3.2 Conservation

Energy Conservation

One of the most powerful properties of energy is that Energy is Conserved.  

Energy never appears or disappears.

Skier Examples

Test your knowledge by trying the problems below.  

Always start your calculation problems with:    E_before = E_after

Example #1:
A skier at the bottom of a hill has 1000J of kinetic energy.    After sliding a ways along the flat, the kinetic energy is 200J.  
a)  With a decreased kinetic energy, what do you know about the skier's velocity?
b)  With the skier sliding on a flat surface, is there any change in gravitational potential energy?
c)   How much energy was lost due to friction? (Use Ebefore = Eafter).

Try before checking solution.

Solution

Example #2:
A skier on a hill has 5000J of kinetic energy and 5000J of potential energy.   After sliding down the hill a ways, their potential energy is 3000J.
a)  Since they slid "down" the hill, what do you expect for change in potential energy (greater or less)?
b)  Assuming that there is no loss due to friction, what would be the kinetic energy at the second position?  (Use Ebefore = Eafter)
c)  Since there's always "some" friction loss, would the "actual" kinetic energy be less or more then your answer in b)?

Try before checking solution.

Solution

Efficiency

Efficiency = the measure of how well a device transfers energy into the form we want.

Even though energy is always conserved, it's not always in the form we want.

When we convert energy, some energy always ends up in a form that we consider wasted energy. The question of how much of the energy is useful is of interest to us, especially as we look to become less wasteful.

As a rule, every energy conversion is less than 100% efficient. The energy is not destroyed, it is just transformed into something that is not that useful such as heat or sound.   Feel the back of your computer - can you feel energy being released that is not very useful to the computer.

If you switch the ratio of Useful Output and Total Input in the formula, you may get an efficiency that is greater than 100%. This would indicate that your machine has created energy, which is a violation of the Law of Conservation of Energy. If this happens, revisit your technique.

Light Bulbs

Test your knowledge by trying the problems below.  

Here's some practice for your new equation:

Example #1:
An "old style" (incandescent) light bulb converts energy as shown in the Sankey diagram below:

a)  For every 100J of energy that the light uses, how much is converted into light energy?
b)  For every 100J of energy that the light uses, how much is converted into heat energy?
c)  We'd consider the "useful energy" to be what?
d)  We'd consider the "wasted energy" to be what?
e)  Calculate the efficiency of the light.
f)   If you were going to use this light bulb to heat a small area, we'd have to redefine what was "useful energy."   What would be the efficiency of the light in this case? 

Try before checking solution.

Solution

Example #2:
An "new style" (LED) light bulb converts energy as shown below:

a)  For every 100J of energy that the light uses, how much is converted into light energy?
b)  For every 100J of energy that the light uses, how much is converted into heat energy?
c)  We'd consider the "useful energy" to be what?
d)  We'd consider the "wasted energy" to be what?
e)  Calculate the efficiency of the light.
f)   If you were going to use this light bulb to heat a small area, what would be the efficiency of the light? 

Try before checking solution.

Solution

Roller Coasters

Test your knowledge by trying the problems below.  

Always start your calculation problems with:    E_before = E_after

Example #1:
A roller coaster uses 1 000 000 J of energy (Work in) to get to the top of the first hill.   During this climb, it gains 400 000 J of potential energy and pauses (velocity = 0) for a fraction of a second at the very top before heading down the other side.
a)  What's the kinetic energy at the very top?
b)  What would be the "useful energy" during it's climb to the top?
c)   How much energy was lost due to friction? (Use Ebefore = Eafter).
d)  Calculate the efficiency of the roller coaster during this part of the ride (the climb).

Try before checking solution.

Solution

Example #2:
The same roller coaster goes over the top of the first hill and heads downwards.  The roller coaster heads down and levels out as it hits the original level.
a)  Since they are back at the original level, what do we know about the potential energy at this point?
b)  If we assumed that there is no loss due to friction, what would be the kinetic energy at the bottom?  (Use Ebefore = Eafter)
c)  The actual kinetic energy at the bottom turned out to be 240 000J, what is the efficiency of the roller coaster during this part of the ride?
d)  Where would the wasted energy have gone?

Try before checking solution.

Solution

Efficiency Ratings

As strive to figure out more ways to survive with less energy, "efficiency ratings" can be found on most new appliances.

The efficiency rating gives us an idea of how much energy a device wastes as heat.   Look for efficiency ratings on devices you intend to buy.  

Often this will help you know that a little extra money now (to pay for the improved technology) will save you money in the long run (paying for less energy).  Of course, better for the environment, as well.

Bill Nye: Efficiency

Interview

What do physicists, technologists, and engineers do? Here's an example.