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Forces: Equilibrium Examples  ,[object Object],Physics 101:  Lecture 02 Phys 101 URL: http://online.physics.uiuc.edu/courses/phys101 Read the course description & FAQ! Office hours start Monday; see web page  for locations & times. Exam I
Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Free Body Diagrams ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Physics hand Gravity Normal friction y x
Book Pushed Across Table ,[object Object],Physics hand Gravity Normal friction x-direction:   F=0 F hand -F friction  = 0   F hand =F friction   F hand =  k  F Normal y-direction:   F=0 F Normal -F Gravity  = 0 F Normal  = F Gravity F Normal   =  x 9.8=9.8  N Combine:   F hand =  k  F Normal     F hand =0.75 x 9.8  N   F hand =   ewtons Constant Speed =>   F=0 y x
Contact Force: Springs ,[object Object],[object Object],[object Object],F 1  +F 2  - F gravity  = 0 F 1  +F 2   = F gravity k 1 x 1  +  k 2 x 2 = m g 2 k x = mg x  = m g / (2k) = (½ m) g / k We know  mg/k = 8 cm.  So: ½ mg /k  = 4 cm. y x F 2 F gravity F 1
Contact Force: Springs ,[object Object],[object Object],[object Object],y x
Contact Force: Tension ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],F = mg = 440 Newtons From Prelecture
Pulley ACT ,[object Object],[object Object],[object Object],[object Object],1 2  F = m a 1) T - m 1  g = 0 2) T – m 2  g = 0 => m 1  = m 2   1 T m 1 g 2 T m 2 g
Tension Example:  ,[object Object], F = m a T + T – W = 0 2 T = W T = m g / 2   = (45   kg   x (9.8   m/s 2 )/ 2 =   220  N ,[object Object],A) 220 N B) 440 N C) 660 N D) 880 N E) 1100 N y x T T W
Tension ACT II ,[object Object], F = m a F c  -T - T – T = 0 F c  = 3 T F c  = 3 x 220 N = 660 N ,[object Object],A) 220 N B) 440 N C) 660 N D) 880 N E) 1100 N y x F c T
Springs Preflight  ,[object Object],[object Object],1 The magnitude of tension in a ideal string is equal everywhere.
Springs ACT ,[object Object],[object Object],In both cases the NET FORCE on the spring is zero, and the force to the right is 550N. Therefore the force to the left is also 550 N. 1 2
Forces in 2 Dimensions: Ramp ,[object Object],[object Object],[object Object],Note, weight is not in x or y direction! Need to decompose it!  y x T N W
Forces in 2 Dimensions: Ramp ,[object Object],  W sin   W cos   y x W T N W
Forces in 2 Dimensions: Ramp ,[object Object],x- direction W sin   – T = 0 T = W sin   m g sin   Newtons  y x T N W
Normal Force ACT ,[object Object],[object Object],In “y” direction  F = ma N – W cos    = 0 N = W cos   N = m g cos    T N W y x W  W sin   W cos  
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 
Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Lecture02

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Editor's Notes

  1. Could add the truck example/demo, or the dog on leash example.
  2. Key idea here is we can do each direction independently!
  3. Maybe simple demo, add twice as much mass, get twice the stretching before showing the slide. Also make note that this is NOT as big a deal as Newton’s laws. Just an example of a contact force.
  4. Maybe simple demo, add twice as much mass, get twice the stretching before showing the slide. Also make note that this is NOT as big a deal as Newton’s laws. Just an example of a contact force. First solve for k = 5*9.8/8 = 6.125 Then FBD
  5. Tell them any choice is OK, but this way only have 1 force to decompose
  6. T = W sin(theta) = 16.8 N
  7. Tell them any choice is OK, but this way only have 1 force to decompose
  8. Could do this on over head to help people work through it.
  9. hhh