AP Physics B Summer Course 2012 2012 年 AP 物理 B 暑假班

1. Ch 10: Free Body Diagrams and Equilibrium AP Physics B Summer Course 20122012年AP物理B暑假班 M Sittig

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 • From http://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 • Draw an appropriate free-body diagram. • Resolve vectors into x- and y-components, if necessary. • 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. • 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 Normal Force (N) Force of Friction (N) Coefficient of Friction (unitless)

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. F 60 ° 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. F θ 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 Distance from fulcrum to Force (m) Torque (N·m) Perpendicular Force(N)

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

28. Example Problem