1. Momentum and Impulse

2. Momentum What is Momentum? Mass in Motion
Momentum is the product of mass and velocity
Measured in kg•m/s or kilogram meters per second
p is momentum in equations
What makes an object difficult to stop?
The more mass, its harder to stop
The more velocity, its harder to stop
p = mv
What is a vector?
BOTH Magnitude and Direction
Momentum can be + or - depending on coordinate system

3. Check for Understanding
What is the momentum of a bee that has a mass of 10 grams and flies down at 2 m/s?
10g=0.01kg (Conversion)
p=mv=0.01 kg x -2 m/s= -0.02kgm/s
What is the momentum of a turtle that has a mass of 1kg and moves at 0.05m/s right?
p=mv=1 kg x 0.05 m/s= 0.05kgm/s
Which one has a greater momentum? The bee or the turtle?
The turtle has more momentum (larger magnitude).

4. Impulse What is impulse?
Change in momentum caused by a force exerted over a time interval
J is impulse in the equations
J = FΔt
J=Δp
What changes in momentum equation?
Velocity
Δp= mΔv

5. Check for Understanding
A bowling ball of 10kg moving at 3m/s bowls through a set of bowling pins. Right before the ball falls down the shoot it is going 2m/s
What is the impulse the bowling pins provide to a bowling ball?
J = mΔv
J = m*(V final – V initial)‏
J = 5*(2-3)=-5kgm/s
This shows that the force was in the negative direction and slowed down the ball
In soccer, a penalty kick with the soccer ball is initially at rest. The soccer ball, 300g, is kicked at 25m/s.  The player's foot was in contact with the ball for 0.1 seconds. What was the impulse on the ball? Find the Average Force
300g=.3kg (Conversion)
J = mΔv = m*(V final-V initial)= .3*(25-0) = 7.5kgm/s
J = FΔt
7.5 = F * 0.1
F= 75 N

6. Impulse-Momentum Theorem
Impulse and change in momentum can also be shown rearranging Newton’s 2nd Law
Recall Newton’s 2nd Law
F=ma
𝐹=𝑚 Δ𝑣 Δ𝑡
𝐹Δt=mΔv

7. Lab Discussions
What was the relationship between the initial momentum and final momentum?
Directly proportional relationship (linear graph)
What was the Slope value? What does it tell us?
Should be numerically 1 ((𝑘𝑔∗ 𝑚 𝑠 )/(𝑘𝑔∗ 𝑚 𝑠 )
Tells us that final momentum is equal to initial momentum
Why did the initial and final momentum not change?
Conservation of Momentum
Only when there is no external force
Momentum stays the same!!
What is the mathematical equation for momentum?
p=mv
Initial momentum = final momentum
m1iv1i+m2iv2i= m1fv1f+m2fv2f

8. Types of Collisions Remember when momentum is conserved
When outside forces are balanced
pi=pf
Two scenarios of collision in carts
Elastic Collison
Cart 1 hits Cart 2 -> Both Carts REPEL each other
m1iv1i+m2iv2i= m1fv1f+m2fv2f
Inelastic Collision
Cart 1 hits Cart 2 -> Cart1 and Cart 2 Masses ATTRACT (STICK) with each other
m1iv1i+m2iv2i =(m1+m2)vf

9. Momentum Bar Chart Representation
1. Write down all scenarios for initial and final situations.
2. Designate objects in the system by listing the object, its mass, and its velocity in the chart -- use variables for unknown quantities.
3. Draw a horizontal bar to represent the size and direction of the momentum for each object.
Write the conservation of momentum equation for the bars
Solve for the unknown quantity.

10. Momentum Bar Chart Representation Practice
A 800 kg car with a speed of 20 m/s and a 500 kg car with a speed of 16 m/s collide together. When they collide, the two cars stick stick together. Determine the velocity of the cars (magnitude and direction)immediately after the collision