Second, only the speed of the roller coaster is considered; there is no information about its direction at any point. This reveals another general truth. When friction is negligible, the speed of a falling body depends only on its initial speed and height, and not on its mass or the path taken. For example, the roller coaster will have the same final speed whether it falls Third, and perhaps unexpectedly, the final speed in part 2 is greater than in part 1, but by far less than 5.
Finally, note that speed can be found at any height along the way by simply using the appropriate value of h at the point of interest. We have seen that work done by or against the gravitational force depends only on the starting and ending points, and not on the path between, allowing us to define the simplifying concept of gravitational potential energy.
We can do the same thing for a few other forces, and we will see that this leads to a formal definition of the law of conservation of energy.
One can study the conversion of gravitational potential energy into kinetic energy in this experiment. On a smooth, level surface, use a ruler of the kind that has a groove running along its length and a book to make an incline see Figure 5.
Place a marble at the cm position on the ruler and let it roll down the ruler. When it hits the level surface, measure the time it takes to roll one meter. Now place the marble at the cm and the cm positions and again measure the times it takes to roll 1 m on the level surface. Find the velocity of the marble on the level surface for all three positions. Plot velocity squared versus the distance traveled by the marble. What is the shape of each plot?
Figure 5. A marble rolls down a ruler, and its speed on the level surface is measured. Figure 6. Hydroelectric facility credit: Denis Belevich, Wikimedia Commons. Figure 7. A toy car moves up a sloped track. That is, the energy stored in the lake is approximately half that in a 9-megaton fusion bomb.
Skip to main content. Work, Energy, and Energy Resources. Search for:. Gravitational Potential Energy Learning Objectives By the end of this section, you will be able to: Explain gravitational potential energy in terms of work done against gravity. Show how knowledge of the potential energy as a function of position can be used to simplify calculations and explain physical phenomena.
Example 1. The Force to Stop Falling A Example 2. What is h referring to? Height, obviously. Consider the example: What is the potential energy of a 1kg mass lifted 2 metres off the ground? I am foreseeing one or both of the following answers, so which one will it be? It doesnt make sense to talk about potential energy in absolute terms, only in terms of gain in potential energy Potential energy is defined in a way where h is the height off the ground I dont buy this I am leaning towards the first one, but I am still generally uncomfortable with the idea that you can't have an absolute P.
Improve this question. But if you take h to be the distance from the centre of mass of the earth to the object can't you have an absolute PE? Add a comment. Active Oldest Votes. This is a really excellent observation! It's a fascinating fact of physics. EDIT: To add to this, let's look at a little extra mathematical formalism.
Here's the payoff: If the forces are the same for two different potential energy functions, then those potential energy functions result in the same physical behavior. Improve this answer.
But its potential energy would be negative if you choose to let the ground level be 0 potential energy. I just added a bunch of mathematical formalism to the end of my answer that you may find useful, but it may be too obtuse. Let me know if you need further clarification. Thanks heaps! StraightUp StraightUp 11 1 1 bronze badge. Featured on Meta.
Now live: A fully responsive profile. Related 3. Hot Network Questions. The correct values have been entered. At least one of the values you entered had an incorrect number of significant figures. Potential energy is energy an object has because of its position relative to some other object.
When you stand at the top of a stairwell you have more potential energy than when you are at the bottom, because the earth can pull you down through the force of gravity, doing work in the process. When you are holding two magnets apart they have more potential energy than when they are close together.
If you let them go, they will move toward each other, doing work in the process. The formula for potential energy depends on the force acting on the two objects. For the gravitational force the formula is P.
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