetic energy (KE). The potential energy decreases while the kinetic energy increases, and the total mechanical energy (TME) of the system remains constant (again, assuming no air resistance).

As the clay hits the ground

When the clay impacts the ground, its kinetic energy is quickly transferred to internal energy (IE) within the clay as it deforms and heats up slightly. The kinetic energy goes to zero as the clay comes to a stop, and the potential energy goes to zero as well, since it is on the ground.

Determine where the initial energy ends up

The initial energy that was put into the clay (as kinetic energy) ends up as internal energy within the clay after it hits the ground. This is due to the deformation and slight heating of the clay upon impact.

Key concepts

Kinetic Energy

Kinetic energy is the energy of motion. It describes how much energy an object has due to its speed. When you throw the clay up into the air, you are directly applying kinetic energy to it. Right at that moment, all the energy you put into the throw is kinetic.

• As the clay rises, it slows down because gravity pulls against its motion. So, its kinetic energy decreases.
• Kinetic energy is expressed as: \( KE = \frac{1}{2} m v^2 \) where \( m \) is mass and \( v \) is velocity.
• When it reaches the top of its path, or apex, its velocity is zero. This means that its kinetic energy is also zero at that instant.

Understanding kinetic energy helps us follow how energy transforms as the clay moves through the air. It's a dynamic form of energy, continuously changing as the clay's speed changes.

Potential Energy

Potential energy is stored energy due to an object's position. When you throw the clay upwards, it gains potential energy, sourced from the kinetic energy it loses as it rises.

• The higher the clay goes, the more potential energy it has.
• Potential energy at a height is expressed as: \( PE = mgh \) where \( m \) is mass, \( g \) is acceleration due to gravity, and \( h \) is the height.
• At the apex of its journey, the clay’s potential energy is at its peak.

During its ascent, all kinetic energy is gradually transformed into potential energy, explaining why the clay eventually stops rising. The energy hasn't disappeared; it's merely shifted to potential energy, ready to convert back to kinetic energy on the way down.

Internal Energy

Internal energy involves energy stored within the object's microscopic components—atoms and molecules. When clay hits the ground, its kinetic energy is changed into internal energy.

• This energy transformation is responsible for clay deforming and slightly warming upon impact.
• Internal energy is the sum of all molecular kinetic and potential energy within the clay.
• It indicates that even when external motion ceases, energy continues to exist within the object as internal energy.

This transformation is pivotal in understanding energy conservation in systems where external movement seems to disappear, like when the clay hits the ground. The initial kinetic energy is conserved but manifests as internal energy, neither created nor destroyed, just transformed into a different form.