1. Momentum, Impulse, and Collisions

2. Momentum (p) expresses the resistance of a body to slowing down.
related to inertia
p = mv
m = mass (kg)
v = velocity (m/s)
Unit is kg m/s

3. Example
A toy car has a mass of 5 kg. If it is moving at a velocity of 4 m/s, what is its momentum?
20 kg•m/s
Given
Unknown
Equation
Substitute
Solve

4. Your Turn
What is the momentum of a 25 kg boy moving at a speed of 1.2 m/s?
30 kg•m/s

5. Impulse (I) measures a change in momentum Impulse = ∆p = m∆v
Impulse = ∆p = m(vf – vi)

6. Impulse (I)
To calculate multiply the average force acting on a body by the length of time the force acts.
Impulse = F(∆t)
F = force (N or Newtons)
∆t = time (s)
Unit is N s
See equation sheet.

7. Putting it all together…
F(t) = m(vf-vi) Notice impulse, on the left side, is equal to the change in momentum of an object.

8. Impulse

9. Example
An 8 N force acts upon an object for 5 seconds. What impulse is given this object?
40 N•s
Given
Unknown
Equation
Substitute
Solve

10. (Hint: use Impulse=F(t))
Your Turn
A ball changes velocity from 20m/s to 30m/s. If it has a mass of 5kg, what impulse was necessary to cause this change?
50N·s
How long would it take a 5N force to change the velocity of the ball?
(Hint: use Impulse=F(t))
10s

11. The Law of Conservation of Momentum
In an isolated system, the total momentum does not change.

12. There are 2 types of collisions
Elastic – Bounce off
m1v1i + m2v2i = m1v1f + m2v2f
Where m1 means mass of object 1, m2 means mass of object 2
Where i means initial & f means final
Inelastic – stick together
m1v1i + m2v2i = mTvT
Where T means total
Use + and – velocities to show direction.

13. 2kg(2m/s)+3kg(-1m/s) = 2kg(v1f)+3kg(1.33m/s)
Example
A 2 kg ball strikes another ball head on at an initial velocity of +2 m/s. If the second ball had a mass of 3 kg and was initially moving at -1 m/s, what is the final velocity of the 2 kg ball if the vf of the 3 kg ball is now +1.33m/s?
Define variables. Then:
m1v1i + m2v2i = m1v1f + m2v2f
2kg(2m/s)+3kg(-1m/s) = 2kg(v1f)+3kg(1.33m/s)
v1f = -1.5m/s

14. 500kg(10m/s)+700kg(25m/s) = 1,200kg(vT)
Last one…
A 500 kg car is driving at a velocity of 10 m/s. Another car (700 kg) hits it from behind at a velocity of 25 m/s and the two cars interlock bumpers. What is the resulting velocity of the two cars?
Define variables. Then:
m1v1i + m2v2i = mTvT
500kg(10m/s)+700kg(25m/s) = 1,200kg(vT)
vT = m/s