Conservation of Energy Using Conservation of Energy to solve problems.

Conservation of Energy One of the simplest examples of conservation of energy is a falling object. At the instant an object such as a ball is released from a height off the ground, it only has gravitational potential energy. (Point A). As it falls, that GPE turns into Kinetic Energy. Halfway down at point C, the object has transformed half of it’s GPE into KE. So at point C, the ball has equal amounts of both. At Point D, it no longer has any height off the ground so it has no GPE left. It has all been converted into KE. It is important that you realize that it is moving when it hits the ground. It stops only after it has hit the ground. And the KE is released as heat and sound. The energy is always the same.

Conservation of Energy The total amount of energy is all the individual types added up at one point. For most of the problems you will doing in this class, we are only going to worry about mechanical energy. Mechanical energy refers to Kinetic, Gravity Potential, and Spring Potential only. Total Energy = KE + GPE + SPE And because energy is conserved the total amount of energy at each point is equal to the total amount of energy at any other point. E A = E B = E C = E D But the form(s) the energy is taking at each point is changing. We can use this to our advantage to make predictions about the object’s movement.

Conservation of Energy You can actually use conservation of energy to determine the impact velocity of an object when it hits the ground, how high a model rocket can go before it will start to fall back down, or how fast something needs to go to NOT come back down (like a shuttle) By the end of this year, you will learn how to do each of these things accurately, but we will start very simple first. Let’s say we know that the object has 100 Joules of GPE when it is first released at point A. Since GPE is the only kind of energy it has, that is also the total amount of energy the object has.

Conservation of Energy At point A, the object has 100 Joules of GPE. And we want to know how much GPE and KE it has at each point. Oftentimes, when solving these kinds of problems it is helpful to either set up a table (like the one below) or a set of equations. We’ll go through the table method first. On the leftmost column, you should have a row for each relevant or labeled point. (shown in green). Across, the top you must add a column for every type of energy that shows up at any point. HeightGPEKETotal Energy Point A100 J0 J100 J Point B Point C Point D Then, fill in all the givens and knowns (shown in red). We know at point A it has 100 Joules because it was given in the problem. And we know KE is zero because it is released from rest. And the total is those two numbers added together.

Conservation of Energy We also know that energy is conserved, which means the total shouldn’t change throughout the situation. So we can fill in 100 J for point B, C, and D on the total. HeightGPEKETotal Energy Point A100 J0 J100 J Point B100 J Point C100 J Point D100 J

Conservation of Energy When the ball hits the ground it no longer has any height so GPE is zero, which means all the energy has to be in KE. The total cannot change. Energy = GPE + KE 100 J = 0 J + KE 100 J = KE HeightGPEKETotal Energy Point A100 J0 J100 J Point B100 J Point C100 J Point D0 J100 J

Conservation of Energy If we assume at point C, we are exactly halfway to the ground, that means we have half the height, which means half the GPE that we started with. Half of 100 Joules is 50. And then again, the total has to add up to 100 J. Energy = GPE + KE 100 J = 50 J + KE -50 J 50 J = KE HeightGPEKETotal Energy Point A100 J0 J100 J Point B Point C50 J 100 J Point D0 J100 J

Conservation of Energy At point B, we know that the ball is moving so it definitely has KE, but it still has more than half of its original height. This means that the ball should have more GPE than KE at this point. In the picture, the ball looks to be at about 70% of its original height. So GPE should be approximately 70 J. And then again, the total has to add up to 100 J. Energy = GPE + KE 100 J = 70 J + KE -70 J 30 J = KE HeightGPEKETotal Energy Point A100 J0 J100 J Point B70 J30 J100 J Point C50 J 100 J Point D0 J100 J Later this year, you will learn how to use GPE and KE to figure out how fast or how high an object is going.