Energy


Start-Up:
What good is an airbag in a car crash?


1.  Remember  F Delta t = Delta p   ? 

    We used that to figure out how the motion of an object changes when we apply a force for a certain amount of time, and figured out momentum from it.

2.  Well what if we want to figure out what happens if we apply a force over a certain _distance_ rather than over a certain time?

    In that case, we'd have:
        F Delta x = ?


3.  Well we know from Newton's 2nd law that F = ma,

so  F Delta x   =  ma Delta x  -- but using   vf^2 - vi^2 = 2ax, we get

F Delta x  =  1/2 * m * (Vf^2 - Vi^2)  = Delta (1/2  m*v^2)

so it looks like we've got another special quantity that comes in as a _change_.

Each of these get special names --

F Delta x  is called WORK   -- sort of like the everyday use of "work", but more specific.

1/2 m*v^2   is called KINETIC ENERGY  -- similar to momentum, but even more useful.

and the other day we had (MV) is called MOMENTUM.



Let's do an example   --
4.  What is the kinetic energy of a 4 kg object moving at 5 m/s?     ANS:  .5*4*5^2  = 50  Joules  (kgm^2/s^2  = N-m)

5.  How much work does one have to do get a 3 kg object moving 6 m/s?    ANS:  .5*3*6^2  = 54 Joules

6.  If you only have 2 meters in which to push on the object, with what force do you need to push to get the kinetic energy up to 54 joules?

  ANS:  Work = Delta (KE), and Delta (KE) = 54 Joules = Work = F Delta (x) = F*2   --> F = 27 Newtons.



The work is equal to the change in the Kinetic Energy.

7.  But there are exceptions -- what if we are trying to lift an object up in the air.  How much force is required to lift a 10 kg  object?
    ANS :  F = m*g  = 10*9.8 = 98 Newtons. 

8.  So if we lift the object 10 meters, how much work is done?    ANS:  Work = F*Delta x = 98 N * 10 m  = 980 Joules.

But is this work equal to the change in KE?  NO  - because the object isn't moving when it gets up there, it's sitting still.

So what's going on?  There's a different kind of energy that this work went into -- it produced POTENTIAL ENERGY -- why do we call it PE?  Because we can get it back as kinetic if we drop the object -- so the work done in lifting the object gives us the potential ability to give kinetic energy to the object later.

What's the PE of the object before --- 980 Joules = m*g*h  -- PE = mgh.


Practice:

Calculate the kinetic energy and potential energy of various objects.  Estimate mass and speed to get KE, estimate mass and height to get PE.


Challenge --  We say that energy is CONSERVED because the total amount of energy doesn't change, unless we do work to change it.  The energy just changes form otherwise (PE becomes KE, or vice versa).  Can you think of an example where the energy is not conserved?  (meaning that the total amount of energy changes, but no work is done to change it?)