POTENTIAL AND KINETIC ENERGY

What is Energy?

Energy is the ability to do work, usually against some force. When you climb stairs you had to do work against gravity to get up here. That required an expenditure of energy.

But, you only borrowed this energy. You can get it back when you go back down the stairs (or simply jump off from that height which of course is not recommended - because that energy will be dissipated mechanically via sound generation and broken bones)

Energy comes in many forms, kinetic, potential (stored), heat, etc. Energy is always conserved. It is not created or destroyed but is just transformed from one form to another.

Kinetic and Potential Energy:

Throwing a ball into the air represents a situation in which the total energy is fixed and there is a continous transformation from kinetic energy to potential energy.

• When the ball is on the ground there and not moving there is no potential energy or kinetic energy

• when the the ball is tossed into the air it will reach a maximum height which is determined by how much kinetic energy it has (air resistance is important however)

• when the ball reaches its maximum height its velocity is 0 and all of the energy in the system is potential energy

• as the ball falls to the ground that potential energy is converted to kinetic energy

• Some amount of energy is loss due to air friction which then heats up the air (just a tiny bit).

Most Energy loss is via heat. This is generally not released. Heat loss is usually irrecoverable. This is a principle feature of the field of thermodynamics that we will discuss later.

Common Types of Energy
Type of Energy	What it is
Kinetic Energy (KE) Gravitational Potential Energy (GPE) Chemical Potential Energy (CPE) Elastic Potential Energy (ELPE) Thermal Energy (H) Electromagnetic Radiation (ER)	energy associated with motion energy associated with position in a gravitational field energy associated with the bonding of molecules in a chemical "spring energy" - a form of stored energy heat dissipation release of photons

Energy is defined as the ability to do work. When the work is actually being done, we term the energy "kinetic." When the work is waiting to be done, when there is the potential for work to be performed, we term the energy "potential." Kinetic energy is the energy of motion, potential energy comes from work having been done on an object.

For example, a rubber band zinged from your finger has kinetic energy. While it was stretched, waiting for you to release it, it had potential energy. The rubber band was stationary, but work had been done on it to move it to its present position.

Now, we know that the further we pull back a rubber band, the faster and further it will fly. Consider this situation in terms of potential and kinetic energy. When you pull back the rubber band to a great distance, You are doing more work to it than if I pulled it back only a small distance.

More work means more energy is provided to and stored by the rubber band. When I release the rubber band, it has more energy to move. More energy means more work can be done by the rubber band. There is a connectedness, then, between potential and kinetic energy for matter.

All of this should be intuitive for you, but nonetheless, doing these simple experiences should help you better understand the connection between potential and kinetic energy as well as given you a feel for energy conservations.

In terms of formulae:

Kinetic energy:

KE = (mass x velocity²)/2 or 1/2 mv²

Although mass and velocity both have great effects on kinetic energy, it is velocity more significantly determines kinetic energy.

The units of energy are Joules.

Sample Problems:

1. What is the kinetic energy of a 45 kg object moving at 13 m/sec?

Identify the information given in the problem:

• Mass = 45 kg
• velocity = 13 m/sec

so KE = 1/2 * 45kg * (13 m/sec)² = 3802.5 Joules

2. If the KE of a moving boat is 52,000 Joules and the mass of the boat is 39,000 kg, what is the velocity of the boat.

Again identify the given information:

• KE = 52,000
• Mass = 39,000 kg

KE = 52,000 = 1/2 * 39000 kg * v²

solve for v to get 1.63 m/sec.

Potential energy, on the other hand, is energy of position, not of motion. The amount of potential energy possessed by an object is proportional to how far it was displaced from its original position. If the displacement occurs vertically,raising an object off of the ground let's say, we term this Gravitational Potential Energy. We can calculate the gravitational potential energy of an object with this formula:

GPE = weight x height above ground

where weight is given by Newton's second law; w = mg

where g is the gravitational acceleration of the earth = 9.8 m/sec² An increase in the weight of an object or the height to which it is raised will result in an increase in the potential energy the object possesses. Once the object is dropped, the potential energy begins to decrease due to reduced height, but we also now see an increase in kinetic energy because the velocity is also increasing.

Sample problem:

A 10 kg cat climbs a tree to a height of 15 meters. What is the potential energy of the cat:

PE = weight * height = 10 kg * 9.8 m/sec² * 15 meters = 1470 J

Assumimg no energy loss, what will the velocity of the cat be when it jumps t the ground.

Since energy is conserved, the total KE of the cat must also = 1470 J.

so 1/2mv² = 1470 since you know m you solve for v; v² = 2*1470/10 = 294 so v = square root of 294 = 17.15 m/sec (which would hurt the cat).