1. Physics 218, Lecture XX1 Physics 218 Lecture 20 Dr. David Toback

2. Physics 218, Lecture XX2 Chapter 11: Static Equilibrium Overview Conditions for Equilibrium How to deal with gravity acting on the center of mass Problem solving

3. Physics 218, Lecture XX3

4. 4 Two important ideas For something to be in static equilibrium two things must be true: The sum of the forces must be zero –No acceleration! The sum of the torques must be zero –No angular acceleration!

5. Physics 218, Lecture XX5 Problem Solving 1.Draw a free-body diagram –Where do the forces act ON the body 2.Pick a useful origin 3.Break into X and Y (and Z if needed) –Do for forces and torques separately! 4.Set  F=0 and  =0 5.Solve simultaneous equations I don’t like the center of gravity method in the book…

6. Physics 218, Lecture XX6 Center of Mass and Gravity For all objects that have mass, you must take the mass of the object into account For an object with mass m: In the force equation, use F g = mg In the torque equation, use F g = mg acting at the center of mass Note: It’s sometimes useful to pick the center of mass at the origin for this reason (but not always)

7. Physics 218, Lecture XX7 M2M2 D M1M1 L=? Tower Crane A tower crane lifts a box with mass M 2. The box is a distance D from the primary support. To do this it must shift it’s counterweight, mass M 1, out along the other side of the crane. Ignoring the crane mass, how far out must the counter weight go so the crane doesn’t tip over? In other words, what is L on the figure?

8. Physics 218, Lecture XX8 Ladder Problem A uniform ladder of mass m and length l leans at an angle  against a frictionless wall. The coefficient of static friction between the ladder and the ground is  What is the minimum angle at which the ladder will not slip?

9. Physics 218, Lecture XX9 Hanging a Sign M1M1 A dinosaur of mass M 1 is suspended from the end of a uniform horizontal rod of length L and mass M 2. The rod is suspended by a cable at an angle  and by a hinge a point P Find the tension in the cable

10. Physics 218, Lecture XX10 Coming up… Thursday: Chapter 12 –Gravitation Homework: –HW10 was due Monday –Recitation on Chap 11 this week –HW11 due Monday Exam 3 coming up: Nov 21 st –Tuesday before Thanksgiving –Mini-practice exam is open and available for people who are caught up. Usual 5 points

11. Physics 218, Lecture XX11