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

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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.

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Force What forces are acting on this box?

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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.

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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.

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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

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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.

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Equilibrium Could this object be in equilibrium?

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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.

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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?

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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?

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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?

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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.

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Practice Problem 5S pg 108 #3

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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.

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

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Example Problems 5S pg 107 #1

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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.

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

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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

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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

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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.

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Practice Problems 5S pg 107 #4, 2

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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.

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Torque

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

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

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Example Problem

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