More Constant Acceleration and Relative Velocity

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More Constant Acceleration and Relative
Velocity
Physics 101 Lecture 07

• Todays lecture will cover more material from
  Textbook Chapters 34

Hour Exam 1 Monday Oct 1, 7 PM Conflict exam,
515 PM Conflict-conflict exam, TBA (email
me) Lectures 1-8 includes centripetal motion!
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Feedback (only the bad ones)

• SLOW DOWN during lecture. It is difficult to
  digest all the material when concentrating solely
  on getting all the notes down.
• Sometimes you go through the lecture slides kind
  of fast and I don't fully understand the material
  before you switch slides.
• I really like all of the demo's, I just think
  that sometimes we go through the notes too fast.
  I feel that the class is going well, but the
  lecture moves very fast and it hard to write
  everything down from the powerpoint because of
  thte speed of the class.
• Sometimes the examples in the lecutre are gone
  over too fast.
• I don't get enough practice problems. Are there
  some in the book that would back good ones?
• To be honest, I am not getting much out of
  lecture or discussion, I learn most of the
  material by looking it over myself and going to
  TA office hours. I'm not sure why this is-- there
  is something about the way the lectures are
  presented that just does not allow me to
  thoroughly understand concepts. I understand the
  specific examples, but then when I try to apply
  what I've learned, I have trouble because what I
  was taught was maybe not generalized enough. I
  really am not sure if this is accurate at all
  though, maybe it is just my learning style that
  is a problem.
• Physics is hard ( I feel stupid because it seems
  like others know what they're doing just by going
  to lecture but I don't fully understand it and
  going to lecture and discussion doesn't help it.
  And the textbook is impossible to understand too.
  (
• You need to shoot zip with a dart more often,
  however, make the dart electric, and play Peter
  Gabriel's 'Shock the Monkey' every time you do -)

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What to do?(within time constraints)

• Me
• Slow down
• You
• Ask questions
• Download lectures after class (1-2 day delay)
  http//online.physics.uiuc.edu/courses/phys101/fal
  l07/physics_101_lectures.html
• Go to office hours http//online.physics.uiuc.edu
  /courses/phys101/fall07/office_hours.html

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Suggested Practice Problems

• Old hour exams http//online.physics.uiuc.edu/cou
  rses/phys101/fall07/practice/index.html
• (centripetal motion is on HE1 this semester!)
• Ch 2
• Examples 2.2, 2.5, 2.8, 2.12, 2.13, 2.14
• Problems 1, 5, 7, 11, 13, 17, 29, 49, 69
• Ch 3
• Examples 3.1, 3.2, 3.6, 3.9, 3.11, 3.13
• Problems 5, 13, 33, 47, 57, 65, 67
• Ch 4
• Examples 4.1, 4.6, 4.7, 4.9, 4.12, 4.14
• Problems 1, 3, 5, 9, 17, 19, 23, 25, 27, 35, 41,
  53, 55
• Ch 5
• Examples
• Problems 1,5,13,39,47

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Last Time

• X and Y directions are Independent! (poor Zip)
• Position, velocity and acceleration are vectors
• SF m a applies in both x and y direction
• Projectile Motion
• ax 0 in horizontal direction
• ay g in vertical direction

8
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Today

• More examples of 2D motion
• Newtons 3rd Law Review
• Relative Motion

10
7
Pulley, Incline and 2 blocks
A block of mass m1 2.6 kg rests upon a
frictionless incline as shown and is connected
to mass m1 via a flexible cord over an ideal
pulley. What is the acceleration of block m1 if
m2 2.0 kg?
X direction SFx m ax Block 1 T m1g
sin(30) m1 a1x T m1g sin(30) m1 a1x
Combine T m2 g
m2 a2y m1g sin(30) m1 a1x m2 g m2 a2y m1g
sin(30) m1 a1x m2 g -m2 a1x m1 a1x m2 a1x
m2 g - m1g sin(30) (m1m2) a1x g (m2 - m1
sin(30))
N
Y direction Fy m ay Block 2 T m2 g m2
a2y Note a1x - a2y
a1x1.49 m/s2
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Newtons Third Law

• For every action, there is an equal and opposite
  reaction.

• Finger pushes on box
• Ffinger?box force exerted on box by finger

• Box pushes on finger
• Fbox?finger force exerted on finger by box

• Third Law
• Fbox?finger - Ffinger?box

fan car demo
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Newtons 3rd Law

• Suppose you are an astronaut in outer space
  giving a brief push to a spacecraft whose mass is
  bigger than your own.
• 1) Compare the magnitude of the force you exert
  on the spacecraft, FS, to the magnitude of the
  force exerted by the spacecraft on you, FA, while
  you are pushing 1. FA FS 2. FA gt FS 3.
  FA lt FS

Third Law!
2) Compare the magnitudes of the acceleration you
experience, aA, to the magnitude of the
acceleration of the spacecraft, aS, while you are
pushing 1. aA aS 2. aA gt aS 3. aA lt aS
aA F/mA as F/ms F same ? lower mass gives
larger a
20
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Newtons 3rd Example

• A rope attached to box 1 is accelerating it to
  the right at a rate of 3 m/s2. Friction keeps
  block 2 on top of block 1 w/o slipping. What is
  the tension in the rope?

M2
X-direction F ma Block 2 f21 m2 a2 Block
1 T f12 m1 a1 N3L says f12
f21 Combine T - m2 a2 m1 a1 T m1
a1 m2 a2 (m1m2) a
T
M1

• Same as if had one block M m1m2 !!!!

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Relative Motion
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12
Relative Velocity

• You are on a train traveling 40 mph North. If you
  walk 5 mph toward the front of the train, what is
  your speed relative to the ground?
• A) 45 mph B) 40 mph C) 35 mph

40 mph N 5 mph N 45 mph N
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Relative Velocity

• You are on a train traveling 40 mph North. If you
  walk 5 mph toward the rear of the train, what is
  your speed relative to the ground?
• A) 45 mph B) 40 mph C) 35 mph

40 mph N - 5 mph N 35 mph N
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Relative Velocity

• You are on a train traveling 40 mph North. If you
  walk 5 mph sideways (West!) across the car, what
  is your speed relative to the ground?
• A) lt 40 mph B) 40 mph C) gt40 mph

40 mph N 5 mph W 41 mph NW
30
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Relative Velocity

• Sometimes your velocity is known relative to a
  reference frame that is moving relative to the
  earth.
• Example 1 A person moving relative to a train,
  which is moving relative to the ground.
• Example 2 a plane moving relative to air, which
  is then moving relative to the ground.
• These velocities are related by vector addition

• vac is the velocity of the object relative to the
  ground
• vab is the velocity of the object relative to a
  moving reference frame
• vbc is the velocity of the moving reference frame
  relative to the ground

32
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Tractor Demo 1

• Which direction should I point the tractor to get
  it across the table fastest?
• A) 30 degrees left
• B) Straight across
• C) 30 degrees right

1 2 3
34
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Tractor Demo (moving table)

• Which direction should I point the tractor to get
  it across the table fastest?
• A) 30 degrees left
• B) Straight across
• C) 30 degrees right

1 2 3
37
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Preflight 7.1

• Three swimmers can swim equally fast relative to
  the water. They have a race to see who can swim
  across a river in the least time. Relative to
  the water, Beth (B) swims perpendicular to the
  flow, Ann (A) swims upstream, and Carly (C) swims
  downstream. Which swimmer wins the race?
• A) Ann
• B) Beth
• C) Carly

14 30 56
t d / vy Ann vy v cos(q) Beth vy v Carly
vy v cos(q)
39
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Think of a swimming pool on a cruise ship
When swimming to the other side of the pool, you
dont worry about the motion of the ship !
A B C
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ACT

• Three swimmers can swim equally fast relative to
  the water. They have a race to see who can swim
  across a river in the least time. Relative to
  the water, Beth (B) swims perpendicular to the
  flow, Ann (A) swims upstream, and Carly (C) swims
  downstream. Who gets across second Ann or Carly?
• A) Ann B) Same C) Carly

t d / vy Ann vy v cos(q) Beth vy v Carly
vy v cos(q)
42
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Swimmer Example

• What angle should Ann take to get directly to the
  other side if she can swim 5 mph relative to the
  water, and the river is flowing at 3 mph?

VAnn,ground VAnn,waterVwater,ground
x-direction 0 Vx,Ann,water 3 mph 0
-VAnn,water sin(q) 3 5 sin(q) 3 sin(q) 3/5
q36.87
48
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Summary of Concepts

• X and Y directions are Independent!
• Position, velocity and acceleration are vectors
• F m a applies in both x and y direction
• Newtons 3rd Law
• Relative Motion (Add vector components)