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Forces and the Laws of MotionSection 1 Preview Section 1 Newton's SecondNewton's Second Section 5 Extra questions

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Section 2Forces and the Laws of Motion Net Force - the Sum of the Forces This car is moving with a constant velocity. –F forward = road pushing the tires –F resistance = force caused by friction and air –Forces are balanced Velocity is constant because the net force (F net ) is zero.

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Section 2Forces and the Laws of Motion Equilibrium The state in which the net force is zero. –All forces are balanced. –Object is at rest or travels with constant velocity. In the diagram, the bob on the fishing line is in equilibrium. –The forces cancel each other. –If either force changes, acceleration will occur.

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Forces and the Laws of MotionSection 2 Classroom Practice Problem An agricultural student is designing a support system to keep a tree upright. Two wires have been attached to the tree and placed at right angles to each other (parallel to the ground). One wire exerts a force of 30.0 N and the other exerts a force of 40.0 N. Determine where to place a third wire and how much force it should exert so that the net force on the tree is zero. Answer: 50.0 N at 143° from the 40.0 N force

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Forces and the Laws of MotionSection 3 Newton’s Second Law Increasing the force will increase the acceleration. –Which produces a greater acceleration on a 3-kg model airplane, a force of 5 N or a force of 7 N? Answer: the 7 N force Increasing the mass will decrease the acceleration. –A force of 5 N is exerted on two model airplanes, one with a mass of 3 kg and one with a mass of 4 kg. Which has a greater acceleration? Answer: the 3 kg airplane

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Forces and the Laws of MotionSection 3 Newton’s Second Law (Equation Form) F represents the vector sum of all forces acting on an object. – F = F net –Units for force: mass units (kg) acceleration units (m/s 2 ) –The units kgm/s 2 are also called newtons (N).

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Forces and the Laws of MotionSection 3 Classroom Practice Problem Space-shuttle astronauts experience accelerations of about 35 m/s 2 during takeoff. What force does a 75 kg astronaut experience during an acceleration of this magnitude? Answer: 2600 kgm/s 2 or 2600 N

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Forces and the Laws of MotionSection 4 What do you think? How do the quantities weight and mass differ from each other? Which of the following terms is most closely related to the term friction? –Heat, energy, force, velocity Explain the relationship.

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Forces and the Laws of MotionSection 4 Weight and Mass Mass is the amount of matter in an object. –Kilograms, slugs Weight is a measure of the gravitational force on an object. –Newtons, pounds –Depends on the acceleration of gravity Weight = mass acceleration of gravity –W = ma g where a g = 9.81 m/s 2 on Earth –Depends on location a g varies slightly with location on Earth. a g is different on other planets.

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Forces and the Laws of MotionSection 4 Normal Force Force on an object perpendicular to the surface (F n ) It may equal the weight (F g ), as it does here. It does not always equal the weight (F g ), as in the second example. F n = mg cos

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Forces and the Laws of MotionSection 4 Static Friction Force that prevents motion Abbreviated F s –How does the applied force (F) compare to the frictional force (F s )? –Would F s change if F was reduced? If so, how? –If F is increased significantly, will F s change? If so, how? –Are there any limits on the value for F s ?

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Forces and the Laws of MotionSection 4 Kinetic Friction Using the picture, describe the motion you would observe. –The jug will accelerate. How could the person push the jug at a constant speed? –Reduce F so it equals F k. Force between surfaces that opposes movement Abbreviated F k Does not depend on the speed

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Forces and the Laws of MotionSection 4 Friction Click below to watch the Visual Concept. Visual Concept

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Forces and the Laws of MotionSection 4 Calculating the Force of Friction (F f ) F f is directly proportional to F n (normal force). Coefficient of friction ( ): –Determined by the nature of the two surfaces – s is for static friction. – k is for kinetic friction. – s > k

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Forces and the Laws of MotionSection 4 Typical Coefficients of Friction Values for have no units and are approximate.

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Forces and the Laws of MotionSection 4 Click below to watch the Visual Concept. Visual Concept Everyday Forces

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Forces and the Laws of MotionSection 4 Classroom Practice Problem A 24 kg crate initially at rest on a horizontal floor requires a 75 N horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor. –Draw a free-body diagram and use it to find: the weight the normal force (F n ) the force of friction (F f ) –Find the coefficient of friction. Answer: s = 0.32

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Forces and the Laws of MotionSection 4 Classroom Practice Problem A student attaches a rope to a 20.0 kg box of books. He pulls with a force of 90.0 N at an angle of 30.0˚ with the horizontal. The coefficient of kinetic friction between the box and the sidewalk is 0.500. Find the magnitude of the acceleration of the box. –Start with a free-body diagram. –Determine the net force. –Find the acceleration. Answer: a = 0.12 m/s 2

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Forces and the Laws of MotionSection 4 The Four Fundamental Forces Electromagnetic –Caused by interactions between protons and electrons –Produces friction Gravitational –The weakest force Strong nuclear force –The strongest force –Short range Weak nuclear force –Short range

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Forces and the Laws of MotionSection 4 Preview Multiple Choice Short Response Extended Response

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Forces and the Laws of MotionSection 4 Multiple Choice Use the passage below to answer questions 1–2. Two blocks of masses m 1 and m 2 are placed in contact with each other on a smooth, horizontal surface. Block m 1 is on the left of block m 2. A constant horizontal force F to the right is applied to m 1. 1. What is the acceleration of the two blocks? A. C. B.D.

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Forces and the Laws of MotionSection 4 Multiple Choice Use the passage below to answer questions 1–2. Two blocks of masses m 1 and m 2 are placed in contact with each other on a smooth, horizontal surface. Block m 1 is on the left of block m 2. A constant horizontal force F to the right is applied to m 1. 1. What is the acceleration of the two blocks? A. C. B.D.

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Forces and the Laws of MotionSection 4 Multiple Choice, continued Use the passage below to answer questions 1–2. Two blocks of masses m 1 and m 2 are placed in contact with each other on a smooth, horizontal surface. Block m 1 is on the left of block m 2. A constant horizontal force F to the right is applied to m 1. 2. What is the horizontal force acting on m 2 ? F. m 1 a G. m 2 a H. (m 1 + m 2 )a J. m 1 m 2 a

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Forces and the Laws of MotionSection 4 Multiple Choice, continued Use the passage below to answer questions 1–2. Two blocks of masses m 1 and m 2 are placed in contact with each other on a smooth, horizontal surface. Block m 1 is on the left of block m 2. A constant horizontal force F to the right is applied to m 1. 2. What is the horizontal force acting on m 2 ? F. m 1 a G. m 2 a H. (m 1 + m 2 )a J. m 1 m 2 a

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Forces and the Laws of MotionSection 4 Multiple Choice, continued 3. A crate is pulled to the right with a force of 82.0 N, to the left with a force of 115 N, upward with a force of 565 N, and downward with a force of 236 N. Find the magnitude and direction of the net force on the crate. A. 3.30 N at 96° counterclockwise from the positive x-axis B. 3.30 N at 6° counterclockwise from the positive x-axis C. 3.30 x 10 2 at 96° counterclockwise from the positive x-axis D. 3.30 x 10 2 at 6° counterclockwise from the positive x-axis

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Forces and the Laws of MotionSection 4 Multiple Choice, continued 3. A crate is pulled to the right with a force of 82.0 N, to the left with a force of 115 N, upward with a force of 565 N, and downward with a force of 236 N. Find the magnitude and direction of the net force on the crate. A. 3.30 N at 96° counterclockwise from the positive x-axis B. 3.30 N at 6° counterclockwise from the positive x-axis C. 3.30 x 10 2 at 96° counterclockwise from the positive x-axis D. 3.30 x 10 2 at 6° counterclockwise from the positive x-axis

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Forces and the Laws of MotionSection 4 Multiple Choice, continued 5. A freight train has a mass of 1.5 x 10 7 kg. If the locomotive can exert a constant pull of 7.5 x 10 5 N, how long would it take to increase the speed of the train from rest to 85 km/h? (Disregard friction.) A. 4.7 x 10 2 s B. 4.7s C. 5.0 x 10 -2 s D. 5.0 x 10 4 s

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Forces and the Laws of MotionSection 4 Multiple Choice, continued 5. A freight train has a mass of 1.5 x 10 7 kg. If the locomotive can exert a constant pull of 7.5 x 10 5 N, how long would it take to increase the speed of the train from rest to 85 km/h? (Disregard friction.) A. 4.7 x 10 2 s B. 4.7s C. 5.0 x 10 -2 s D. 5.0 x 10 4 s

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Forces and the Laws of MotionSection 4 Multiple Choice, continued Use the passage below to answer questions 6–7. A truck driver slams on the brakes and skids to a stop through a displacement x. 6. A. x/4 B. x C. 2 x D. 4 x If the truck’s mass doubles, find the truck’s skidding distance in terms of x. (Hint: Increasing the mass increases the normal force.)

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Forces and the Laws of MotionSection 4 Short Response Base your answers to questions 10–12 on the information below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball. 10.How long does the ball take to hit the ground?

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Forces and the Laws of MotionSection 4 Short Response Base your answers to questions 10–12 on the information below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball. 10.How long does the ball take to hit the ground? Answer: 6.00 s

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Forces and the Laws of MotionSection 4 Short Response, continued Base your answers to questions 10–12 on the information below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball. 11. How far from the building does the ball hit the ground?

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Forces and the Laws of MotionSection 4 Base your answers to questions 10–12 on the information below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball. 11. How far from the building does the ball hit the ground? Answer: 72.0 m Short Response, continued

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Forces and the Laws of MotionSection 4 Base your answers to questions 10–12 on the information below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball. 12. When the ball hits the ground, what is its speed? Short Response, continued

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Forces and the Laws of MotionSection 4 Base your answers to questions 10–12 on the information below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball. 12. When the ball hits the ground, what is its speed? Answer: 63.6 m/s Short Response, continued

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Forces and the Laws of MotionSection 4 16. A student pulls a rope attached to a 10.0 kg wooden sled and moves the sled across dry snow. The student pulls with a force of 15.0 N at an angle of 45.0º. If k between the sled and the snow is 0.040, what is the sled’s acceleration? Show your work. Extended Response

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Forces and the Laws of MotionSection 4 16. A student pulls a rope attached to a 10.0 kg wooden sled and moves the sled across dry snow. The student pulls with a force of 15.0 N at an angle of 45.0º. If k between the sled and the snow is 0.040, what is the sled’s acceleration? Show your work. Answer: 0.71 m/s 2 Extended Response

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Forces and the Laws of MotionSection 4 Extended Response, continued 17. You can keep a 3 kg book from dropping by pushing it horizontally against a wall. Draw force diagrams, and identify all the forces involved. How do they combine to result in a zero net force? Will the force you must supply to hold the book up be different for different types of walls? Design a series of experiments to test your answer. Identify exactly which measurements will be necessary and what equipment you will need.

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Forces and the Laws of MotionSection 4 17. You can keep a 3 kg book from dropping by pushing it horizontally against a wall. Draw force diagrams, and identify all the forces involved. How do they combine to result in a zero net force? Will the force you must supply to hold the book up be different for different types of walls? Design a series of experiments to test your answer. Identify exactly which measurements will be necessary and what equipment you will need. Answer: Plans should involve measuring forces such as weight, applied force, normal force, and friction. Extended Response, continued

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