Kinematics lecture covering textbook sections 3.1-3.3 and chapter 4

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]

Kinematics lecture covering textbook sections 3.1-3.3 and chapter 4

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Kinematics lecture covering textbook sections 3.1-3.3 and chapter 4

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