Name: ____________________________________
Write the formal definition of the Law of Conservation here:
Neatly write the mathematical formulas here and identify all the symbols.
There are two types of collisions. They are:
____________________ and ___________________
Define Inelastic collision:
What makes these collisions different from Elastic collisions?
Write out the formula here :
Date: _________ Period: ____
Provide some examples (3) of inelastic collisions and identify where the objects are “together” and where they are apart. a.
b.
c.
1.
2.
3.
4.
What is an elastic collision?
What are the formula for elastic collisions (be sure to identify the symbols for each equation.
Inelastic Collision Example Steps to solve

Example: Inelastic Collision
• A mineral wagon is moving at a speed of 4 meters per second. It’s mass is 2000 kg. It collides with a car that is not moving whose mass is 4000 kg. The cars stick together. What is the velocity of the two cars after they collide?
BEFORE AFTER
TOK: TOK:
What formulas will you use to solve this problem?
Final velocity = _________________________________
Elastic Collision (your turn):
The mineral wagon has a mass of 2,000 kg and is moving at 4.0 m/s toward the guard van on a level frictionless track. The guard van is moving at 1.0 m/s toward the mineral wagon and has a mass of 4,000 kg. The trains collide but do not lock together. Find the velocity of the guard van if the mineral wagon is moving at 1.0 m/s to the left after the collision.
1.
If you have only one object and are determining momentum a.
Momentum = mass x velocity i.
The units are kg*m/sec (or cm/sec etc) ii.
If an object is not moving momentum = 0
2.
If you have only one object and are determining change in momentum a.
If you are changing the momentum of a “single object” some force MUST have been applied to change the momentum. b.
Change in momentum can be calculated by subtracting the initial momentum FROM the final momentum i.
 f
-
 i
=
  ii.
Change in momentum is equivalent to impulse (J) c.
So, what is an impulse? i.
An impulse is the product (you multiply) of the average force (F) exerted on the object (remember to change momentum you need to apply a force) and the amount of time (

t) that you applied that impulse. ii.
J = F

t = momentum iii.
Momentum can change in a positive direction
(faster motion or higher mass) or a negative direction (slower motion or lower mass) iv.
Typically, we change the velocity (and the mass stays constant). d.
Since a change in momentum = impulse, if you can calculate either J or
  you automatically have the other value…Pretty cool. So J =
 
3.
In the lab we looked at conservation of momentum.
Conservation of momentum is generally demonstrated by

looking at the momentum of two objects in a BEFORE and an
AFTER situation. a.
In a CLOSED SYSTEM:
Momentum initial (before) = momentum after i.

I -
 f ii.
 i1
+
 i2
=
 f1
+
 f2 iii.
m i1
v i1
+ m i2
v i2
= m f1
v i1
+ m f2
v f2 b.
In the lab, we used two carts. One cart had a plunger that could “bump” the other cart. c.
Because both carts were “standing still” at the beginning, the momentum of each cart was 0. The two carts together are considered a “system”. d.
Once the plunger was “fired”, both carts traveled, but in opposite directions. e.
Velocity (displacement/time) is a VECTOR measurement, which means we must take into account
the direction of the motion. One cart went in a positive direction, and the other in a negative direction. If the cart travels in a negative direction (to the left), it has a negative velocity and therefore a negative momentum
(mass is always positive) f.
Since an equal force is applied to the carts over an equal amount of time (both carts had to hit the “ends” at the same time), we can measure the velocity (distance traveled in a “time unit” (tu)) and multiply by the mass to get the momentum for each cart. g.
The carts were not exactly equal masses. Since the cart with the plunger has a slightly greater mass, you would expect this cart to always be a bit “slower” than what you predicted. h.
BIGGEST MISTAKE MADE – forgetting the negative sign!
4.
Using conservation of motion to solve collision problems. a.
Collisions involve TWO objects. b.
ELASTIC COLLISIONS i.
The objects are “separate” to begin with (each having its own momentum), then interact (hit each other), then each go their own separate way. ii.
 i1
+
 i2
=
 f1
+
 f2 iii.
m i1
v i1
+ m i2
v i2
= m f1
v i1
+ m f2
v f2 c.
INELASTIC COLLISIONS i.
The objects are “separate” to begin with (each having its own momentum), then interact (hit each other), and stay together after the impact.
1.
In this case, to calculate final momentum you add the two masses together FIRST, then find the final velocity
2.
Example: two train cars that “couple”
3.
m i1
v i1
+ m i2
v i2
= ( m f1
+ m f2
)(v f
) ii.
The objects are together to begin with (one mass, with one momentum) and then one or more “pieces” separate.
1.
In this case the initial momentum is calculated by multiplying the entire mass by the initial velocity. The final momentum is calculated by calculating the momentum of each “piece”
2.
( m i1
+ m i2
)(v i
) = ( m f1
v f1
+ m f2
v f2
)
3.
In our class there will only be two pieces and each will go in the opposite direction)

REVIEW PROBLEMS
1.
Typically, a tennis ball hit during a serve travels away at about 51 m/s. If the ball is at rest in mid-air when struck, and it has a mass of
0.058 kg, what is the change in momentum of the tennis ball when it leaves the racket? a.
What are we asked to find? b.
Draw a picture of what is happening (initial and final) c.
Write a table of knowns (initial and final) d.
What equation will you use (BE SURE THAT IT AGREES WITH THE
QUESTION YOU ARE ANSWERING). Write the equation (in letters) and solve the problem.
2.
During a soccer game a ball (mass 0.425 kg), which is initially at rest, is kicked by one of the players. The ball moves off at a speed of 26 m/s. Given that the impact lasted for 8.0 ms, what was the average force exerted on the ball? a.
What are we asked to find? b.
Draw a picture of what is happening (initial and final) c.
Write a table of knowns (initial and final) d.
What equation will you use (BE SURE THAT IT AGREES WITH
THE QUESTION YOU ARE ANSWERING). Write the equation
(in letters) and solve the problem.

3.
An empty 15000 kg coal cart is coasting on a level track at 5.00 m/s.
Suddenly 5000 kg of coal is dumped into it from directly above it.
The coal initially has a zero horizontal velocity. Find the initial momentum of the cart. Find the final momentum of the coal cart.
Find the final speed of the car a.
What are we asked to find? b.
Draw a picture of what is happening (initial and final) c.
Write a table of knowns (initial and final) d.
What equation will you use (BE SURE THAT IT AGREES WITH
THE QUESTION YOU ARE ANSWERING). Write the equation
(in letters) and solve the problem.
4.
A 40000 kg freight car is coasting at a speed of 5.0 m/s along a straight track when it strikes a 30000 kg stationary freight car and couples to it. Find the momentum of each train car before the collision. What will be the combined speed of the cars after the impact? a.
What are we asked to find? b.
Draw a picture of what is happening (initial and final) c.
Write a table of knowns (initial and final) d.
What equation will you use (BE SURE THAT IT AGREES WITH
THE QUESTION YOU ARE ANSWERING). Write the equation
(in letters) and solve the problem.

5.
A ball of mass 1m sits at the coordinate origin when it explodes into two pieces that shoot along the x-axis in opposite directions. When one of the pieces (which has mass 0.270m) is moving at 35 m/s, how fast and in what direction is the other piece moving? a.
What are we asked to find? b.
Draw a picture of what is happening (initial and final) c.
Write a table of knowns (initial and final) d.
What equation will you use (BE SURE THAT IT AGREES WITH
THE QUESTION YOU ARE ANSWERING). Write the equation
(in letters) and solve the problem.
6.
What average resisting force must act on a 3 kg mass to reduce its speed from 65 cm/s to 15 cm/s in 0.20 s? (Hint : Find the change in momentum.) a.
What are we asked to find? b.
Draw a picture of what is happening (initial and final) c.
Write a table of knowns (initial and final) d.
What equation will you use (BE SURE THAT IT AGREES WITH
THE QUESTION YOU ARE ANSWERING). Write the equation
(in letters) and solve the problem.