Physics 218

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Physics 218
Lecture 20 Statics Equilibrium

• Alexei Safonov

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Rotating Rod

• A rod of mass uniform density, mass m and length
  l pivots at a hinge. It starts at rest at a
  right angle. You let it go. Neglecting friction
  in the pivot point
• What is w when it reaches the bottom?
• What is the velocity of the tip at the bottom?
• Hint Iml/3

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From Last Time Yo-Yo

• Three identical yo-yos are initially at rest. You
  pull on the string as shown below. There is
  enough friction for yo-yo to roll without
  slipping in each case.
• I which direction will each of the yo-yo rotate

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Same Yo-Yo in General Case

• A yo-yo (mass m, inner/outer radii are r and R,
  moment of inertia is ½mR2) is initially at rest
  on a rough surface (coefficient of friction is
  m). You apply force F that gradually grows from 0
  to some large value Fmax and then abruptly
  disappears.

• Calculate linear/angular accelerations as a
  function of F
• Describe the motion of the yo-yo (direction of
  motion, direction of rotation) as a function of
  time

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Chapter 11 Static Equilibrium

• Overview
• Conditions for Equilibrium
• How to deal with gravity (center of mass)
• Problem solving

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Two important ideas

• For something to be in
• static equilibrium it must have
• The sum of the forces must be zero
• No acceleration!
• The sum of the torques must be zero
• No angular acceleration!

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Problem solving

• Draw a diagram
• Where do the forces act ON the body
• Pick a useful origin
• Break into X and Y (and Z if needed)
• Do for forces and torques separately!
• Set SF0 and St0
• Solve simultaneous equations

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Center of Mass and Gravity

• For all objects that have mass, you must take the
  mass of the object into account.
• For an object with mass m
• In the force equation, use Fg mg
• In the torque equation, use Fg mg acting at the
  center of mass
• Note Its sometimes useful to pick the center of
  mass at the origin for this reason (i.e., tg Fg
  x 00) , but not always

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Tower Crane

• A tower crane lifts a box with mass M2. The box
  is a distance D from the primary support. To do
  this it must shift its counterweight, mass M1,
  out along the other side of the crane.
• Ignoring the crane mass, how far out must the
  counter weight go so the crane doesnt tip over?

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Ladder Problem

• A uniform ladder of mass m and length l leans at
  an angle q against a frictionless wall. The
  coefficient of static friction between the ladder
  and the ground is m
• What is the minimum angle at which the ladder
  will not slip?

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Hanging a Sign

• A dinosaur of mass M1 is suspended from the end
  of a horizontal rod of length L and mass M2. The
  rod is suspended by a cable at an angle q and by
  a hinge a point P
• Find the tension in the cable

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Next Week

• Monday Finish Chapter 11
• Including a Reading Quiz before the lectrue
• Hints Q11.8-11.12, 11.16-11.18
• Start Chapter 12
• Gravitation
• Reading Quiz for Ch 12 (end of lecture)
• Hints Q12.2-12.8 and 12.17-12.21
• HW9 was due last Monday
• HW10 is due coming Monday
• Exam 3 coming up soon

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Hoop on a String

• A string is wrapped around the rim of a small
  hoop (mass m and radius r). The free end of the
  string is held in place and the hoop is released
  from rest
• Find
• Angular speed of the hoop and the speed of its
  center after the hoop has descended distance d
• Acceleration of the center of the hoop