# Total Energy

### Model Description

This is a demonstration of the concept of total energy.  There are three principle components to total energy for introductory thermodynamics: potential energy, kinetic energy, and internal energy.  This demonstration should take 3-5 minutes.

### Engineering Principle

Total energy is the sum of all forms of energy for a system.  In introductory thermodynamics it is convenient to ignore electrical, magnetic, nuclear, and related forms of energy.  Thus we can simplify our definition of total energy as the sum of the potential (PE), kinetic (KE), and internal energies (U). $E = PE + KE + U$; $PE = mgh$; $KE = \frac{1}{2}mV^2$

The PE equation states that the potential energy of a system is the product of the mass (m), gravitation acceleration (g) and the height (h) above some reference.  Similarly, the kinetic energy is proportional to the mass and the square of velocity.  An increase in any of these three forms of energy increases the total energy of the system.

### What You Need

Item Quantity Description/Clarification
Tennis Ball 1 A tennis ball.

### How It’s Done

In Class: After a discussion of the components of total energy, hold up the tennis ball.  Compare the increase in potential energy and therefore in total energy when you raise the tennis ball from the desk to above your head.  Toss the tennis ball in the air, against a wall, or bounce it on the floor.  Discuss the increase in kinetic energy during these activities. Discuss ways you can increase the internal energy of the ball (putting it in a microwave vs. bouncing it on the floor). Students should be able to identify the three different forms of internal energy.

Additional Application: Conservation of energy.  When bouncing the ball against the floor, a change in kinetic and internal energy occurs.  On the way down, there is a decrease in potential energy and a corresponding increase in kinetic energy.  On the way up, the ball decelerates and trades kinetic energy for potential energy.  If the ball bounces enough times (i.e. during a tennis match), the ball warms up.  This is an increase in internal energy.  Because the collisions between the floor and the ball are not perfectly elastic, there are losses associated with each impact.  The conservation of energy states that the total energy must not change during this process, so the loss of kinetic energy after the collision must be compensated by a corresponding increase in internal energy.  The losses associated with each bounce can also lead to a discussion of the second law in terms of an increase of entropy in the system.  The ball does not return to the exact height from which we released it.  The decrement in height is associated with frictional losses and the internal losses from the elastic stretching of the polymer strands in the rubber.

### Cite this work as:

Phil Root (2019), "Total Energy," https://www.handsonmechanics.org/thermal/648.