1. Car Crash Video

2. Momentum, Impulse, and Collisions

3. Momentum (ρ)
expresses the resistance of a body to slowing down or speeding up
related to an object’s inertia
p = mv
m = mass (kg)
v = velocity (m/s)
Unit is kg m/s

4. 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
Givens
Unknown
Equation
Substitute
Solve

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

6. Impulse (J) Definition: measures a change in momentum J = ∆p = pf - pi
∆p = m∆v = m(vf - vi)

7. Impulse (J) = ∆p = m∆v = F(∆t)
To calculate multiply the average force (F) acting on a body by the length of time (∆t) the force acts.
J = F(∆t)
F = force (N or Newtons)
∆t = time (s)
Unit is N s
Impulse (J) = ∆p = m∆v = F(∆t)

8. Putting it all together…
Newton’s 2nd Law F = ma
a = Δv/t
F=mΔv / t
F(t) = m(vf-vi) Notice impulse, on the left side, is equal to the change in momentum of an object.

9. Impulse

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

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

12. One more…
A ball changes velocity from 20 m/s to 30 m/s. If it has a mass of 5 kg, what impulse was necessary to cause this change?
50 N·s
Givens
Unknown
Equation
Substitute
Solve

13. (Hint: use Impulse=F(t))
Your Turn
How long would it take a 5 N force to change the velocity of the ball?
(Hint: use Impulse=F(t))
10 s
Givens
Unknown
Equation
Substitute
Solve

14. Classwork
Work momentum and impulse problems

15. The Law of Conservation of Momentum
In an isolated system, the total momentum does not change.
Momentum is conserved in all types of collisions!

16. There are 2 types of collisions
Elastic: Objects bounce off each other
Kinetic energy is conserved
m1v1i + m2v2i = m1v1f + m2v2f
Where m1 is mass of object 1, and m2 is mass of object 2
Where i stands for initial and f stands for final
Use + and – velocities to show direction!

17. 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 +1.4 m/s?
Givens
Unknown
Equation & Substitute
Solve

18. There are 2 types of collisions
Inelastic: Objects stick together
Kinetic energy is NOT conserved
m1v1i + m2v2i = (m1 + m2)vf
Where vf is the velocity of 2 objects stuck together after the collision
Remember + and – velocities to show direction!

19. Example
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?
Givens
Unknown
Equation & Substitute
Solve