1. PH 201 Dr. Cecilia Vogel Lecture 23

2. REVIEW  equilibrium  stable vs. unstable  static OUTLINE  eqlb  universal gravitation

3. Static Equilibrium  Static means not moving  equilibrium means no net force  And no net torque  This is the object at rest, remaining at rest

4. 2-D Static Equilibrium  Generally, need to consider  3-D forces,  and torques around two axes  We will do 2-D problems   F x =0,  F y =0,   =0 around axis parallel to z-axis  For 3-D problems, easiest to do 2-D twice  Side view and overhead view, for example

5. Eqlb Examples  crane holding a block  The system in Figure 12-37 is in equilibrium. A concrete block of mass 222 kg hangs from the end of the uniform strut of mass 45.5 kg. Angle  = 30.0° and  = 45.0°. Find the tension T in the cable. Find the force on the strut from the hinge

6. Hinges and Hips  The socket (or outer hinge part) exerts   on the ball (or inner hinge part)  a circular surface can exert a normal force 

7. Eqlb Examples  crane holding a beam, cont’d 

8. Eqlb Example Answer  3 eqn, 3 unknown  T =6553 N FHx =5675 N FHy=5898 N Hinge force vector is not along strut

9. Gravity  Recall  F g = mg and U = mgh  only true near earth surface!  further from the earth, the force gets weaker

10. Universal Gravity  Newton’s Universal Law of Gravity:  m 1 and m 2 are the two masses  r is distance between the two masses  G is gravitation constant 6.67X10 -11 Nm 2 /kg 2  PE always negative  farther, smaller neg, higher PE  negative F means opposite the vector r  means it is always attractive

11. Gravity Pulls on Earth  Which pulls harder on the earth, the moon or the sun?  moon is closer  sun more massive  hmm….