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Kinematics ,[object Object],[object Object],[object Object],Physics 101:  Lecture 03 Exam I
Announcements ,[object Object],[object Object],[object Object],[object Object]
Force at Angle Example ,[object Object],x- direction:   F x  = ma x F push  cos(  ) – F friction  = 0 F push  cos(  ) –    F Normal  = 0 F Normal  = F push  cos(  ) /   y- direction:   F y  = ma y F Normal  –F weight  – F Push  sin(  ) = 0 F Normal  –mg – F Push  sin(  ) = 0 Combine: F push  cos(  ) /   –mg – F Push  sin(  ) = 0 F push  ( cos(  ) /     - sin(  )) = mg F push  = m g / ( cos(  )/   – sin(  )) F push  = 80 N y x Normal Weight Pushing  Friction 
Homework 2 Example ,[object Object],x-direction:   F=ma -T L +T R  cos(  )= 0 T L  = T R  cos(  ) y-direction:   F=ma T R  sin(  ) – Mg = 0 T R  = Mg / sin(  ) Combine: T L  = Mg cos(  )/sin(  ) Work through example?  A: Yes  B: No T L W  T R y x
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Position vs Time Plots ,[object Object],[object Object],[object Object],x (m) t 4 3 -3 Position at t=3,   x(3) =  Displacement between t=5 and t=1.    x =  Average  velocity between t=5 and t=1 . v =  1 -1.0 m -0.25 m/s 1.0 m  - 2.0 m = -1.0 m -1 m / 4 s = -0.25 m/s
Velocity vs Time Plots ,[object Object],[object Object],[object Object],1.5 6 v (m/s) t 4 3 -3 3 m/s  7.5 m   t=0 to t=1:  ½ (3m/s) (1 s) = 1.5 m 7.5 m / 3s  =  2.5 m/s -2 m/s – 3 m/s  =  -5 m/s -5 m/s / (2 s) =  -2.5 m/s 2 t=1 to t=3:  (3m/s) (2 s) = 6 m velocity at t=2,  v(2) =  Change in v between t=5 and t=3.   v =  Average acceleration between t=5 and t=3: a =  Displacement between t=0 and t=3:   x= Average velocity between t=0 and t=3?  v=
Acceleration vs Time Plots ,[object Object],[object Object],2 6 a (m/s 2 ) t 4 3 -3 -2 m/s 2 t=1-3:   v = (3m/s 2 )(2s) = 6 m/s t=3-4:   v = (-2m/s 2 )(1s) = -2 m/s +4 m/s Acceleration at t=4,  a(4) =  Change in v between t=4 and t=1.   v =
[object Object],[object Object],[object Object],Acceleration Preflights If the velocity of some object is not zero, can its acceleration ever be zero ?  1 - Yes  2 - No  88% 12% 87% 13% “ The velocity could be non-zero and constant. A constant velocity has no acceleration..” “ the object could be slowing down.”
Velocity ACT  ,[object Object],[object Object],[object Object],Drive north 5 miles, put car in reverse and drive south 2 miles. Average velocity is positive.
Dropped Ball ,[object Object],[object Object],-6 v t 0.5 9 -6 v t 0.5  9 -6 v t 0.5 9 -6 v t 0.5 9 v t 0.5 9 -6 A B C D E y x
Dropped Ball ,[object Object],[object Object],[object Object],v t x t a t A ball is dropped for a height of two meters above the ground.
Tossed Ball ,[object Object],[object Object],v v v -6 -6 t 1 9 -6 t 1 9 -6 t 1 9 -6 v t 1 9 v t 1 9 A B C D E y x
Tossed Ball ,[object Object],[object Object],[object Object],v t x t a t ,[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],ACT   V ave  =   Y/  t = (Y f  – Y i ) / (t f  – t i ) a ave  =   V/  t = (V f  – V i ) / (t f  – t i ) Not 0 since V f  and V i  are not the same ! = 0
[object Object],[object Object],Relative Velocity (first pass) 40 mph N + 5 mph N = 45 mph N 40 5 45
Relative Velocity ,[object Object],[object Object],40 mph N - 5 mph N = 35 mph N 40 5 35
Relative Velocity ,[object Object],[object Object],40 mph N + 5 mph W = 41 mph N 40 5
Relative Velocity ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Tractor Demo 1 ,[object Object],[object Object],[object Object],[object Object],1  2  3
Tractor Demo (moving table) ,[object Object],[object Object],[object Object],[object Object],1  2  3
Summary of Concepts ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Kinematics lecture covering textbook sections 3.1-3.3 and chapter 4

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Editor's Notes

  1. X-direction F_normal = F_push cos(t)/mu Y-direction: F_normal-mg-Fpush sin(t) = 0 Combine F_push = mg / ( cos(t)/mu - sin(t)) = 80 N
  2. Do on transparency
  3. What about negative acceleration and speeding up?