Conservation of Energy

Chapter 5 Section 3

What is Conservation?

When something is conserved, it is said that it remains constant.

The same holds true for energy. Energy can not be created or

destroyed, it can only be converted from one form of energy to another.

Conservation of Energy

Conservation of Energy - The total amount of energy in an isolated system remains constant. Where energy can neither be created nor destroyed, it can only be transformed from one state to another.

Mechanical Energy Forms

There are three forms of mechanical energy: Kinetic Energy Gravitational Potential Energy Elastic Potential Energy

Mechanical Energy

Mechanical energy is often conserved when the objects energy changes between two or more mechanical energy forms. Example:

An object falls off a table and lands on the ground.

At first it had gravitational potential energy and as it fell, it lost some of the potential energy and it converted into kinetic energy.

Conservation of Mechanical Energy

Conservation of Mechanical Energy - The total amount of mechanical energy in an isolated system remains constant over time. Where energy can neither be created nor destroyed, it can only be transformed from one state to another mechanical form of energy.

Example of Conservation of Mechanical Energy

Rollercoaster's use the ideas of Conservation of Mechanical Energy when they are designed. It uses kinetic energy and

gravitational potential energy to determine the height of the slope and velocity of the coaster at the base of the incline.

Conservation of Mechanical Energy

Equation

MEi = MEf

Initial mechanical energy = Final mechanical energy(In the absence of friction)

KEi + PEi = KEf + PEf

ffii mghmvmghmv 22

2

1

2

1

Acceleration Doesn’t Have to Remain Constant

Using the kinematic equations, the acceleration needed to remain constant in order to solve a problem. This is not the case when using the

Conservation of Mechanical Energy equation.

The acceleration can change throughout the problem and it will not effect the outcome of the problem.

As long as friction is negligible…

Example Problem

A rock with a mass of 30kg falls off a cliff that is 57 meters tall and lands on the ground below. What was the velocity of the rock when it hits the ground below? (air resistance is negligible)

Example Problem Answer

KEi + PEi = KEf + PEf

½(30kg)(0m/s)² + (30kg)(9.8m/s²)(57m) = ½(30kg)(vf)² + (30kg)(9.8m/s²)(0m)

(30kg)(9.8m/s²)(57m) = ½(30kg)(vf)²

Vf = [(2)(9.8m/s²)(57m)]^½

Vf = 33.4m/s

ffii mghmvmghmv 22

2

1

2

1

Included Forces In The Equation

If other forces (except friction) are present, simply add the appropriate potential energy terms associated with each force. Example:

Elastic Force – Then the elastic potential energy equation would be added to the Conservation of Mechanical Energy equation.

Friction

When friction is present within a system, conservation of mechanical energy no longer holds true.

Total energy on the other hand is always conserved! The kinetic energy is being converted

to heat energy and other non-mechanical forms.