# Gravitational potential energy and work relationship

### Potential Energy Gravitational potential energy is energy an object possesses because of its the potential energy at a height h above that point is equal to the work which would. Learn what gravitational potential energy means and how to calculate it. It represents the potential an object has to do work as a result of being located at . of the inverse-square relationship, we can reach an asymptote where gravitational. Gravitational potential energy (GPE) is associated with an object's mass and its position. It is equal to the work one must do to lift an object some distance.

Power 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. Gravitational Potential Energy 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.

## Potential Energy

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: 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. Since many of our labs are done on tabletops, it is often customary to assign the tabletop to be the zero height position.

Note that the work in this equation is the work done by the net force, rather than the work done by an individual force. Gravitational potential energy Let's say you're dropping a ball from a certain height, and you'd like to know how fast it's traveling the instant it hits the ground. You could apply the projectile motion equations, or you could think of the situation in terms of energy actually, one of the projectile motion equations is really an energy equation in disguise.

If you drop an object it falls down, picking up speed along the way. This means there must be a net force on the object, doing work. This force is the force of gravity, with a magnitude equal to mg, the weight of the object.

The work done by the force of gravity is the force multiplied by the distance, so if the object drops a distance h, gravity does work on the object equal to the force multiplied by the height lost, which is: An object with potential energy has the potential to do work. In the case of gravitational potential energy, the object has the potential to do work because of where it is, at a certain height above the ground, or at least above something. Spring potential energy Energy can also be stored in a stretched or compressed spring. An ideal spring is one in which the amount the spring stretches or compresses is proportional to the applied force. This linear relationship between the force and the displacement is known as Hooke's law. For a spring this can be written: The larger k is, the stiffer the spring is and the harder the spring is to stretch. If an object applies a force to a spring, the spring applies an equal and opposite force to the object.

This is a restoring force, because when the spring is stretched, the force exerted by by the spring is opposite to the direction it is stretched.

Physics, Gravitational Potential Energy, Work Done By an External Force

This accounts for the oscillating motion of a mass on a spring. If a mass hanging down from a spring is pulled down and let go, the spring exerts an upward force on the mass, moving it back to the equilibrium position, and then beyond.

### What is gravitational potential energy? (article) | Khan Academy

This compresses the spring, so the spring exerts a downward force on the mass, stopping it, and then moving it back to the equilibrium and beyond, at which point the cycle repeats. This kind of motion is known as simple harmonic motion, which we'll come back to later in the course.

The potential energy stored in a spring is given by: In a perfect spring, no energy is lost; the energy is simply transferred back and forth between the kinetic energy of the mass on the spring and the potential energy of the spring gravitational PE might be involved, too. Conservation of energy We'll take all of the different kinds of energy we know about, and even all the other ones we don't, and relate them through one of the fundamental laws of the universe.