What Is Energy?
Prerequisites
Students should have some experience with physical systems, and knowing the expressions for the kinetic energy of a particle and the potential energy of a particle near the surface of the earth would be helpful.
Learning Outcomes
Students will develop an understanding of five basic properties of energy:
Instructions
Students should know how the applet functions, as described in Help and ShowMe.
The applet should be open. The step-by-step instructions in the following text are to be done in the applet. You may need to toggle back and forth between instructions and applet if your screen space is limited.
Transforming One Kind of Energy into
Another and Energy Conservation
Energy is a very abstract quantity. One of the most widely applicable principles of physics is the Principle of Energy Conservation.
The principle says that any physical system has something called energy and that, as long as the system is isolated, the value of the energy stays the same no matter what may be happening in the system. Being isolated means that the system is not interacting with anything outside the system. ("Energy" means "total energy" here.)
This quantity may take very different forms. E.g., a particle of mass m and speed v has energy in the form of kinetic energy. The kinetic energy KE is equal to
KE = ½mv2. (1)
Another example is the potential energy of a system consisting of a particle of mass m and the earth. If the particle is near the surface of the earth, this system has potential energy PE equal to
PE = mgh (2)
where h is the elevation of the particle above the earth's surface and g is the magnitude of the acceleration due to gravity.
These are two very different looking energy expressions. There are many others. The principle of energy conservation asserts that, no matter what system one is dealing with, one can always find energy expressions for the system such that the total energy of the system is conserved, if the system is isolated.
Exercise 1. Suppose there is an isolated system that has only potential and kinetic energy. At time t = t1, these energies are equal to PE1 = 10 J and KE1 = 4 J, respectively. At another time t = t2, the potential energy is equal to PE2 = 2 J. What is the kinetic energy KE2 at this moment?
Although different systems can have different kinds of energy, all energies have some properties in common. The applet can illustrate five of these. This illustration implements a model of energy invented by R.P. Feynman and described in the book by R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lectures on Physics, vol. 1. Feynman is comparing energy to colored building blocks with which a child is playing in a room. The child can repaint the blocks, can throw blocks out of the window, etc.
The applet shows a physical system as a white rectangle with a border around it. This particular system has two kinds of energy, potential and kinetic, symbolized by blue and red blocks.
Other systems may have other forms of energy: chemical, nuclear, thermal, electromagnetic, etc.
Energy comes in different forms. Different mathematical expressions are used to express different energies in terms of system properties.
Exercise 2. Consider a system consisting of the earth and a shotput. The shotput has mass 4 kg and a speed of 5 m/s when it is 3 m above the ground, what are the kinetic and potential energies of this system? Use Expressions (1) and (2) above with g = 9.8 m/s2.
If a system has parts that have separate energies, or if some parts have several kinds of energy, all these energies can be added to give the total energy of the system.
Exercise 3. What is the total energy of the system in Exercise 2?
Not all physical quantities have the additivity property. Can you think of one that does not have this property? What about temperature? Does it make sense to add the temperatures in different rooms of a building? Does it make sense to add the energies present in different rooms of a building?
Double-click on a blue block. It changes into a red block. 1 J of potential energy has been transformed into 1 J of kinetic energy. The sum of the kinetic and potential energies of the system, i.e., the total energy of the system, has not changed. The total energy of an isolated system is conserved.
You can use this property to make the following kind of prediction. Suppose that initially your system has 25 blocks and that you are not letting the system interact with its environment. Now trnsform the colors of some of the blocks until you have 10 red blocks. How many blue blocks do you predict will be in the system? Check it with the applet.
Exercise 4. Suppose your system is the system from Exercise 2. Assume that the system is isolated. What is the system's kinetic energy when the shotput is 1 m above the ground? Would you be able to work out the speed of the shotput from this value?
A system that is not isolated can have energy transferred into it or out of it. In the process, the system's energy changes, but the total energy of the system and its environment does not. One can think of the system and its environment as a larger isolated system.
Exercise 5. Transfer 4 J of energy out of the system and then transfer 3 J of energy back into the system. Observe the changes in the three kinds of energy simulated by the applet, represented by red, blue, and green blocks. Does the combined energy of the system plus environment remain the same?
The number of blocks in the applet is a scalar quantity. So is energy a scalar quantity.
Energy does not have direction. One might think that kinetic energy should have a direction, the direction in which the particle is moving. However, this is not how energy is defined. There are other forms of energy, e.g., potential energy or chemical energy (energy stored in a battery) that definitely don't have direction.
If one kind of energy does not have direction, then another kind cannot have direction either if one wants to be able to add these energies.
Mathematically, it is easier to work with scalars than vectors. Therefore, energies are easier to work with than forces. Many questions in mechanics can be answered by considering the energies involved, and this is often easier than considering the forces.
Exercise 6. Use energy considerations to calculate the speed of the shotput from Example 2 when the shotput is 1 m above the ground. (See Example 4.) If you like, try to get the same answer by using forces.