Potential Energy with Examples

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Objects have energy because of their positions relative to other objects. We call this energy as potential energy. For example, apples on the tree, or compressed spring or a stone thrown from any height with respect to ground are examples of potential energy. In all these examples there is a potential to do work. If we release the spring it does work or if we drop the apples they do work. To move the objects or elevate them with respect to the ground we do work. The energy of the objects due to their positions with respect to the ground is called gravitational potential energy.

potential energy image potential energy image2

The pictures given above are the examples of gravitational potential energy. They both have a height from the ground and because of their positions they have energy or potential to do work. Look at the given examples below. They are a little bit different that of given above.

spring potential energy image

In the first picture, system including a spring and a box is at rest. However, in second picture the box compresses the spring and loads it with potential energy. If we release the box spring does work and pushes the box back. These two examples of gravitational and spring potential energy are calculated differently. Let me begin with the calculation of gravitational potential energy. We will look at which factors effects the magnitude of potential energy or which does not effect. Work done against to the earth to elevate the objects is multiplication of its weight and distance which is height. Thus, as we said before energy is the potential of doing work.

Then, gravitational potential energy becomes;


Now, look at the given picture and try to calculate the potential energies of the given ball in three situations.

potential energy example




We see that gravitational potential energy depends on the weight and height of the object. Now let’s solve some more examples related to this topic before passing to the kinetic energy.

Example In the pictures given below, if the potential energy of the ball in the first picture is P find the potential energy of the ball in second situation in terms of P.

potential energy example2




Situation 1 Situation 2

P=m.g.h=mgh P’=m.g.2h=2mgh=2P


By compressing the spring or stretching it you load a potential energy to it. Well, if I apply same force to different springs having different thicknesses, are they loaded with the same energy? I hear that you all say no! You are absolutely right. Of course the thinner spring is more compressed than the thicker one where the quantity of compression shows the loaded potential energy. What I want to say is that, potential energy of the spring depends on the type of spring and the amount of compression. The mathematical representation of this definition is given below.


Where k is the spring constant and x is the amount of compression.

spring image

Now, we look at the origin of this formula. This is a picture of a spring at rest. There is no compression or stretching. Thus, we can not talk about the potential energy of the spring. However, in the pictures given below springs are not at rest position. Let’s examine the behavior of the springs in two situations.

potential energy of spring



 In the first picture, we apply a force, Fapplied, and spring reacts this force with Fspring=-kx. The amount of compression is X. In the second picture we stretch the spring by the amount of X. We apply force of F and spring gives reaction to this force with Fspring=-kx where x is the stretching amount and k is the spring constant. The given graph below is force versus distance graph of springs. We find the energy equation of spring by using this graph.

As I said before area under the force vs distance graph gives us the work and energy is the capability of doing work. So, area under this graph must give us the potential energy of the spring.



Example 50N of force is applied to a spring having 150N/m spring constant. Find the amount of compression of the spring.

force distance graphFspring=-kx=Fapplied


X=-3m “-“shows the direction of compression.




Work Power Energy Exams and Solutions


example situations of potential energy
force vs distance graph gravitational potential energy
spring compression fx graph
potential energy compressed spring
example image of potential energy
is work the area of a potential energy vs distance graph?
example of effect of potential energy
example situation for potential energy
graph of gravitational potential energy against distance
examples of potentia energy
potential energy example situations
potential energy vs height graph work
potential energy from earth example graph
example of potential energy w/ pictures
2 situations that involves potential energy and height
picture of example of compression force
area under force vs distance graph
spring force versus distance graph
compressed spring picture
examples of spring energy
potential vs height graph
graph of gravitational potential energy
formula of potential energyif 2 distance are given
spring compression for a dropped package graph
estimate force given potential energy and distance x from graph
height vs energy graph
potential energy vs distance graph work force
gravitational energy example picture
how to graph gravitational potential energy v height
compressed spring force examples
potential energy graph compressed spring
gravitational potential energy of spring graph vs x
gravitational potential energy vs weight graph
potential energy graph for 2 situations
potential energy and picture examples
pictures of potential energy vs position graphs
conservation of energy box released after compress the spring
compression spring calculation with gravitational potential energy
compression spring force vs température
gravitational distance pictures
spring and rest and example
solving height from a object resting on a compressed spring
examples of compression force
graph of spring against potential energy
how to calculate force from PE vs Height graph
potential energy vs position graph of a compressed spring
energy vs height graph
graph of kinetic energy and potential energy and height
graph of gravitational potential energy vs distance