Statics

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Chapter 8

• Statics

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Equilibrium

• An object either at rest or moving with a
  constant velocity is said to be in equilibrium
• The net force acting on the object is zero (since
  the acceleration is zero)

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1st Condition for Equilibrium

• Net force vanishes

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Method

• Isolate object of interest
• Draw picture, label all forces
• Choose appropriate coordinate system
• Resolve into components
• Write equations for equilibrium
• Solve equations for unknowns

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Example

• Mass m on table top
• 200 lb man hanging from rope

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Example (ex 2)

• Find tensions in the ropes.

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Example 8.4

• Two objects are in equilibrium. Find the weight
  of the one on the left and tensions.

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Force vs. Torque

• Forces cause accelerations
• Torques cause angular accelerations
• rotation
• Force and torque are related

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Torque

• The door is free to rotate about an axis through
  O
• There are three factors that determine the
  effectiveness of the force in opening the door
• The magnitude of the force
• The position of the application of the force
• The angle at which the force is applied

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Torque, cont

• Torque, t, is the tendency of a force to rotate
  an object about some axis
• t is the torque
• F is the force
• symbol is the Greek tau
• l is the lever arm
• SI unit is N.m
• Lever Arm Perpendicular distance from the pivot
  point to the line of force

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Direction of Torque

• Torque is a vector quantity
• We will treat only 2-d torque so no need for
  vector notion.
• If the turning tendency of the force is
  counterclockwise, the torque will be positive ()
• If the turning tendency is clockwise, the torque
  will be negative (-)

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Multiple Torques

• When two or more torques are acting on an object,
  the torques are added
• with the signs
• If the net torque is zero, the objects rate of
  rotation doesnt change

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General Definition of Torque

• The applied force is not always perpendicular to
  the position vector
• The component of the force perpendicular to the
  object will cause it to rotate

• F is the force
• L is distance between pivot and point of action
• q is the angle

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Example (8.20)

• Torque problem

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Center of Gravity

• The weight of an object can cause object to pivot
• C.G. used as pivot will have no torque due to
  gravity
• In finding the torque produced by the force of
  gravity, all of the weight of the object can be
  considered to be concentrated at a single point,
  C.G.

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Center of Gravity of a Uniform Object

• The center of gravity of a homogenous, symmetric
  body must lie on the axis of symmetry.
• Often, the center of gravity of such an object is
  the geometric center of the object.

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Experimentally Determining the Center of Gravity

• The wrench is hung freely from two different
  pivots
• The intersection of the lines indicates the
  center of gravity
• A rigid object can be balanced by a single force
  equal in magnitude to its weight as long as the
  force is acting upward through the objects
  center of gravity

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2nd Condition for Equilibrium

• No rotation
• Net torque vanishes

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Example

• 1000 N sign painter on an uniform 250N board
  suspended by two ropes. The board is 5m long. If
  the rope can hold only 900 N, is it safe for him
  to stand 1m from a rope?

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Example

• 600 N worker standing 1.5 m from the wall on 5m
  long and 300N beam as show.
• Find tension in the cable and the force on the
  beam by the wall.

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