Download Conservation Of Momentum

Linear Momentum, Impulse & Conservation of Momentum
Conceptual Physics
Momentum: Momentum is inertia in motion, or mass in motion. Momentum is a characteristic of a
moving object that is equal to its mass times its velocity. Momentum is also called progression.
(Objects in motion have a tendency to progress in their state of motion.)
Quantity
Variable
Unit
Equation
Consider two vehicles: A stationary Navigator and a Mini Cooper moving at 20 m/s.
Which has more inertia?
Which has more momentum?
Why?
Problem #1:
a. Calculate the momentum of a 72 kg person
riding on a 175 kg motorcycle at a speed of 26.7 m/s.
(60 miles per hour).
b. Calculate the momentum of a 18,200 kg
tractor trailer moving at a speed of 26.7 m/s.
(60 miles per hour).
Problem #2: Consider a boy running down a hill, being followed by a large boulder. If the boulder and
the boy have the same momentum, will the boulder crush the boy? Why?
Problem #3: A 3 kg cart (blue) rolls at a constant speed of 2 m/s. A 2 kg red cart is stationary. Draw a
diagram of the carts. Calculate each cart's momentum.
What happens after the blue cart hits the red cart?
 
The blue cart ....
 The red cart...
Why?
Recall Newton's Laws of Motion:
When object interact with each other, the velocity of each object can change. What causes the change
in velocity?
Each object applies an unbalanced force on the other when they interact with each other, and as a
result, individual objects' velocity changes. During events, the velocities of the individual objects
change. Therefore, each object's momentum (p = mv) changed during the event.
What caused the change in momentum?
THE IMPULSE!
The Impulse is what causes the momentum of an object to change when it physically interacts with
another object. Impulse is equal to force times time. (the force that occurs during the impact, times the
time during which the impact occurs.)
Quantity
Variable
Unit
Equations
Impulse
Problem #4: A truck with a mass of 2000 kg is travelling at 15 m/s.
What is the momentum of the truck? What size impulse is required to stop the truck?
What size force occurs if
the truck stops in 0.75 sec?
What size force occurs if
the truck stops in 12 sec?
How are cars designed to keep you safe? How does this relate to the concept of impulse?
Using the concept of impulse (Force times time), explain why you can catch a raw egg with a sheet!
Learning Activity: How does a collision affect the motion of marbles?
Momentum is a quantity that describes a moving object. Momentum is mass in motion.
For each directive, draw a diagram indicating the position and motion of the marbles before the collision and
position and motion of the marbles after the collision. Write numbers on each marble in your diagram to keep
track of which ones are moving and which are stationary. Also describe in words any changes in motion that
occur as a result of the collision.
A. Place five identical marbles in the center groove of a ruler. Launch a sixth marble toward the five stationary
marbles. Draw and describe what happens.
B. Place four marbles in the center groove of the ruler. Launch two marbles at the four stationary marbles.
Draw and describe what happens. Repeat this activity, rolling 3 into 3, 4 into 2, and 5 into 1.
C. Remove all but two marbles from the ruler. Roll these two marbles toward each other with equal speed.
Draw and describe what happens.
Analyze and Conclude:
1. How did the approximate speed of the marbles before each collision compare to the speed of the marble
after each collision?
2. What factors determine how the speed of the marbles changes in a collision?
3. What do you think would happen if three marbles rolling to the right collided with two marbles rolling to the
left (if they were all rolling with the same speed). Make a prediction and then test your answer.
Conservation Of Momentum
Collisions and Explosions: (physical interactions between objects)
What happens to objects during collisions and explosions?
The objects…..
During events, mechanical energy usually is not conserved because it takes energy to make objects
bend, break, deform or stick together. Also, friction acts, so some of the energy is transformed into
heat.
Since energy is not conserved during events, it can’t be used to study the events. Linear Momentum is
conserved during events (if no other forces act during the event) so it can be used to study the events.
The Law of Conservation of Momentum states that the momentum of the system before the event is
equal to the momentum of the system after the event.
=
Also means that the change in momentum (gain) of one object in the system is equal the change of
momentum (loss) of the other object in the system.
How to draw a diagram for conservation of momentum problems.
The diagram will also serve as your table of variables.
Definitions:
system – two or more objects that interact with each other during an event. They experience equal and
opposite forces during the event, so they have the same impulse.
event – the physical interaction between two or more objects during which an impulse occurs. collisions
and explosions. Events are depicted with diagrams of the system before the event, during the event
and after the event.
Elastic Collision
mA
mB
mA
mB
mA
mB
Inelastic collision
mA
mB
mA
mB
mA
mB
Explosion
mA
mA
mA
mB
mB
mB
Problems:
1. A 2 kg cart moving to the left with a velocity of 5 m/s collides with an 6 kg cart that was at rest. The
6 kg cart moves to the left with a velocity of 3 m/s after the collision. What is the velocity of the 2 kg
cart after the collision? (speed and direction)
2. A 3 kg fish is in motion at 2 m/s when it encounters a 1.0 kg fish at rest. The large fish swallows the
smaller fish and continues in motion at a reduced speed. What is the speed of the large fish (and
the smaller fish) after the collision?
3. A 2 kg cart and 6 kg cart are together with a compressed spring placed between them. The spring is
released and the carts explode away from each other. The carts were moving to the left at 1 m/s
before the explosion. If the 6 kg cart moves to the left with a velocity of 2.5 m/s, what is the velocity
of the 2 kg cart?
Linear Momentum Problems
1. An 8 N force acts on a 5 kg object for 3 sec. What impulse is given the object? What change in momentum
does this impulse cause? If the object’s initial velocity was 25 m/s. what is its final velocity?
2. A 6 N force acts on a 3 kg object for 10 sec. What will be the final velocity of the object if its initial velocity
was 10 m/s?
3. A 2041 kg truck is acted upon by a force that decreases its speed from 10 m/s to 5 m/s in 5 sec. What is the
magnitude of the force?
4. A 2000 N force acts on a rocket of mass 1000 kg, increasing its speed from rest to 200 m/s. How long did the
force act?
5. A 65 kg person is in a car that is moving at 20 m/s (45 miles per hour). What size impulse is required to stop
the person? Some people think they can stop themselves in an accident by putting their arms on the
dashboard. If the dashboard stops the person in 1.2 s, what is the average force that acts on the person
while they are stopping? Can you bench press that much weight? (divide the force by 2.2 kg per pound to
determine the weight in pounds). How do seat belts and air bags help keep people safe during accidents?
6. Julie is at rest in her 1502 kg car at a red light. A 2000 kg car behind her, moving at 4.5 m/s, applies it's
breaks to slow down, but slips on a patch of ice and runs into the back of Julie's car. The two cars stick
together and move at a velocity of 2.57 m/s.
a. Calculate the momentum of each of the cars before the collision and after the collision.
b. What is the change in momentum of each of the cars?
c. If the collision took place over .8 seconds, what force does each car experience?
7. A 700 kg car moving at 20 m/s collides with a stationary truck with mass 1400 kg. The two vehicles interlock
as a result of the collision. What kind of event occurs? What is the velocity of the car/truck?
8. A .015 kg pellet moving at 600 m/s hits a stationary .1 kg block and becomes embedded in the block. What
kind of event occurs? With what speed do they move off together?
9. A 0.5 kg ball traveling at 6 m/s collides head-on with a 1 kg ball moving in the opposite direction at 12 m/s.
The 0.5 kg ball moves away at 14 m/s in the opposite direction after the collision. What kind of event occurs?
Find the velocity of the 1 kg ball after the collision.
10. A plastic ball of mass 0.2 kg moves at 0.6 m/s, east. It collides with a 0.1 kg ball moving at 0.8 m/s, west.
After the collision, the velocity of the 0.1 kg ball is 0.6 m/s, east. What kind of event occurs? What is the
velocity of the 0.2 kg ball after the collision?
11. A .025 kg ball moving at 10 m/s, right, collides head-on with a .050 kg ball moving at 3 m/s, left. After the
collision, the .025 kg ball moves at 6 m/s, left. What is the velocity of the .050 kg ball after the collision?
12. A 3 kg can containing a .1 kg firecracker is thrown into the air. As the can stops moving up, the firecracker
explodes, exiting the can at 25 m/s toward the left. The can moves towards the right. What is the speed of
the can after the explosion?
13. A thread holds two carts together that are separated by a compressed spring. The thread is broken. One cart,
with mass of 1.5 kg, moves with a velocity of .27 m/s to the left. What kind of event occurs? What is the
velocity of the other cart with mass of 4.5 kg?
1. 24 Nsec; 24 Nsec; 29.8 m/s
2. 30 m/s
3. -2040.82 N
4. 100 sec
5. 1300 kgm/s; 1083 N; 492 lbs ….
6. 0 kgm/s; 9000 kgm/s; 3860 kgm/s, -3860 kgm/s; 4825 N
7. 6.67 m/s
8. 78.26 m/s
9. -2 m/s
10. 0.1 m/s, west
11. 5 m/s, right
12.: -0.83 m/s (to the right)
13. 0.09 m/s, right