Potential energy how does it work

It's all about the system. If you want a potential energy, you need to pick a system that includes more than just a mass. Let's consider a ball released from rest near the surface of the Earth that falls a distance h. If I choose a system just consisting of the ball which is sort of like a point mass then I can look at the work done on this ball as it falls.

What forces are acting on the ball? Just the gravitational force mg. Since the gravitation force is in the same direction as the displacement, the angle between these two is zero. I can write:. From here, you could solve for the velocity at the bottom position. Not too difficult. In that case, I can subtract the work done by the gravitational force from both sides of the equation.

I would get this:. Algebraically, this is the same equation as before. However, this says that there is no work done on the system and instead we have a change in gravitational potential energy U. The change in potential is then defined as the negative of the work done by that force. This is technically the gravitational potential energy of the ball-Earth system. In the end, you would get the same expression as before with the system of just the point particle.

Be careful. You can't have work done by gravity AND a change in gravitational potential energy. You have to do it one way or the other. This means that the most important step in solving work-energy problems is choosing a system.

For internal forces like gravity in a system, you will have a potential energy term. What about those special cases of conservation of energy? Yes, they can be useful at times - but you have to be careful to realize that they are just special cases. As I read over this post, it seems like I am that guy from Spinal Tap that tries to explain why his amplifier is better because the dial goes to Yes, it might seem like I am basically saying the same thing as the textbooks. An object can store energy as the result of its position.

For example, the heavy ball of a demolition machine is storing energy when it is held at an elevated position. This stored energy of position is referred to as potential energy. Similarly, a drawn bow is able to store energy as the result of its position.

When assuming its usual position i. Yet when its position is altered from its usual equilibrium position, the bow is able to store energy by virtue of its position. Potential energy is the stored energy of position possessed by an object.

The two examples above illustrate the two forms of potential energy to be discussed in this course - gravitational potential energy and elastic potential energy.

Gravitational potential energy is the energy stored in an object as the result of its vertical position or height. The energy is stored as the result of the gravitational attraction of the Earth for the object. The gravitational potential energy of the massive ball of a demolition machine is dependent on two variables - the mass of the ball and the height to which it is raised.

There is a direct relation between gravitational potential energy and the mass of an object. More massive objects have greater gravitational potential energy. There is also a direct relation between gravitational potential energy and the height of an object. The higher that an object is elevated, the greater the gravitational potential energy. These relationships are expressed by the following equation:.

In the above equation, m represents the mass of the object, h represents the height of the object and g represents the gravitational field strength 9. To determine the gravitational potential energy of an object, a zero height position must first be arbitrarily assigned.

Typically, the ground is considered to be a position of zero height. But this is merely an arbitrarily assigned position that most people agree upon. Calculating the elastic potential energy and potential energy differences from Figure involves solving for the potential energies based on the given lengths of the spring. When the length of the spring in Figure changes from an initial value of Using 0. A simple system embodying both gravitational and elastic types of potential energy is a one-dimensional, vertical mass-spring system.

This consists of a massive particle or block , hung from one end of a perfectly elastic, massless spring, the other end of which is fixed, as illustrated in Figure.

Assuming the spring is massless, the system of the block and Earth gains and loses potential energy. We need to define the constant in the potential energy function of Figure.

Note that this choice is arbitrary, and the problem can be solved correctly even if another choice is picked. We must also define the elastic potential energy of the system and the corresponding constant, as detailed in Figure. The equilibrium location is the most suitable mathematically to choose for where the potential energy of the spring is zero.

Therefore, based on this convention, each potential energy and kinetic energy can be written out for three critical points of the system: 1 the lowest pulled point, 2 the equilibrium position of the spring, and 3 the highest point achieved.

We note that the total energy of the system is conserved, so any total energy in this chart could be matched up to solve for an unknown quantity. The results are shown in Figure. The block is pulled down an additional [latex] 5. In parts a and b , we want to find a difference in potential energy, so we can use Figure and Figure , respectively. Each of these expressions takes into consideration the change in the energy relative to another position, further emphasizing that potential energy is calculated with a reference or second point in mind.

By choosing the conventions of the lowest point in the diagram where the gravitational potential energy is zero and the equilibrium position of the spring where the elastic potential energy is zero, these differences in energies can now be calculated. In part c , we take a look at the differences between the two potential energies. The difference between the two results in kinetic energy, since there is no friction or drag in this system that can take energy from the system.

Even though the potential energies are relative to a chosen zero location, the solutions to this problem would be the same if the zero energy points were chosen at different locations. Suppose the mass in Figure is in equilibrium, and you pull it down another 3. Does the total potential energy increase, decrease, or remain the same?

View this simulation to learn about conservation of energy with a skater! Build tracks, ramps and jumps for the skater and view the kinetic energy, potential energy and friction as he moves. You can also take the skater to different planets or even space! A sample chart of a variety of energies is shown in Figure to give you an idea about typical energy values associated with certain events. Some of these are calculated using kinetic energy, whereas others are calculated by using quantities found in a form of potential energy that may not have been discussed at this point.

The kinetic energy of a system must always be positive or zero. Explain whether this is true for the potential energy of a system. The potential energy of a system can be negative because its value is relative to a defined point. The force exerted by a diving board is conservative, provided the internal friction is negligible. Assuming friction is negligible, describe changes in the potential energy of a diving board as a swimmer drives from it, starting just before the swimmer steps on the board until just after his feet leave it.

Describe the gravitational potential energy transfers and transformations for a javelin, starting from the point at which an athlete picks up the javelin and ending when the javelin is stuck into the ground after being thrown. If the reference point of the ground is zero gravitational potential energy, the javelin first increases its gravitational potential energy, followed by a decrease in its gravitational potential energy as it is thrown until it hits the ground.

The overall change in gravitational potential energy of the javelin is zero unless the center of mass of the javelin is lower than from where it is initially thrown, and therefore would have slightly less gravitational potential energy.

A couple of soccer balls of equal mass are kicked off the ground at the same speed but at different angles. Soccer ball A is kicked off at an angle slightly above the horizontal, whereas ball B is kicked slightly below the vertical.

How do each of the following compare for ball A and ball B? If the energy in part a differs from part b , explain why there is a difference between the two energies.

What is the dominant factor that affects the speed of an object that started from rest down a frictionless incline if the only work done on the object is from gravitational forces? Two people observe a leaf falling from a tree. One person is standing on a ladder and the other is on the ground. If each person were to compare the energy of the leaf observed, would each person find the following to be the same or different for the leaf, from the point where it falls off the tree to when it hits the ground: a the kinetic energy of the leaf; b the change in gravitational potential energy; c the final gravitational potential energy?

Using values from Figure , how many DNA molecules could be broken by the energy carried by a single electron in the beam of an old-fashioned TV tube?

These electrons were not dangerous in themselves, but they did create dangerous X-rays.