1. Static Equilibrium AP Physics Chapter 9

2. Static Equilibrium 8.4 Torque

3. Rotational Dynamics – the causes of rotational motion Caused by Torque, or a force applied at a distance from the pivot point  =torque (Nm) F=force (N) r=torque arm (m) 8-4

4. S-47 An asteroid with a mass of 450,000 kg is traveling through space at 125000 m/s. A secret base on the asteroid explodes, breaking the asteroid into two pieces. If the first piece with a mass of 200,000 kg is shot off at 75,000 m/s 82 o to the original path, what is the speed and direction of the rest of the asteroid?

5. 8.4 Torque Force causes no rotation if it is applied at the pivot point 8-4

6. 8.4 Torque If the force is applied at an angle then only the perpendicular component matters So  must be the angle Between the force And the torque arm 8-4

7. Static Equilibrium 9.1 The Conditions of Equilibirum

8. 9.1 The Conditions for Equilibrium Two Conditions 1.The sum of all forces is zero mathematically examples Called Translational equilibrium 9.1

9. 9.1 The Conditions for Equilibrium 2.The second condition for equilibrium – the sum of all torques equals zero The pivot point chosen does not matter since there is no real rotation 9.1

10. 9.1 The Conditions for Equilibrium Counterclockwise is considered positive torque Clockwise negative torque Mass – negative torque Spring scale – positive torque 9.1

11. 9.1 The Conditions for Equilibrium Steps in Problem Solving Make a free body diagram Choose a coordinate system and resolve the forces into their components Write down the equilibrium equations for the forces Write down the torque equilibrium equation Solve 9.1

12. 9.1 The Conditions for Equilibrium Example: A happy 50 kg dude stands 2 m from the left side of a 5 m long bridge. The bridge is supported at each end by pylons. What is the force on each pylon? 9.1

13. 9.1 The Conditions for Equilibrium Example: A happy 50 kg dude stands 2 m from the left side of a 5 m long bridge. The bridge is supported at each end by pylons. What is the force on each pylon? Free Body Diagram 9.1 P1P1 P2P2 W 5m 2m

14. 9.1 The Conditions for Equilibrium Example: A happy 50 kg dude stands 2 m from the left side of a 5 m long bridge. The bridge is supported at each end by pylons. What is the force on each pylon? Force Equations 9.1 P1P1 P2P2 W 5m 2m

15. 9.1 The Conditions for Equilibrium Example: A happy 50 kg dude stands 2 m from the left side of a 5 m long bridge. The bridge is supported at each end by pylons. What is the force on each pylon? Pivot Point 9.1 P1P1 P2P2 W 5m 2m

16. 9.1 The Conditions for Equilibrium Example: A happy 50 kg dude stands 2 m from the left side of a 5 m long bridge. The bridge is supported at each end by pylons. What is the force on each pylon? Torque Equation Angles 9.1 P1P1 P2P2 W 5m 2m

17. 9.1 The Conditions for Equilibrium Example: A happy 50 kg dude stands 2 m from the left side of a 5 m long bridge. The bridge is supported at each end by pylons. What is the force on each pylon? Torque Equation 9.1 P1P1 P2P2 W 5m 2m

18. 9.1 The Conditions for Equilibrium Example: A happy 50 kg dude stands 2 m from the left side of a 5 m long bridge. The bridge is supported at each end by pylons. What is the force on each pylon? Solve 9.1

19. S-48 A 12.5 kg police pigeon sits on a 1.2 m long branch. What is the torque of the pigeon about the joint of the branch.

20. 9.1 The Conditions for Equilibrium Example: A happy 50 kg dude stands 2 m from the left side of a 5 m long bridge. The bridge is supported at each end by pylons. What is the force on each pylon? Solve 9.1

21. 9.1 The Conditions for Equilibrium Example: A 5 m long ladder leans against a wall at a point 4 m above a cement floor. The ladder is uniform and has a mass of 12 kg. Assuming the wall is frictionless (but the floor is not) determine the forces exerted on the ladder by the floor and by the wall. 9.1

22. 9.1 The Conditions for Equilibrium Example: A 5 m long ladder leans against a wall at a point 4 m above a cement floor. The ladder is uniform and has a mass of 12 kg. Assuming the wall is frictionless (but the floor is not) determine the forces exerted on the ladder by the floor and by the wall. Free body diagram 9.1 NwNw mg f NCNC 4 m

23. 9.1 The Conditions for Equilibrium Example: A 5 m long ladder leans against a wall at a point 4 m above a cement floor. The ladder is uniform and has a mass of 12 kg. Assuming the wall is frictionless (but the floor is not) determine the forces exerted on the ladder by the floor and by the wall. Axis? 9.1 NwNw mg f NCNC 4 m

24. 9.1 The Conditions for Equilibrium Example: A 5 m long ladder leans against a wall at a point 4 m above a cement floor. The ladder is uniform and has a mass of 12 kg. Assuming the wall is frictionless (but the floor is not) determine the forces exerted on the ladder by the floor and by the wall. Force Equations 9.1 NwNw mg f NCNC 4 m

25. 9.1 The Conditions for Equilibrium Example: A 5 m long ladder leans against a wall at a point 4 m above a cement floor. The ladder is uniform and has a mass of 12 kg. Assuming the wall is frictionless (but the floor is not) determine the forces exerted on the ladder by the floor and by the wall. Torque Equations Pick a pivot the eliminates variable Calculate angles 9.1 NwNw mg f NCNC 4 m 53 o 37 o

26. 9.1 The Conditions for Equilibrium Example: A 5 m long ladder leans against a wall at a point 4 m above a cement floor. The ladder is uniform and has a mass of 12 kg. Assuming the wall is frictionless (but the floor is not) determine the forces exerted on the ladder by the floor and by the wall. Torque Equations Write your torque equation 9.1 NwNw mg f NCNC 4 m 53 o 37 o

27. 9.1 The Conditions for Equilibrium

28. S-49 What is the mass of the smallest rock? And what is the upward force provided by the bottom rock? mg 9800N 18800N 7m 5m 1m

29. S-50 Frisco the 7.5 kg cat is sitting 0.2 cm from the end of a ceiling fan blade. If there are five blades, each 0.7 m long, what additional mass (all identical) must be added to each blade so that the fan is in equilibrium?

30. S-51 A 522 kg bear climbs a 10 m long ladder sitting at an angle of 50 o to the horizontal. The coefficient of friction between the ladder and the ground it 0.25, and the ladder has a mass of 65 kg. How far can the bear climb up the ladder before it begins to slide (ignore friction at the top)?

31. 9.1 The Conditions for Equilibrium Example: A 5 m long ladder leans against a wall at a point 4 m above a cement floor. The ladder is uniform and has a mass of 12 kg. Assuming the wall is frictionless (but the floor is not) determine the forces exerted on the ladder by the floor and by the wall. Solve

32. 9.1 The Conditions for Equilibrium Example: A 5 m long ladder leans against a wall at a point 4 m above a cement floor. The ladder is uniform and has a mass of 12 kg. Assuming the wall is frictionless (but the floor is not) determine the forces exerted on the ladder by the floor and by the wall. Solve

33. S-52 A man balances on a ladder. A.What force of friction is needed to keep him from falling? B.What would the coefficient of friction have to be? m=? m=30kg  =20 o  =75 o L=6.5m L=0.7m

34. S-53 Boat in the sand. What is the magnitude and direction of the force of friction needed to maintain equilibrium? Normal W=39600 N W=1960 N  =28 o L=3.5m L=1m

35. Practice

36. S-54 This dog has many large muscles. The other one is rather wimpy. They both wish you good luck on your test