1. MOMENTUM & INERTIA
Herron Physics, Unit 4

2. What is momentum? “Inertia in motion” Think about it…
Which would hurt worse to get hit with, a baseball or a golf ball?
Depends on their motion!
What factors contribute to how badly something will hurt when it hits you?
Mass
Speed (velocity)

3. p=mv EQUATION The equation for Momentum is: Where:
p = momentum measured in ____
m = mass measured in kg
v = velocity measured in m/s

4. Rearranging & Proportions
Rearrange this equation for v and for m.
How is each pair proportional:
p & m?
p & v?
m & v?

5. How/when could a roller skate and a truck have the same momentum ?
Question:
The roller skate and truck can have the same momentum if the skate is moving quickly and the truck is moving slowly.
OR if they are both at rest.
A 1000 kg truck moving at 0.01 m/s has the same momentum as a 1 kg skate moving at 10 m/s. Both have a momentum of 10 kg m/s.
(1000kg x .01m/s = 1kg x 10m/s )
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

6. Practice Problem
A 30 kg goose flies south for the winter. If it flies at a velocity of 4 m/s, what is its momentum?
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

7. Practice Problem
A baby goose flies at the same velocity, but has 1/5 of the momentum of its mother (who has a mass of 30kg). What is the mass of the baby goose?
Hint: don’t use an equation!!
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

8. Practice Problem
My .7 kg piece of toast has a momentum of .58 kg m/s as it pops out of the toaster. What is the velocity of the toast as it pops up?
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

9. Practice Problem
Two rockets are launched into space with the same momentum. Rocket A travels with a velocity of 400 m/s, Rocket B has four times the mass. What must the velocity of Rocket B be?
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

10. Practice Problem
I try to move my (full) filing cabinet by myself. I push on it for 30 seconds, but it does not budge. What is its momentum while I push on it, if it has a mass of 200 kg?
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

11. A moving object has Momentum energy. speed. all of the above.
A. momentum.
energy.
speed.
all of the above.
D. all of the above.

12. all of the above. A moving object has Momentum A. momentum. energy.
speed.
all of the above.
D. all of the above.

13. When the speed of an object is doubled, its momentum
A. remains unchanged.
doubles.
quadruples.
decreases.
B. doubles.

14. When the speed of an object is doubled, its momentum
A. remains unchanged.
doubles.
quadruples.
decreases.
B. doubles.

15. Impulse and Momentum
In order to change an object’s momentum, we will change its velocity.
How do we change something’s velocity?
Put a FORCE on it!
(More force = more change)
What else will affect how much the momentum of the object changes?
How much TIME we apply the force for!
(More time = more change)
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

16. Drawing an arrow back in a bow
Examples:
Hitting a baseball, golf ball, etc.
(follow through!)
Drawing an arrow back in a bow
Long cannon
vs.
short cannon
Pulling a Slingshot
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

17. Impulse and Momentum
How would we write the symbol for change in momentum?
We also call this Impulse (I)
If we know that MORE force = MORE change in momentum, MORE time = MORE change in momentum, and if I want the same change in momentum but use MORE force, I can push for LESS time, what should the equation be for change in momentum?
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

18. EQUATIONS I=Ft Δp=Ft so, I=Δp
The equations for Impulse/Change in Momentum are:
I=Ft Δp=Ft so, I=Δp
Where:
I= Impulse Measured in Ns (N*s)
Δp = Change in Momentum measured in kg m/s
F=Force measured in N
t = time measured in s
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

19. Practice Problem
An ceramic plate feels a net force of 6 N upward for .2 seconds as it hits the floor. What is the impulse on the plate?
What is the change in momentum
of the plate?
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

20. Practice Problem
A bike rider slams on his breaks for 4 seconds to come to a stop at a stop sign. If he started with a momentum of 80 kg m/s, how much force did he put on himself to stop in time?
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

21. Practice Problem
A shopper on black Friday is trying to get in the doors first. Her shopping cart is already moving with a momentum of 55 kg m/s and she pushes it hard for .5 seconds to make sure it gets in first. Now it has a momentum of 100 kg m/s. With how much force did she push?
A1 10:00 a.m. – 10:37 a.m.
A2 10:42 a.m. – 11:19 a.m.
A3 11:24 a.m. – 12:01 p.m.
A4 12:06 p.m. – 12:43 p.m.
Lunch in A4 or outside: 12:48 p.m.–1:12 p.m.
B1 1:17 p.m. – 1:54 p.m.
B2 1:59 p.m. – 2:36 p.m.
B3 2:41 p.m. – 3:18 p.m.
B4 3:23 p.m. – 4:00 p.m.

22. Impulse and Momentum Ft Which would it be more safe to hit in a car ?
Decreasing Momentum
Which would it be more safe to hit in a car ?
Knowing the physics helps us understand why hitting a soft object is better than hitting a hard one. mv Ft

23. Impulse and Momentum
In each case, the momentum is decreased by the same amount or impulse (force x time)
Hitting the haystack extends the impact time (the time in which the momentum is brought to zero).
This will decrease the force put on the object.
Whenever it is desired to decrease the force of impact, extend the time of impact !

24. Proportions that keep you safe
EXAMPLES :
Airbags in cars
Safety nets in circuses
Moving your hand backward as you catch a fast-moving ball with your bare hand
Flexing your knees when jumping from a higher place to the ground
Elastic cords for bungee jumping
Using wrestling mats instead of hardwood floors.
Dropping a glass dish onto a carpet instead of a sidewalk.

25. Decreasing Momentum Ft = change in POOF ! CRUNCH !
Bruiser Bruno on boxing …
Increased impact time reduces force of impact
Stretchy Sam on bungee Jumping …
Ft = change in
momentum
Ft = change in
momentum
POOF !
CRUNCH !
Because the rubber cord stretches for
a long time the average force on the
jumper is small.

26. Impulse
When the force that produces an impulse acts for twice as much time, the impulse is
A. not changed.
doubled.
increased by four times.
decreased by half.
B. increased by twice.

27. Impulse = force  time = Ft
When the force that produces an impulse acts for twice as much time, the impulse is
A. not changed.
doubled.
increased by four times.
decreased by half.
Impulse = force  time = Ft
B. increased by twice.

28. Impulse
When the force that produces an impulse acts for twice as much time, the impulse is
A. not changed.
doubled.
increased by four times.
decreased by half.
B. increased by twice.

29. Impulse = force  time = Ft
When the force that produces an impulse acts for twice as much time, the impulse is
A. not changed.
doubled.
increased by four times.
decreased by half.
Impulse = force  time = Ft
B. increased by twice.

30. Impulse–Momentum Relationship
A cannonball shot from a cannon with a long barrel will emerge with greater speed, because the cannonball receives a greater
A. average force.
impulse.
both of the above.
neither of the above.
B. impulse.

31. Impulse–Momentum Relationship
A cannonball shot from a cannon with a long barrel will emerge with greater speed, because the cannonball receives a greater…
A. average force.
impulse.
both of the above.
neither of the above.
Explanation:
The force on the cannonball will be the same for a short or long-barreled cannon. The longer barrel provides for a longer time for the force to act and therefore a greater impulse. (The long barrel also provides a longer distance that the force acts, providing greater work and greater KE of the cannonball.)
B. impulse.

32. Impulse–Momentum Relationship
A fast-moving car hitting a haystack or hitting a cement wall produces vastly different results. Both experience
the same change in momentum.
the same impulse.
the same force.
A and B.
D. Both A and B.

33. Impulse–Momentum Relationship
A fast-moving car hitting a haystack or hitting a cement wall produces vastly different results. Both experience
the same change in momentum.
the same impulse.
the same force.
A and B.
Explanation:
Although stopping the momentum is the same whether done slowly or quickly, the force is vastly different. Be sure to distinguish between momentum, impulse, and force.
D. Both A and B.

34. Impulse–Momentum Relationship
When a dish falls, will the change in momentum be less if it lands on a carpet than if it lands on a hard floor? (Careful!)
A. No, both are the same.
Yes, less if it lands on the carpet.
No, less if it lands on a hard floor.
No, more if it lands on a hard floor.
A. No, both are the same.

35. Impulse–Momentum Relationship
When a dish falls, will the change in momentum be less if it lands on a carpet than if it lands on a hard floor? (Careful!)
A. No, both are the same.
Yes, less if it lands on the carpet.
No, less if it lands on a hard floor.
No, more if it lands on a hard floor.
Explanation:
The momentum becomes zero in both cases, so both change by the same amount. Although the momentum change and impulse are the same, the force is less when the time of momentum change is extended. Be careful to distinguish between force, impulse, and momentum.
A. No, both are the same.

36. WHITEBOARD PROBLEMS:
If I want my impulse to be triple from what it previously was, how can I change my force to adjust the way I want?

37. WHITEBOARD PROBLEMS:
If I quadruple my force and nothing happens to my impulse, what must have happened to my time?

38. WHITEBOARD PROBLEMS:
 Yesterday, I lifted a book and put an impulse of 8 Ns on it. If I am feeling more energetic and the same lift (same force) takes me half the time instead, how much impulse am I putting on the book?

39. WHITEBOARD PROBLEMS:
I have a golf ball rolling across a golf course feeling a force of friction of 12 Newtons. It takes 4 seconds for the ball to come to rest. Another golf ball rolls down the sidewalk of the golf course and feels a friction force of only 3 Newtons. If they experience the same change in momentum, how long does the second ball take to stop?

40. WHITEBOARD PROBLEMS:
An 89 kg student takes off at a run to make it to class. he starts from rest and reaches a final velocity of 4 m/s.
What is the initial momentum of the student?
What is the final momentum of the student?
What is the change in momentum of the student?   
What is the impulse on the student? .

41. WHITEBOARD PROBLEMS:
An two smart cars (one red, one blue) try to stop at a stop sign. They start at the same velocity, but the blue car driver hits the brakes harder. If the blue car stops in 10 seconds using a force of 800 Newtons, and the red car stops in 50 seconds, how much force does the red car put on itself to stop?

42. Conservation of Momentum
Momentum Notes, Part II

43. Definitions
A “system” is a a group of objects,
Conservation is the idea that something stays the same over a certain amount of time.
Where else have you heard this?
A system of objects must have the same total momentum before and after a collision.
We call this physics concept “conservation of momentum.”

44. Law of Conservation of Momentum
The total momentum before a collision is equal to the total momentum after the collision.

45. Changing Mass

46. Elastic Collisions
A collision where objects collide and bounce off of each other in some way.

47. Inelastic Collisions
A collision where the objects stick together.

48. The math behind conservation
Total momentum before = total momentum after
(momentum 1)before+(momentum 2)before=(momentum 1)after+(momentum 2)after
p1i p2i = p1f p2f
m1v1i m2v2i = m1v1f m2v2f

49. Subscripts tell us…
Which object
1 = object 1
2 = object 2
What point in the collision
i = initial, or beginning
f = final, or end

50. Inelastic Collisions are a special case:
Since they are stuck together, the final velocities are the same.
This tells us that v1f= v1f
We can write them as one variable, vf
m1v1i m2v2i = m1vf m2vf
We can FACTOR out the common variable (vf)
m1v1i m2v2i = (m m2)vf

51. Plug in & Solve

52. Practice Problem:
A 2 kg basketball is moving at 4 m/s towards a 1 kg tennis ball at rest. They collide and bounce off each other. After the collision, the basketball is moving with a final velocity of 2 m/s. What is the final velocity of the tennis ball?
Elastic or Inelastic?
Object 1: ____________ Object 2: ____________
m1 = ________ v1i = _________ v1f = _________
m2 = ________ v2i = _________ v2f = _________

53. Plug in & Solve

54. Practice Problem
A 10 kg chunk of clay is flying through the air at 12 m/s towards another 10 kg chunk of clay at rest. They collide and stick together. What is their final velocity after the collision? Elastic or Inelastic? Object 1: ____________ Object 2: ____________ m1 = ________ v1i = _________ v1f = _________ m2 = ________ v2i = _________ v2f = _________