1 / 14

Short Version : 12. Static Equilibrium

Short Version : 12. Static Equilibrium. 12.1. Conditions for Equilibrium. (Mechanical) equilibrium = zero net external force & torque. Static equilibrium = equilibrium + at rest. For all pivot points. Pivot point = origin of r i . Prob 55:. .

yaron
Download Presentation

Short Version : 12. Static Equilibrium

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Short Version : 12. Static Equilibrium

  2. 12.1. Conditions for Equilibrium (Mechanical) equilibrium = zero net external force & torque. Static equilibrium = equilibrium + at rest. For all pivot points Pivot point = origin of ri . Prob 55:  is the same for all choices of pivot points

  3. Example 12.1. Drawbridge The raised span has a mass of 11,000 kg uniformly distributed over a length of 14 m. Find the tension in the supporting cable. Force Fh at hinge not known.  Choose pivot point at hinge.  y 2 Tension T 15 1 30 x Another choice of pivot: Ex 15 Hinge force Fh Gravity mg

  4. GOT IT? 12.1. Which pair, acting as the only forces on the object, results in static equilibrium? Explain why the others don’t. (C) (A): F 0. (B):   0.

  5. 12.2. Center of Gravity Total torque on mass M in uniform gravitational field : Center of gravity = point at which gravity seems to act CG does not exist if net is not  Fnet. for uniform gravitational field

  6. Conceptual Example 12.1. Finding the Center of Gravity Explain how you can find an object’s center of gravity by suspending it from a string. 2nd pivot 1st pivot

  7. 12.3. Examples of Static Equilibrium All forces co-planar:  2 eqs in x-y plane  1 eq along z-axis Tips: choose pivot point wisely.

  8. Example 12.2. Ladder Safety A ladder of mass m & length L leans against a frictionless wall. The coefficient of static friction between ladder & floor is . Find the minimum angle  at which the ladder can lean without slipping. Fnet x : n2  y Fnet y :  Choose pivot point at bottom of ladder. z : mg n1  x fS = n1i   0    90

  9. Example 12.3. Arm Holding Pumpkin Find the magnitudes of the biceps tension & the contact force at the elbow joint. Fnet x : Fnet y : Pivot point at elbow. z : y T  Fc 80 x mg Mg ~ 10 M g

  10. 12.4. Stability Stable equilibrium: Original configuration regained after small disturbance. Unstable equilibrium: Original configuration lost after small disturbance. Stable equilibrium unstable equilibrium

  11. Equilibrium: Fnet = 0. Stable V at global min Unstable V at local max Neutrally stable V = const Metastable V at local min

  12. Metastable equilibrium : PE at local min Stable equilibrium : PE at global min

  13. Example 12.4. Semiconductor Engineering A new semiconductor device has electron in a potential U(x) = a x2 – b x4 , where x is in nm, U in aJ (1018 J), a = 8 aJ / nm2, b = 1 aJ / nm4. Find the equilibrium positions for the electron and describe their stability. equilibria Equilibrium criterion :  or Metastable x = 0 is (meta) stable x = (a/2b) are unstable

  14. Saddle Point Equilibrium condition stable Saddle point stable unstable unstable

More Related