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# PH 121 10.5-10.7

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## Richard Datwyler

on 11 June 2018

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#### Transcript of PH 121 10.5-10.7

Energy and Elastic Collisions
You'll recall we had a demonstration of spring constant and ballistic pendulum yesterday.
This was a demonstration of conservation of energy.

The spring seems almost out of sorts, save that we can discuss the energy stored in a spring.
Now we need the potential energy of a spring.

Note it is an energy of position, not motion, thus it is a potential
energy, specifically elastic potential energy.
Again make note of the delta x. This is a change in position from the
equilibrium. It can thus be either a stretching or a compressing of the
spring.
Because the term is squared, the sign turns positive no matter what.

Note it is also a scalar, no direction, and the units are Joules

Finally I ask, can you have a negative potential energy of a spring?
When a spring is horizontal the only energy
is kinetic and potential of the spring.

where as when it is vertical the potential energy
can be store both in the spring and due to gravity.

tomorrow there is an example in the workbook (13)
lets solve this problem. With spring constant
k = 250 N/m
m = 5.0 kg
h = 40 cm

Take a step back.
As we do these problems it is all about conservation of energy.
What energy do we have initially, and what energy do we have
finally.

Realize that some problems can be solved with kinematics.
but others not.

Elastic Collisions
An elastic collision is one where the total
mechanical energy is conserved.

Meaning that the kinetic energy gets transferred
to a spring potential in the atoms, and then that
in turn gets transferred back to kinetic energy,
none of which is lost.
When we had inelastic collisions there were generally
3 unknown variables. Now there are four.
This can be problematic if you don't know either
of the final velocities.
But we now have another equation to help us, energy.
Here are both equations of conservation:

momentum

energy.
If we make some assumptions we can solve for the final velocities
First we will assume the second mass is stationary.
Use this and solve for momentum equation as follows
This we can substitute back into the energy equation.
This solved for one final velocity
now substitute back into find the
other.
Here is that substitution.
Things to note.
This collision is perfectly elastic
It is head on (no glancing only 1D)
Also the second mass is initially at rest

This last seems to be the deal breaker,
but it isn't we can change our coordinate
system to make it work.

Before example consider 3 cases
Ball 1, with a mass of 100 g and traveling at 10 m/s collides head on with ball 2, which has a mass of 300 g and is initially at rest. What is the final velocity of each ball if the collision is
A. perfectly elastic
b. perfectly inelastic?
As noted we can also do a transfer of
coordinate system to make this problem
more fun.

Energy diagrams
As noted earlier, one of the tactics to solving
these problems is finding the initial energy, and have that be conserved.

One way of visualizing this is an energy diagram

Most of this book's little diagrams, I don't agree with,
This one however works well.
This first one is of a gravitational potential only
This is a spring potential
This one is even more general, it could be any type of potential
This brings up the idea of Equilibrium positions

An equilibrium is where an object doesn't move.
or where the forces are balanced.

There are multiple types

Stable, and unstable as well as others.
To be stable, a small perturbation from the equilibrium will

Unstable is when a small perturbation leads to greater movement
away form the equilibrium
how many equilibrium
are there in this graph
A. 1
B. 2
C. 3
D. 4

How many of these
equilibrium are
stable?
A. 1
B. 2
C. 3

Lastly the section ends with
piece on molecular bonds
It uses one of these energy diagrams
and it makes for a bit of an interesting
read, but it glosses over some things.
So we'll leave it until we get to atomic
physics.

A 100 G ball moving to the right at 4.0 m/s catches up and collides with a 400 g ball that is moving to the right at 1.0 m/s. If the collision is perfectly elastic what are the speed and direction of each ball after the collision?
A 100 g granite cube slides down a 40 degree frictionless ramp. At the bottom, just as it exits onto a horizontal table, it collides with a 200 g steel cube at rest. how high above the table should the granite cube be released to give the steel cube a speed of 150 cm/s. (assume elastic)
.638 m
-5 & 5 m/s
2.5 m/s
-0.8 & 2.2 m/s
25.8 cm
"So could we ever really have a truly perfectly elastic or inelastic collision?"
"How do Galilean reference frames make mechanical conservation problems easier?"
"I want to get strait all of the equations for all of these different energies. Could you give them to us again?"
"Can you do example 10.6 or 10.7 in class?"
"Can we review how to use reference frames and Galilean transformation?"
"can you explain a little bit more about the energy diagrams?"
Full transcript