Welcome Back to PHY211

1
Welcome Back to PHY211!
2
Scheduling

• Lectures (Stolkin)
• M001 Tuesdays and Thursdays 1130am-1250 pm
• M002/U001 Tuesdays and Thursdays 600pm-715pm
• Recitations (B129W or 104)
• M003-008,011,012 Wednesday, Friday
• M017,U002 Tuesday and Thursday 715pm-805pm

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In your opinion, the tutorial yesterday was

• 1. too easy
• 2. about right
• 3. a bit difficult
• 4. much too difficult

4
Summary of Tutorial

• Distance between dots is proportional to velocity
  - different tapes were for different velocities
• Ticker tape segments were cut from a single tape
  of a single accelerated motion
• Each piece looked like constant velocity
• average velocity computed from a single piece
  gives good estimate of instantaneous velocity

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Recap from lecture 1

• Motion described by position s(t) (1D)
• Important concept
• displacement DssF-sI
• time interval DttF-tI
• (average) velocity VavDs/Dt
• For v. small Dt defines instantaneous velocity

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Graphing Motion

• Plot displacment vertically, time horizontally
• Discussed how to read motion from curve of s(t)
• Instantaneous velocity is slope of s vs t curve

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Examples
s
t
8
Cart experiment

• Transmitter sends out signal which is reflected
  back by cart - can calculate distance to cart at
  any instant.
• cart is not subject to any forces on track -
  expect constant velocity
• computer shows position vs time plot for motion
  (and velocity plot)
• 2 different speeds and directions

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Describing Motion

• We have seen that in describing motion its useful
  to introduce the concept of velocity
• v Ds/Dt
• Two velocities encountered
• average velocity vav
• instantaneous velocity vinst
• Motions with constant velocity
• vav vinst

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Acceleration

• Similarly when velocity changes it is useful
  (crucial!) to introduce acceleration a
• a Dv/Dt (vF-vI)/Dt
• Average acceleration - keep time interval Dt
  non-zero
• Instantaneous acceleration
• ainst limDt-gt0 Dv/Dtdv/dt

11
Graphing acceleration
Q
a is ? PQ QR RT
v
T
P
R
t
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Graph interpretation

• Plot now v vs t
• Slope measures acceleration
• Positive a means v is increasing
• Negative a means v decreasing (deceleration)

13
Examples
v
t
14
Fan cart experiment

• Attach fan to cart - provides a constant force
  (will see implies constant acceleration)
• Force acts to slow initial motion
• Sketch graphs of position, velocity and
  acceleration for cart that slows down and then
  turns around

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• You are throwing a ball up in the air. At its
• highest point the balls
• Velocity v and acceleration a are zero
• v is non-zero but a is zero
• Acceleration is non-zero but v is zero
• V and a are both non-zero

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Acceleration from s vs t plot ?

• If s vs t plot is linear zero accel.
• Is s vs t is curved accel is non-zero
• If slope is going from positive to negative
• a is negative
• If slope is going from negative to positive
• a is positive
• Accel is rate of change of slope!

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a
s
b
T
t

• The graph shows 2 trains running on
• parallel tracks. Which is true
• At time T both trains have same v
• Both trains speed up all time
• Both trains have same v for some tltT
• Somewhere, both trains have same a

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Mastering Physics

• http//www.masteringphysics.com
• click register
• type in code from textbook
• Enter personal info name, email, school
• Choose login name and password
• LOGIN enter course IDMPCATTERALL0001, and SUID

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Displacement from velocity curve

• Suppose I know v(t) (say as graph) can I learn
  anything about s(t) ?
• Consider a small time interval Dt
• v Ds/Dt ? Ds vDt
• So total displacement is the sum of all these
  small displacements Ds
• s S Ds S v(t)Dt

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Graphical interpretation
v
v(t)
T1
T2
t
Dt
Displacment between T1 and T2 is Area under v(t)
curve
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Velocity from accel curve

• Similarly change in velocity in some time
  interval is just area enclosed between curve a(t)
  and t axis in that interval.