# Relationship between work and gravitational potential energy

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

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. Work = FDcos(θ). If you are doing work parallel to the force of gravity then the change in GPE is equal to the work done on the object(cos(0) = 1).If the work is. In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potential energy of an object that . In this section the relationship between work and potential energy is.

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. 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. Again this is merely arbitrary. If the tabletop is the zero position, then the potential energy of an object is based upon its height relative to the tabletop. For example, a pendulum bob swinging to and from above the tabletop has a potential energy that can be measured based on its height above the tabletop.

By measuring the mass of the bob and the height of the bob above the tabletop, the potential energy of the bob can be determined. Since the gravitational potential energy of an object is directly proportional to its height above the zero position, a doubling of the height will result in a doubling of the gravitational potential energy.

A tripling of the height will result in a tripling of the gravitational potential energy. Use this principle to determine the blanks in the following diagram. The work-energy principle There is a strong connection between work and energy, in a sense that when there is a net force doing work on an object, the object's kinetic energy will change by an amount equal to the work done: 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.

### Potential energy - Wikipedia

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.

**Electric Potential & Electric Potential Energy Physics Problems**

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.

## Potential energy

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. 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. 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.