Conservation of Energy

- in cases where there isn't friciton we can observe that when an object's height above the ground decreases, its speed will increase  or vice versa (i.e.  rolling up or down an incline, dropping down or being thrown up, a pendulum swinging back and forth)

- since kinetic energy depends on speed and potential energy depends on height, we can say that when the potential energy decreases, the kinetic energy increases and vice versa.  Again, this is if there isn't friction.

- if we actually make measurements we'll find that the amount that the PE decreases is equal to the amount the kinetic energy increases (if PE decreases by 10 J, KE will increase by 10 J).  

- another way to explain this is to say that the energy transforms from one type to another (KE->PE or PE->KE).

- we say that energy is conserved (total energy is the same at all times)

- when solving Conservation of Energy problems, we find the total energy (Etot = KE + PE) at one point and set it equal to the total energy (Etot = KE + PE) at another point

KE and PE

Energy is teh ability to cause change (damage or work).

Kinetic Energy

One type of energy is kinetic energy- energy due to motion (speed).  If an object is moving, it can do damage (by crashing into another object)

KE = 1/2 mv^2

Potential Energy

Potential energy is energy due to position (height).  If an object has a height above ground, it can cause damage (again by crashing into another object).

PE = mgh

h is not always directly given.  Sometimes you have to calculate it.

- if it at the top of a loop, the height is equal to twice the radius of the loop.

- if it is on a slope, use trigonometry:  either sin, cos, or tan

Total Energy

The total energy of an object is the sum of its potentail and kinetic energies.

E = PE + KE

Impulse-Momentum

- momentum tells us how hard it is to stop an object

- the Impulse-Momentum Theorem tells us how to do it (more specifically, how to change the momentum of an object):

F(T) = p

- the equation above tells us that in order to change the momentum (from some inital momentum, pi to some final momentum, pf) you need to apply a force for a certain amount of time.

- the force multiplied by time, F( t) in the equation is called impulse

- notice that for a certain value of impulse (e.g. 50 N s), you can apply a large force (25 N) for a short time (2 s) or a smaller force (10 N) for a longer time (5 s).

- usually we want a small force in a collision.  So in order to do that you need try to extend the time as long as possible.  So remember:  make the time longer in order to have a smaller force!

Conservation of Momentum

Conservation of Momentum Notes

Momentum

- when looking at collisions we want to see what factors are important in determining the outcome of the collision (what will deteremine if each objects moves one way versus the other, whether they will stop or stick together, etc)

- after observing different kinds of collisions we can see that 2 factors are important: the mass of each object and the velocity of each object.

- each of the 2 factors are not significant by themselves but taken together they give useful information in a collision.


- so we look at a quantity that incoporatate mass and velocity and we call it momentum, designated by the letter p.

p = mv (when using this formula m is in kg, v is in m/s, and p will be in kg m/s)