1. Momentum & Impulse

2. Impulse
Impulse = the average force applied to an object multiplied by the time over which the force acts
vector quantity (same direction as the force)
unit is a N s (Newton-second)
J = Impulse
F = Force
t = time
J = F Δt

3. Impulse Problem
Steve hits a baseball and gives it an impulse of 100 N s. His bat is in contact with the ball for 1.5 ms.
How much force did he use?
J = 100 Ns
t =1.5 ms = 1.5x10-3 s
F = ?
J=FΔt
F=J/ Δt= 100/1.5x10-3
F = 6.67 x 104 N

4. p=mv Momentum “inertia in motion” Momentum = an object’s mass
Momentum
“inertia in motion”
Momentum = an object’s mass
times its velocity
vector quantity (same direction as velocity)
unit is kg m/s (kilogram-meter per second)
p = momentum
m = mass
v = velocity
p=mv

5. Momentum Problems
A baseball of mass 0.10 kg is moving at 35 m/s. Find the momentum of the baseball.
m = 0.10 kg
v = 35 m/s
p = ?
p = mv = (.10)(35)
p = 3.5 kg m/s

6. Momentum Problems
A compact car, mass 725 kg, is moving at 25 m/s. Find its momentum. At what velocity is the momentum of a larger car, mass 2175kg equal to that of the smaller car?
m=725 kg
v = 25 m/s
p = ?
p = mv
p2= p1
p2 = 18,125 kg m/s
m2 = 2175 kg
p = mv
v = p/m
p = 725(25)
= 18,125
2175
p = 18,125 kg m/s
v = 8.3 m/s

7. The Relation Between Force and Momentum
Newton’s 2nd Law
Recall the definition of acceleration
Substituting,
Remember momentum
Therefore,
So,
F Δt = Impulse (J)
J = Δp
F=ma
Δp=m Δv
Δp=F Δt
Note: This derivation is the basis for the impulse-momentum theorem

8. Impulse-Momentum Theorem
Impulse-Momentum Theorem = the impulse of an object equals the change in momentum of that object
J=Δp
FΔt = mΔv = m vf – m vo

9. Impulse-Momentum Theorem
the impulse of an object equals the change in momentum of that object.
FΔt = mΔv = m vf – m vo
J=Δp

10. Examples of Impulse Increasing Momentum:
apply greatest force possible (large F)
extend time of contact (t)
ex. Baseball player and golfer as they follow through. (they increase t)
Changing Force
1. over a long time:
want to lessen force
extend impact time, reduce impact force
ex. Airbags in cars (increases t)
2. over a short time:
the impact force is large
ex. Breaking blocks by using karate
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.

11. Movie Punches How does a stuntman take a punch? Why?

12. Clicker Understanding
Raindrops keep falling …
What would do more damage to your car a raindrop or hailstone of equal masses hitting it? Why?
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Raindrop
Hailstone
Same

13. Impulse Momentum Problem
. A snowmobile has a mass of 2500 kg. A constant force is exerted on it for 60 sec. The snowmobile’s initial velocity is 6m/s and its final velocity 28m/s. What is the change in momentum? What is the force exerted on it?
m =2500 kg
t = 60 s
vi= 6 m/s
vf = 28 m/s
Δp = m Δv= m(vf-vo)
Δp = 2500(28-6)
Δp = 55,000 kg m/s

14. Momentum  Changing Forces
If the force acting on the body is not constant we can write
Δp = average force × Δt
Suppose the force acting on a body varies as shown below.
During the first three seconds the change in momentum was
During the next four seconds the change in momentum was
Δp2 = 8 × 6 = 48 Ns
So the total change in momentum was 60 Ns
Notice that the change in momentum can be found by calculating the area under the graph of force against time.

15. Graphical Interpretaion of Impulse
J = Impulse = area under the force curve
𝐽= 𝐹 𝑎𝑣𝑔 ∆𝑡

16. Clicker Understanding
Two 1-kg stationary cue balls are struck by cue sticks. The cues exert the forces shown. Which ball has the greater final speed?
Ball 1
Ball 2
Both balls have the same final speed
Slide 9-13

17. Conservation of Momentum
Momentum is conserved
The total momentum before collision or interaction equals the total momentum after a collision.
The change in momentum of one object is equal and opposite to the change in momentum of the other object in a collision.
(Newton’s 3rd Law)
po=pf
Δp1=-Δp2

18. Conservation of Momentum
Assumption:
No net external forces are acting on an isolated system of objects, the total vector momentum of the system remains constant.
Derive from Newton’s 2nd & 3rd Laws

19. Derivation: Conservation of Momentum
Initial Conditions
ma with va and mb with vb
After the collision the velocities change to ua and ub
Assume F is the force that object A experiences for a time Δt during the collisions
Newton’s 2nd Law

20. Derivation: Conservation of Momentum
Newton’s 3rd Law
Force experienced by B is -F
thus,
pinitial = pfinal
Conservation of Momentum

21. Conservation of Momentum

22. Clicker Understanding
Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the time intervals to stop them compare?
It takes less time to stop the ping-pong ball.
Both take the same time
It takes more time to stop the ping-pong ball.

23. Clicker Understanding
Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the distances needed to stop them compare?
It takes a shorter distance to stop the ping-pong ball.
Both take the same distance
It takes a longer distance to stop the ping-pong ball.

24. Collisions Conservation of Momentum always occurs Types of collisions:
Elastic:
a collision in which kinetic energy is conserved.
Inelastic:
a collision in which kinetic energy is NOT conserved.
some K.E. is converted to other forms of energy.
Totally Inelastic (Perfectly Inelastic)
after collision the two objects stick together and move with the same velocity.

25. Types of collisions
Objects collide and bounce off each other (Elastic and Inelastic Collisions) Solving,

26. Conservation of Momentum Examples
Glider A of mass kg moves along a frictionless air track with a velocity of m/s. It collides with glider B of mass kg moving in the same direction at a speed of m/s. After the collision, glider A continues in the same direction with a velocity of m/s. What is the velocity of glider B after the collision?

27. Totally Inelastic Collision
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.

28. Types of collisions
Totally Inelastic collision = 2 objects collide and stick together, moving off together
Usually one of the objects is initially at rest
Solving,

29. Swallowing: a Fish Story
What is the final velocities of the two fish?

30. Totally Inelastic Example
Calculate the final velocity of the engine and flatbed car after the collision.

31. Conservation of Momentum Examples
A kg hockey puck moving at 48 m/s is caught by a 75kg goalie at rest. With what speed does the goalie slide on the ice?

32. Inelastic vs Totally Inelastic Collisions
Momentum Conserved
KE Not Conserved
Objects stick together after collision.
Objects have the same velocity after the collision.
Similarities
Inelastic:
Momentum Conserved
KE Not Conserved
Objects move separately after collision.
Objects have different velocities after the collision.
Differences
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.

33. Elastic Collisions
If initially one object is moving and the other is stationary

34. Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.
Types of Collisions
Copywrited by Holt, Rinehart, & Winston

35. Explosions Is momentum conserved during explosions?

36. Types of collisions
Explosions- both objects start at rest and move in opposite directions Solving,

37. Clicker Understanding
A person attempts to knock down a large wooden bowling pin by throwing a ball at it. The person has two balls of equal size and mass, one made of rubber and the other of putty. The rubber ball bounces back, while the ball of putty sticks to the pin. Which ball is most likely to topple the bowling pin?
The rubber ball
The ball of putty
Makes no difference
Need more information

38. Identify the type of Collision

39. Identify the type of Collision

40. Identify the type of Collision

41. Clicker Understanding
Think fast! You’ve just driven around a curve in a narrow, one-way street at 25 mph when you notice a car identical to yours coming straight toward you at 25 mph. You have only two options: hitting the other car head-on or swerving into a massive concrete wall, also head on. In the split second before the impact, you decide to
Hit the other car.
Hit the wall.
Hit either one – it makes no difference.
Consult your notes.
Myth Busters

42. Review
In a head-on collision: Which truck will experience the greatest force? Which truck will experience the greatest impulse? Which truck will experience the greatest change in momentum? Which truck will experience the greatest change in velocity? Which truck will experience the greatest acceleration? Which truck would you rather be in during the collision?

43. 2-D Collisions
Since momentum is a vector, Conservation of momentum can be extended to two dimensional scenarios.
The x and y components of momentum as well as its total magnitude must be the same before and after the collision.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.

44. 2-D Collisions

45. Example Problem:
Two pucks on an air hockey table collide. Puck A has a mass of kg and is moving along the x axis with a speed of 5.5 m/s. It collides with puck B, which has a mass of kg and is initially at rest. After the collision the two puck fly apart as shown. Find the final speed of puck A and B.
Cutnell & Johnson, Wiley Publishing, Physics 5th Ed.