Equilibrium

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© 1998-2008 by Glenn Elert -- A Work in Progress
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Discussion

Physics is an essential part of a nutritious breakfast.

Summary

• Statics is the branch of mechanics dealing with forces acting on an object at rest.
• Static Equilibrium (Point Bodies)
  • A point body is in static equilibrium when the net force on it is zero.
  • A point body in static equilibrium will not accelerate.
    It will remain at rest or continue moving with a constant velocity.
• 2 Forces in Equilibrium
  • Two forces are in equilibrium if they are
    • equal (have equal magnitudes) and
    • opposite (180° apart).
• 3 Forces in Equilibrium
  • Resultant-Equilibrant
    • Select 2 forces and find their resultant.
    • The remaining force is called an equilibrant if it is equal and opposite the resultant.
  • Triangle of Forces
    • Three forces are in equilibrium if they can be arranged to form a triangle.
• N Forces in Equilibrium
  • Polygon of Forces
    • Three or more forces are in equilibrium if they can be arranged to form a polygon.
  • Components
    • Resolve all forces into components in some convenient coordinate system.
    • Combine the components along each axis.
      (Add the components parallel to the axis and
      subtract the components anti-parallel to the axis.)
    • If the resultant along each axis is zero the object is in equilibrium.

∑  F = 0 ⇒		⎧ ⎪ ⎨ ⎪ ⎩		∑ F+x = ∑ F−x
				∑ F+y = ∑ F−y
				∑ F+z = ∑ F−z
No Net Force in Any Direction

Problems

practice

1. Write something.
   • Answer it.
2. Three forces act on a point: 3 N at 0°, 4 N at 90°, and 5 N at 217°.
   1. What is the net force?
   2. What fourth force will put the point in equilibrium?
   Solutions …
   1. Answer it.
   2. Answwer the rest.
3. Inclined Plane Problem
   • Answer it.
4. Write something completely different.
   • Answer it.

numerical

1. A push broom of mass m is pushed across a horizontal floor at a constant velocity by a force of magnitude F directed at an angle θ with respect to the floor.
   1. Make a free body diagram showing all the forces acting on the head of the broom.
   2. Find the coefficient of kinetic friction on the broom in terms of the variables m, g, F, and θ.

Resources

• general
  • statics.org originally the home of "Statics Simply Stated", now just another wasted url

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