Conservation of Mechanical Energy

Introduction “The laws of conservation are the cornerstone of physics.”

Definition  When a physical quantity is conserved, the numeric value of the quantity remains the same throughout the physical process.  Although the form of the quantity may change, the final and initial value is consistent.

Example

Let’s Explain  The kinetic energy of an object falling solely under the influence of gravity is constantly changing.  During this time the gravitational potential energy is also changing.

Individually?  These quantities are not conserved individually; however, as a system, they are.

Recall that  A system is defined as a definite quantity of matter enclosed by boundaries.  In general the amount of energy remains constant when no mechanical work is done on or by the system, and no energy is transmitted to or from the system.

Example

The Law of Conservation of Energy The total energy of an isolated system is always conserved!

Conversions  Within an isolated system, energy may be converted from one form to another.  However, the total amount of all forms of energy is not going to change!

Random Thought  Did you know that total energy can neither be created nor destroyed?  This means that energy as a whole, (taking the entire universe as our system) is conserved and constantly being changed from one form to another.

Conservation of Energy  We can say that because: W = ΔKE + ΔPE and the net work done on the system is to be 0 Then, ΔKE = - ΔPE

We can expand…  We can expand this equation and say that: KE i + PE i = KE f + PE f According to this equation, the sum of the kinetic and potential energy remains the same before and after.

Example

Example continued  With the absence of non-conservative forces such as air resistance and friction, the trading of energy is exactly even.  Fortunately for the skydivers, this is not the case. They have their parachutes which create resistive forces that slow them down.

 Allowing for a nice, smooth landing!

So, the rule is  In any isolated system of objects interacting only through conservative forces, the total mechanical energy is: E = KE + PE

Example  A diver of mass m drops from a board 10.0 meters above the waters surface. (a) Use conservation of mechanical energy to find the divers speed 5 meters above the surface. (b) his speed when he hits the water. (Neglect air resistance)

Example  Suppose the same diver vaults off the springboard, leaving it with an initial speed of 3.50 m/s upwards. Use the law of conservation of energy to find his speed when he strikes the water.

Example  A waterslide is 21.9 meters high. With what speed will a 60 kg woman be travelling when she reaches the bottom?