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Equilibrium

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Zero Net Force Most objects we encounter are not accelerating. These objects are following the law of inertia. The net force is zeroThe net force is zero The object is in equilibriumThe object is in equilibrium The net force is due to the sum of forces acting on the object. The forces are vectorsThe forces are vectors

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Static Equilibrium The law of inertia applies to objects at rest and at constant velocity. An object at rest with no net force is in static equilibrium.

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Equilibrium in One Dimension Two weights are hung supported by strings. On the lower block the two forces balance: F T2 = m 2 gOn the lower block the two forces balance: F T2 = m 2 g On the upper block there are three: F T1 = m 1 g + F T2On the upper block there are three: F T1 = m 1 g + F T2 F T1 = (m 1 + m 2 )gF T1 = (m 1 + m 2 )g The upper string has more tension than the lower string. m1m1 F T1 m1gm1g 3 forces on the upper block F T2 m2m2 m2gm2g 2 forces on the lower block

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At Rest Failure to maintain equilibrium results in net force and acceleration. Hyatt Regency Kansas City, 1981 Designed to have a single pole from the ceiling to the lower deck Two pins instead of one on the upper deck Twice the force on the top pin caused collapse mg mg mg

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Equilibrium in Two Dimensions The forces in each component must be zero. Use a tilted set of coordinates to find components of gravity. F N1 = mg sin F N2 = mg cos Normal forces F N1 F g = mg Gravity force F N2 m

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Constant Velocity Constant velocity means no acceleration. Zero net force here, as wellZero net force here, as well Motion can be at equilibriumMotion can be at equilibrium Dynamic equilibrium applies in states of constant, non- zero velocity. All the forces add to zero net force. v0v0 FgFg FyFy FxFx F fr FNFN

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Matching Components Vertical component F N = F g + F yF N = F g + F y Horizontal component F x = F frF x = F fr Applied force v0v0 FgFg FyFy FxFx F fr FNFN next

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