More Constant Acceleration and Relative Velocity

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More Constant Acceleration and Relative
Velocity
Physics 101 Lecture 07
Exam I
Exam 1 is one week from Monday Today is the last
lecture for Exam 1 material No circular motion
on exam 1 different from past years! I will
hold a special office hour 10-11 Friday in 235
Loomis
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Some Charts
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Top Ten Comments

• You dont need to spend as much time explaining
  basic algebra
• please explain how to do the math equations
  more.
• I LOVE PHYSICS!!! CHEERS!!!
• The quizzes are just so confusing
• If you could increase the volume of the
  microphone that would be GREAT
• Physics fills me with glee.
• I enjoy the demonstrations.
• Nervous for the first exam.

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Extra Problems

• Ch 2 Problems 1,5,7,11,13,17,29,49,69
• Ch 3 Problems 5,13,33,47,57,65,67
• Ch 4 MC all, Problems 1, 3,5,9,
  17,19,23,25,27,35,41,53,55

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Last Time

• X and Y directions are Independent!
• 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

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Today

• More 2-D Examples
• Newtons 3rd Law Review
• Relative Motion

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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
1.49 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

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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 pushing1. FA FS 2. FA gt FS3. 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
aF/m F same ? lower mass give larger a
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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
T
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
M1

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

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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 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 N
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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

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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
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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
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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

t d / vy Ann vy v cos(q) Beth vy v Carly
vy v cos(q)
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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)
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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 0 -VAnn,Water
sin(q) 3 5 sin(q) 3 sin(q) 3/5
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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
HW swimmer
Demo - bulldozer
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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)