Chapter 11.2 Notes

Conservation of energy

There are three quantities in physics that are always conserved:


The law of conservation of energy states that


There are only two forms of mechanical energy:

In this section, we practice with problems in which energy transforms between them.

For ideal mechanical systems, the total energy E is seen as

E = KE + PE or


In conservation of energy problems, Work plays an important role :

In conservation of mechanical energy problems, we idealize our systems such that they are isolated from outside sources of energy transfer, and make the assumption that

In energy problems we use the same principle:

This says that the total energy E of a closed, isolated system remains constant, and so does the sum of KE + PE before, during and after any event that results in a transformation of the mechanical energy.

A useful expansion of this formula can also be written as

We can use this relationship to solve for such values as the velocity of an object after it has gained kinetic energy and lost potential.

YOU TRY: Do the practice problems 9-11 on page 261-2. For number 9, you should get about 3.1 x 103 J for the kinetic energy before going up the hill, and a value of 3.7 m as the increase in vertical heigth as the kinetic energy drains away and is transformed into PE. If you can get these results for number 9, you should have no difficulty with number 10 and 11

video: The Mechanical Universe: Conservation of Energy

lab: finding the changes in PE and KE in a real situation (not closed and isolated).. Dynamics Cart on a Ramp

View some exemplary write ups for the Dynamics cart lab. 1 2

Homework: Set 4: problems 57-66