1. Equilibrium

2. 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

3. 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.

4. 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

5. 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

6. 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

7. 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

8. 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