1. AP Physics B Summer Course 2012 2012 年 AP 物理 B 暑假班 M Sittig Ch 10: Free Body Diagrams and Equilibrium

2. Force  Free-body diagrams help visualize forces.  What is a force?  A force is an interaction between two objects (a push or pull).  What is the net force?  Net force is the vector sum of all the forces acting on an object.

3. Force  What forces are acting on this box?

4. Free-Body Diagram Practice  A book is at rest on a tabletop. Diagram the forces acting on the book.  A girl is suspended motionless from the ceiling by two ropes. Diagram the forces acting on the combination of girl and bar.  An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it is falling.  A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance. Diagram the forces acting on the squirrel.  A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. Diagram the forces acting on the book.

5. Free-Body Diagram Practice  A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. Diagram the vertical forces acting on the backpack.  A skydiver is descending with a constant velocity. Consider air resistance. Diagram the forces acting upon the skydiver.  A force is applied to the right to drag a sled across loosely packed snow with a rightward acceleration. Diagram the forces acting upon the sled.  A football is moving upwards towards its peak after having been booted by the punter. Diagram the forces acting upon the football as it rises upward towards its peak.  A car is coasting to the right and slowing down. Diagram the forces acting upon the car.

6. Free-Body Diagram How-To  free-body-diagrams.swf free-body-diagrams.swf  From http://www.wisc-online.com/Objects/ViewObject.aspx?ID=tp1502http://www.wisc-online.com/Objects/ViewObject.aspx?ID=tp1502

7. What is Equilibrium?  When the net force on an object equals zero.  An object is either at rest or moving with a constant velocity  Constant velocity: speed, direction not changing.

8. Equilibrium  Could this object be in equilibrium?

9. How to Solve Equilibrium Problems 1. Draw an appropriate free-body diagram. 2. Resolve vectors into x- and y-components, if necessary. 3. Write an expression for the vector sum of the left-right vectors. Then write an expression for the vector sum of the up- down vectors. Set each of these expressions equal to zero. 4. Solve the resulting equations.

10. Example Problem  Two astronauts tug on opposite sides of a satellite. The first astronaut tugs to the left with a force of 30 N. With what force does the second astronaut tug in order to keep the satellite at rest?

11. Example Problem  Two astronauts tug on opposite sides of a satellite. The first astronaut tugs to the left with a force of 30 N. With what force does the second astronaut tug in order to keep the satellite moving toward him a constant speed of 20 m/s?

12. Example Problem  A man is pushing a box across the floor with a force of 15 N at an angle of 60° from the horizontal. If the box is moving at a constant velocity, what is the size of the friction force on the box?

13. What is a normal force?  A contact force.  A support force.  Acts perpendicular to the surface on which an object rests.  Not always equal to the weight of the object.

14. Practice Problem  5S pg 108 #3

15. What is tension?  The force applied by a rope or string.  Acts along the direction of the rope.  Is always a pulling force, at both ends of the rope.

16. Example Problem  Two blocks suspended over a pulley are at rest. Find the masses of each block.

17. Example Problems  5S pg 107 #1

18. Friction  A force that resists motion.  Acts in parallel to two surfaces pressed together.  Acts in the opposite direction to motion or intended motion.  Static friction: when the object is at rest.  Kinetic friction: when the object is moving.

19. Friction Force of Friction (N) Coefficient of Friction (unitless) Normal Force (N)

20. Force  Find the force F that the man needs to push with to keep this box moving across the floor at a constant velocity. 60 ° F 12 kg μ = 0.45

21. Force  Find the force F that the man needs to push with to keep this box moving across the floor at a constant velocity. θ F m μ

22. Inclined Planes  Normal force is perpendicular to the plane.  Smarter to choose axes parallel (∥) and perpendicular ( ⊥ ) to the plane.  Draw a free-body diagram for the block.

23. Practice Problems  5S pg 107 #4, 2

24. Torque  A force that causes an object to turn, not move in a straight line.  Equal to the product of ① the distance from the fulcrum, and ② the component of the force perpendicular to that distance.

25. Torque

26. Torque (N·m) Perpendicular Force(N) Distance from fulcrum to Force (m)

27. Torque and Equilibrium  Balanced torques, not forces.  Turning (torque) can be clockwise or counterclockwise.  So,

28. Example Problem