The topic of energy is difficult and easy at the same time. The difficult part is the concept of energy itself. The easy part is that once you understand what energy is all the problem solving becomes much less of a challenge.
To find an answer to the question: “What is energy?” is difficult. The term energy is used in a many different contexts and only very few of them relate to how we use energy in physics. This means that understanding energy and finding a meaning becomes difficult.
In class we did an eight-page tutorial that helped us understand energy and how it is different from momentum. That this is difficult becomes clear if you consider that it took some of the greatest minds of the 17th century many years to come to an agreement. It took another 100 years to formalize this agreement.
When we first talked about energy we related it to damage done onto something. We interpreted energy as the capacity of an object to do damage. It became clear that this capacity depends on the speed with which the object hits as well as on its mass. Therefore we called this energy, energy of motion, or kinetic energy. The operational definition of kinetic energy, or the equation used to calculate it, is KE = ½ mv. In short moving objects can do damage because they have both speed and mass. We discussed how this is different form momentum in the tutorial.
A moving object can slow down for different reasons. One is because of friction and another one would be because it slows down, if you throw it up into the air for instance. Both objects are slowing down and therefore their kinetic energy decreases. There is a big difference, however, between these two cases.
What happens to the energy
When a sled slows down at the bottom of the hill it is dues to friction. The sled will never speed up again on its own, the kinetic energy has disappeared and is gone. When a juggler throws a ball in the air the ball also slows down, its kinetic energy goes to zero until none is present at the turnaround point. The difference to the sled example is that the ball will seed up again it’s own on the way down. So, the kinetic energy will increase again. The energy while gone at one point will reappear.
In the sled example, we say that friction changes the kinetic energy of the object. The energy is actually not completely lost, it turns into heat (try rubbing your hands together and feel them getting warmer). But we won’t deal with heat at this point, so we say the energy is gone.
For the juggler example it would be kind of awkward to say that the kinetic energy first disappears (on the way up) then reappears again (on the way down). Rather, we say that the energy gets transformed into another energy form (not like heat above, but into one we can relate to). This energy form should have be at its maximum at the highest point when the kinetic energy is zero. Remember that our interpretation of energy is the ability to do damage. Therefore this new energy form is related to the height, the higher the more damage it can do. It also has to do with mass and gravity and therefore we calculate what we call potential energy PE = mgh. An object with potential energy can do damage because it is lifted up, o dislocated form the ground. You can imagine other dislocations that can do damage, a spring being compressed or two magnets being pulled apart.
It is clear to see that in the magnet example you have to have two magnets in order to have potential energy or to do damage. For the potential energy of objects being lifted up it is important to include the earth in your SYSTEM. Without the earth we would have no potential energy.
A sidebar here: When a sled slows down, friction changes its kinetic energy. When a ball being thrown upward slows down, you could say that the gravitational force slows down the ball and therefore changes it’s potential energy. If, however, we include the earth in our system this gravitational force becomes internal to the system and is cancelled out by the third law force pair of the gravitational force of the ball on the earth. Then there would be no more outside force that would be able to change the kinetic energy.
If we include the earth in our system the kinetic energy changes to potential energy and then back to kinetic. It’s like moving money from your checking to your savings account. The amount of money you have stays the same. In the case of energy we say “the energy is conserved”.
Energy conservation is a powerful tool when solving problems. Consider a roller coaster car going down the first hill. What would be the speed at the bottom if the hill is 30 m high (we ignore friction)? Check out the calculations in the picture below.