The potential energy formula is affected by the force operating on **the two objects**. The formula for **gravitational force** is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m/s2 at the earth's surface), and h is the height in meters. Potential energy can be increased by raising an object high in the air or decreased by lowering it deep in a hole.

When a baseball player swings a bat, the energy from his/her arm is converted into potential energy that drives the ball down toward the ground. When the batter hits the ball, the potential energy is transformed into kinetic energy - the same energy that drives the ball across the field when it's hit by a baseball player- as the mass of the ball converts it into motion. At any point in time, a baseball has both kinetic and potential energy. It is their interaction that allows the ball to travel so far.

An object's potential energy is the maximum amount of energy it can store. Once an object reaches this limit, **more energy** must be supplied to it to increase **its speed**. This is why rockets need fuel - they use the energy in their fuel to produce more energy, which increases their speed. As long as a rocket has enough fuel, it can keep increasing its speed until it escapes Earth's gravity and goes into orbit.

As rockets gain altitude, their potential energy increases.

- What is the relationship between mass, weight, and height to the potential energy of an object?
- At what height is potential energy equal to kinetic energy?
- What is the relationship of mass and height?
- What is the gravitational potential energy of an object equal to its weight multiplied by?
- What is the formula for the energy of an elevated object?

It is worth noting that gravitational potential energy is measured in **the same units** as kinetic energy, kg m2/s2. So, if we know one of these quantities, then we can calculate the other.

Gravitational potential energy is defined as mgH, where H is the height of the object above a fixed point such as the ground. If we assume that all the mass is located at one end of the string then the total potential energy is simply half of its weight in meters multiplied by its height.

For example, if you drop a book from a height of **1 meter** then the potential energy it contains is 2 J. Now, if you repeat **this experiment** but this time using a book with a mass of 20 kg then the potential energy stored in the book will be 40 J.

This shows that increasing the mass of an object increases **its potential energy**. Gravitational potential energy is also called absolute energy because it doesn't depend on the motion of the object having potential energy. Instead, it depends only on the mass and height of the object.

So, finding out how much potential energy an object has is useful for calculating how heavy it must be to lift a given amount of weight.

An object's gravitational potential energy is the "stored energy" that the object possesses as a result of existing at that height. This is equal to its mass multiplied by the force of gravity, g (a determined constant of 9.8 m/s2) multiplied by the object's height. Potential energy Equals mass multiplied by gravity multiplied by height. Potential energy is the energy an object has because it is at **a high altitude** above sea level.

When an object loses potential energy, this energy is converted into other forms of energy. For example, when objects fall toward the Earth they lose potential energy and thus become more massive than they were before they fell. Objects also gain kinetic energy when they move, and this can be anything from walking down the road at 5 miles per hour to playing football at Michigan State University during home games (which averages out to about 60 kilometers per hour).

Potential energy is important because it tells us **how much energy** an object has stored up. For example, if you climb a mountain then when you reach the top you will have gained potential energy. This energy was stored in the form of gravitational potential energy due to the fact that you are at a higher altitude than you were at the bottom of the mountain. When you leave the mountain you will need to release **this energy** in order to do work against the force of gravity; work is defined as any effect that causes a change in direction of an object's motion or an increase in its velocity relative to a surrounding frame of reference.

An object's gravitational potential energy is equal to its weight multiplied by its height. If the object is located at the surface of the Earth, then its weight is 9.8 m/s2 and its potential energy is 478 J.

The effort done in elevating an item through a height h is the product of mgh near the Earth's surface, therefore U=mgh. Using the gravitational constant G, the gravitational potential energy, U, of a system of masses m1 and M2 at a distance r is U = -Gm1M2r. U is equal to -G m 1 M 2 r. If we let m 2 = m 1 = m, then U is equal to -Gr2m2.

Thus, the energy E of a system is its potential energy at a point above the ground. E = U. For example, if someone were to lift a car off the ground by pulling on the trunk, this would require putting forth an energy of magnitude 1030 joules (9.81 x 105 newtons). The human body is not capable of producing **such a large amount** of energy, so another source must be involved. Most often, the energy used in lifting a car comes from gasoline engines or electric motors.

In general, the energy of a system is the integral of **its force** times the displacement from the point where the force is acting. For example, the energy of a box being lifted up by a string is zero unless the box has mass. If the box has mass, then the energy it gives up as it is lifted is equal to mgz, where z is the height above **ground level**. This equation shows that the energy of the box and the string together is always greater than zero, even when they first begin to move away from each other.