Static Equilibrium. Lecture 24. Chapter 12. Physics I. Department of Physics and Applied Physics

Transcription

1 Lecture 24 Chapter 12 Physics I Static Equilibrium Course website:

2 IN THIS CHAPTER, you will discuss static equilibrium of an object Today we are going to discuss: Chapter 12: Static Equilibrium: Section 12.8

3 Bicycle wheel/turntable as a demo of Angular Momentum Conservation

4 Bicycle wheel/ang. Mom. Conservation Initial situation Final situation w L z L x in Lz 0 p L z w - wheel p - person Angular Momentum Conservation (z comp): in fin Lz Lz fin w p p w 0 Lz Lz Lz Lz Lz I p p I w w clockwise I w p ( )w I p counterclockwise

5 ConcepTest You are holding a spinning bicycle wheel while standing on a stationary turntable. If you suddenly flip the wheel over so that it is spinning in the opposite direction, the turntable will: Spinning Bicycle Wheel A) remain stationary B) start to spin in the same direction as before flipping C) start to spin in the same direction as after flipping L in z L fin z L L L me table L me table 2 L L z 2L The total angular momentum of the system is L upward, and it is conserved. So if the wheel has L downward, you and the table must have +2L upward. L

6 The 1st Condition for Equilibrium prevents translational motion N. 2 nd law describes translational motion x F F ma He doesn t want to have any sliding of a ladder, i.e. 0 0 F 0 F 0 F 0 y Force equilibrium z a

7 The 2nd Condition for Equilibrium prevents rotational motion v Rotational N. 2 nd law describes rotational motion: I He doesn t want to have any rotation of a ladder, i.e. 0 0 Torque equilibrium There must be no net torque around any axis (the choice of axis is arbitrary) x y z

8 ConcepTest Static equilibrium Consider a light rod subject to the two forces of equal magnitude as shown in figure. Choose the correct statement with regard to this situation: (A) (B) (C) (D) The object is in force equilibrium but not torque equilibrium. The object is in torque equilibrium but not force equilibrium The object is in both force equilibrium and torque equilibrium The object is in neither force equilibrium nor torque equilibrium F F F 0 0 ext 1 2 X force equilibrium torque equilibrium origin 2 r F Here, the 1st condition is satisfied but the 2 nd isn t, so there will be rotation. So, to have static situation, both conditions must be satisfied. 1

9 1 st condition: x Reduce # of Equilibrium Equations For simplicity, we will restrict the applications to situations in which all the forces lie in the xy plane. y z F 0 F 0 F 0 2 nd condition: x y z r F r, F There are three resulting equations, which we will use 1) F 0 2) F 0 3) 0 x y z

10 Axis of rotation for the 3 rd equation z 0 Does it matter which axis you choose for calculating torques? If an object is in a force equilibrium F 0 and the net torque is zero about one axis, then the net torque must be zero about any other axis So. The choice of an axis is arbitrary We should be smart to choose a rotation axis to simplify problems H E Any axis of rotation works. It is up to you which one to choose

11 Any axis of rotation works for the 3 rd equation (proof) (Read only if you want) z The choice of an axis is arbitrary 0

12 Concurrent/Nonconcurrent forces F F 2 1 F 3 Concurrent forces: when the lines of action of the forces intersect at a common point, there will be no rotation. So z F F F 0 F x y x F 3 Nonconcurrent forces: when the lines of action of the forces do not intersect at a common point, there will be rotation. So z F F 0 y Automatically satisfied

13 Recall how to calculate torque (shortcut) Line of force (action) r r F r F rf sin r F Draw a line of force Find the perpend. distance (r ) from the axis of rotation to that line. Magnitude of torque is r F Torque is positive if it tries to rotate an object CCW Lecture 20

14 Example Ladder stability (12.58) A 3.0-m-long ladder leans against a frictionless wall. The coefficient of static friction between the ladder and the floor is What is the minimum angle the ladder can make with the floor without slipping? The forces are nonconcurrent, so we need all equilibrium conditions Fx z 0 0 Fy 0

15 Example Traffic light Find the tension in the two wires supporting the traffic light

16 Solving Statics Problems 1. Choose one object at a time, and make a free-body diagram by showing all the forces on it and where they act. 2. Choose a coordinate system and resolve forces into components. 3. Write equilibrium equations for the forces. 4. Choose any axis perpendicular to the plane of the forces and write the torque equilibrium equation. A clever choice here can simplify the problem enormously. 5. Solve.

17 Thank you See you on the Final Exam