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LPH 105 W15 7.intro

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Richard Datwyler

on 24 May 2016

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Transcript of LPH 105 W15 7.intro

Momentum
Impulse - momentum
Conservation of Momentum
Collisions
Elastic
Inelastic
2-D Collisions
Center of Mass
Relates: Force, time, and momentum
No outside forces
Momentum you start with, is what you end with
Both KE and Momentum are conserved. BOUNCE
Only momentum is conserved, some KE is "lost", STICK
Can be Elastic or inelastic
Do it by COMPONENTS
find in both X and Y directions, same process
As we begin we need to place this information
somewhere we have been.
So we can make an association with what we have
learned.
Momentum and its relation to force
We call this the impulse momentum theorem.
mv
mv
mv'
mv'
A
A
A
A
A
A
A
B
B
B
B
B
B
B
F
F
A from B
B from A
This equation is the conservation of momentum.
The caveat is that there must be no outside forces.
Collisions
Thought process

A really light mass collided with a really heavy mass, what would happen if...
The heavy mass was very solid, and the light mass was 'squishy' ?
They were both very solid?
Note, momentum is a vector, what about kinetic energy?
Kinetic energy is conserved if the collision is Elastic
Elastic collisions
Only outside forces are an issue.
Newton's Cradle
Energy going in = energy going out

momentum in = momentum out
Final answer. If you have two masses
one initially moving, other at rest,
and they collide elastically, their final
velocities are:
V = 0
2
i
Elastic
linear
Elastic collisions.
If 2nd mass not initially at rest......
If not elastic --- no good
If not linear --- no good.
Change your coordinate system.
Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one ball's initial speed was 2.00 m/s and the other was 3.00 m/s what will be their speeds and directions after the collision?
Here my collision equation
takes on the following form

Because Kinetic energy is not conserved,
there is a 'loss'
thus my energy equation looks like the above.

Inelastic collisions
In this type of collision, momentum is still conserved
but the kinetic energy is Not.

In a perfectly inelastic collision, the two objects 'stick'
together after the collision.

These are often modeled by clay, or a ballistic problem.
The equations we have written for conservation of momentum are vector equations.
Thus we can write them in their x & y components and be alright.

2-D Collisions
Demo
https://video.byui.edu/media/Collision+demonstration/0_3bil8221/20172242
Center of mass
Physically we think of it as a balance point,
and this is probably the easiest way to actually
solve for the center of mass.

If you balance off two directions, the intersection
of those lines, will be the center of mass.

Like wise if you spin something, in the air (no other forces)
it will spin around the center of mass.

Computationally.
I can solve for the center of mass by adding up
all the masses at all the locations, and multiplying
those masses by their distance, and then dividing
that whole sum by the total mass.....
like this:
"Im having a little trouble following the collisions in two dimensions problems. "
"can you clarify how to do a FBD or the equivalent to it for this chapter? specifically collisions in two dimensions. "
"I don't understand the difference between inertia and momentum. "
"I didn't get what an impulse was..."
"Momentum vs kinetic energy in a collision?"
Can you explain the first question on the quiz?
Newton's second law can be written as the change of momentum divided by the change in time
Full transcript