1. Equilibrium of large objects Rotation Exercises

2. Last nights homework Pg 203 #11 F = 140 N #13 Θ = 36.6˚ #15 Horizontal Torque = 115 Nm Vertical Torque = 0 Nm (any force acting through the pivot point will generate no torque)

3. Using torque to solve equilibrium problems of large object A large object is any object where the shape of the object plays a significant role Large objects can rotate because forces can be applied that do not go through the pivot point. Large objects are in equilibrium when the net force and the net torque equal zero

4. See-saw problem

5. Bill (50 kg) and Jane (45 kg) play on a see-saw with Bubba (110 kg). Bubba sits 1.25 meters from the pivot point. Bill sits 1.8 meters from the pivot point. The seesaw weight is not significant. A) What is the upward force on the seesaw at the pivot point (fulcrum) ? B) for the seesaw to be in equilibrium, where must Jane sit?

6. Space to work problem

7. If the weight of a large object is significant… Can represent the weight as a single force placed at the object’s center of mass

8. Mobile problems Similar to seesaw problems

9. Art mobiles Each layer of a mobile must be in equilibrium in still air Each layer becomes an object hanging down from every other layer to which it is connected Cross bar weight is usually significant

10. Art-mobile problem One bar, pivot at center point, 2 objects, beam has weight

11. Art mobile questions Where does the second object have to be placed to produce equilibrium Does the weight of beam create torque? What is the total weight of the beam, where should a single force vector that represents the total be located on the beam?

12. Cantilever beams In an art mobile- is a beam where the external weight only hangs from one side of the pivot point Pivot point is NOT at center of beam The weight of the beam creates torque

13. Cantilever example Where does the only hanging weight have to be placed so the beam is in equilibrium

14. Space to work Cantilever problem

15. Large mobile problem-Homework

16. Book work Pg 227 1-3 and 7 Class mobile problem