More Constant Acceleration and Relative Velocity

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More Constant Acceleration and Relative
Velocity
CPI Lecture 07

• Todays lecture will cover Textbook Sections 3.5

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Last Time

• X and Y directions are Independent!
• Position, velocity and acceleration are vectors
• F m a applies in both x and y direction
• Projective Motion
• ax 0 in horizontal direction
• ay g in vertical direction

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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?
X direction Fx m ax Block 1 T m1g
sin(30) m1 a1x T m1g sin(30) m1 a1x
N
Y direction Fy m ay Block 2 T m2 g m2
a2y Note a1x - a2y
Combine m1g sin(30) m1 a1x m2 g m2 a2y
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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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Pre-Flight Questions 1 2

• 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?
• 1) 45 mph 2) 40 mph 3) 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?
• 1) 45 mph 2) 40 mph 3) 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?
• 1) lt 40 mph 2) 40 mph 3) gt40 mph

40 mph N 5 mph W 41 mph N
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Tractor Demo 1

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

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Tractor Demo (moving table)

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

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Pre-Flight 78(some of the hardest preflights
you will see)

• 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

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Great answer for B
All three swimmers are carried downstream along
with the current (the x component of their
displacement) at different rates, depending on if
they swim upstream, downstream, or perpendicular
to the flow, as this adds to or subtracts from
the vector of their horizontal speed. Only the
component of their velocity perpendicular to the
flow of the river matters in determining how long
it takes them to reach the opposite shore.
Because Beth is swimming the most direct path to
the opposite shore, she will reach it first.
Time to get across width of river /
y-component of velocity
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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)