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Preview Section 1 Newton's Second Section 5 Extra questions

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**Net Force - the Sum of the Forces**

This car is moving with a constant velocity. Fforward = road pushing the tires Fresistance = force caused by friction and air Forces are balanced Velocity is constant because the net force (Fnet) is zero. Ask students how to increase the speed of the car. Answer: Increase the forward force (accelerator) or decrease the resistance force (make the car more aerodynamic). Ask students how to decrease the speed of the car. Answer: Increase the resistance force (the brakes) or decrease the forward force (accelerator). This will provide a nice introduction to Newton’s 2nd Law.

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**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. After reviewing this slide, return to the previous slide and ask students if the car is in equilibrium.

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**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 Be sure students have looked at Sample Problem B in the Student Edition before trying this problem. Give students some time to work on this problem and then go through each step with them. After completing this problem, show the students that any two of the three forces will be cancelled by the third force. These balanced forces produce equilibrium.

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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 Be sure students understand what is meant by the terms “directly proportional” and “inversely proportional.” A simulation from the Phet web site is available to help students visualize the force and the acceleration. The web address is: Choose the “Motion” simulations, then select “motion in 2D.” You can turn off the vectors and just allow students to observe the motion. Then ask the students to predict the acceleration vector. Which way will it point? Will it have a constant size? After predicting, show the acceleration vector. Next, have them predict the force vector’s direction and size. After predicting, show the force vector and both vectors. Then you can try the other motions described on the screen and ask them to observe the motion, describe the acceleration, and describe the forces. This exercise allows students to see that accelerations are caused by forces. We see the accelerations, but often do not see the forces.

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**Newton’s Second Law (Equation Form)**

F represents the vector sum of all forces acting on an object. F = Fnet Units for force: mass units (kg) acceleration units (m/s2) The units kg•m/s2 are also called newtons (N). It is often useful to write the equation as a = F/m to show students the relationship between force and acceleration and between mass and acceleration. It is easier to see that forces cause accelerations when the equation is written in this form. Even though students saw these units in section 1, they may not recall the fact that newtons are simply a short name for the SI units of kg•m/s2. When solving problems, they will need to know this equivalence in order to cancel units. Remind students of the other units for force, such as dynes (g•cm/s2) and pounds (slug•ft/s2).

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**Classroom Practice Problem**

Space-shuttle astronauts experience accelerations of about 35 m/s2 during takeoff. What force does a 75 kg astronaut experience during an acceleration of this magnitude? Answer: 2600 kg•m/s2 or 2600 N

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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. When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally. Weight and mass are often confused. Students learned earlier that mass was the amount of matter in an object and weight was the force of gravity, but they often still confuse the issue. When eliciting their responses, ask them to discuss appropriate units for each. You might discuss “weightlessness” and ask if objects can be massless as well. Friction is often confused with heat or thermal energy. Students likely will think of friction as being related to many of the quantities listed above.

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**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 = mag where ag = 9.81 m/s2 on Earth Depends on location ag varies slightly with location on Earth. ag is different on other planets. Mention that weight is less on the moon because ag on the moon is 1.6 m/s2 . Reinforce that converting between mass and weight is simple, just multiply or divide by 9.81 m/s2 . Point out that each kg has a weight of 9.81 N on Earth.

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**Normal Force Force on an object perpendicular to the surface (Fn)**

It may equal the weight (Fg), as it does here. It does not always equal the weight (Fg), as in the second example. Fn = mg cos Point out that the equation for normal force applies to the first example also. Because cos(0)=1, the equation reduces to Fn = mg when the forces are directly opposite one another.

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**Static Friction Force that prevents motion Abbreviated Fs**

How does the applied force (F) compare to the frictional force (Fs)? Would Fs change if F was reduced? If so, how? If F is increased significantly, will Fs change? If so, how? Are there any limits on the value for Fs? These questions should help students understand that static friction balances the external force (F), so it increases and decreases as F increases and decreases. Eventually, F will be so large that the static frictional force (Fs) will no longer be able to balance it, and the net force will cause the object to slide. At this point, frictional forces become kinetic (see next slide).

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**Kinetic Friction Force between surfaces that opposes movement**

Abbreviated Fk Does not depend on the speed 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 Fk. Ask students if it requires more force to get an object moving when it is at rest or to keep it moving once it is already in motion. When pushing an object, we exert enough force to overcome static friction. At that point the object moves. The opposing force is now kinetic friction, which is less than static friction. Therefore, in order to maintain a constant speed and not accelerate, the force pushing the object is reduced.

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**Friction Click below to watch the Visual Concept. Visual Concept**

This Visual Concept discusses the nature of friction and the factors that affect the amount of friction. Before running the video, ask students to explain what causes the force of friction. Lead this discussion by asking students how the force of friction is affected by changing the types of surfaces or by adding a lubricant (such as water or glycerin on glass tubing). They should see these things clearly when you play the video. Make sure the students are focused on the magnified view of the surfaces. This will help them understand the effect of increased normal force and the effect of different surface types. During the comments on swimming, ask them how swimmers reduce the force of friction. Have them draw a free-body diagram of a swimmer showing the force propelling him forward (water pushing against his hand) and the frictional force in the opposite direction. Ask students how the swimmer can accelerate. They should respond that he can reduce friction or increase the force of the water on his hand.

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**Calculating the Force of Friction (Ff)**

Ff is directly proportional to Fn (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 Point out to students that Ff is the general term for both static friction (Fs) and kinetic friction (Fk).

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**Typical Coefficients of Friction**

Values for have no units and are approximate. Point out that static is greater than kinetic for each example. Also explain that the coefficient is generally less than 1 but there could be sticky surfaces where the frictional force was greater than the normal force. This would lead to coefficients greater than 1.

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**Everyday Forces Click below to watch the Visual Concept.**

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**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 (Fn) the force of friction (Ff) Find the coefficient of friction. Answer: s = 0.32 This is a relatively simple example from the book (Sample Problem D). Ask students to follow the steps. It is easy to get the answer by skipping the free-body diagram, but they need this diagram to understand that normal force = weight, and the 75 N horizontal push is equal to the force of friction. More complicated problems (next slide) can’t be solved without a free- body diagram.

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**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 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/s2 This is Sample Problem E from the book. The free-body diagram is essential to solving this problem. Students often make the mistake of assuming the normal force equals the weight. These two forces are not equal because the student is pulling upward on the box, thus reducing the normal force. So, Fn = weight - (90.0 N)(sin 30)°. Students can then determine the value for Fk and subtract it from (90.0 N)(cos 30°) to get the net force. At this point, they can use Newton’s second law to find the acceleration.

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**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

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Preview Multiple Choice Short Response Extended Response

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**Multiple Choice Use the passage below to answer questions 1–2.**

Two blocks of masses m1 and m2 are placed in contact with each other on a smooth, horizontal surface. Block m1 is on the left of block m2. A constant horizontal force F to the right is applied to m1. 1. What is the acceleration of the two blocks? A. C. B. D.

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**Multiple Choice Use the passage below to answer questions 1–2.**

Two blocks of masses m1 and m2 are placed in contact with each other on a smooth, horizontal surface. Block m1 is on the left of block m2. A constant horizontal force F to the right is applied to m1. 1. What is the acceleration of the two blocks? A. C. B. D.

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**Multiple Choice, continued**

Use the passage below to answer questions 1–2. Two blocks of masses m1 and m2 are placed in contact with each other on a smooth, horizontal surface. Block m1 is on the left of block m2. A constant horizontal force F to the right is applied to m1. 2. What is the horizontal force acting on m2? F. m1a G. m2a H. (m1 + m2)a J. m1m2a

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**Multiple Choice, continued**

Use the passage below to answer questions 1–2. Two blocks of masses m1 and m2 are placed in contact with each other on a smooth, horizontal surface. Block m1 is on the left of block m2. A constant horizontal force F to the right is applied to m1. 2. What is the horizontal force acting on m2? F. m1a G. m2a H. (m1 + m2)a J. m1m2a

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**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 N at 96° counterclockwise from the positive x-axis B N at 6° counterclockwise from the positive x-axis C x 102 at 96° counterclockwise from the positive x-axis D x 102 at 6° counterclockwise from the positive x-axis

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**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 N at 96° counterclockwise from the positive x-axis B N at 6° counterclockwise from the positive x-axis C x 102 at 96° counterclockwise from the positive x-axis D x 102 at 6° counterclockwise from the positive x-axis

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**Multiple Choice, continued**

5. A freight train has a mass of 1.5 x 107 kg. If the locomotive can exert a constant pull of 7.5 x 105 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 102s B. 4.7s C. 5.0 x 10-2s D. 5.0 x 104s

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**Multiple Choice, continued**

5. A freight train has a mass of 1.5 x 107 kg. If the locomotive can exert a constant pull of 7.5 x 105 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 102s B. 4.7s C. 5.0 x 10-2s D. 5.0 x 104s

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**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 Dx. 6. A. Dx/4 B. Dx C. 2Dx D. 4Dx If the truck’s mass doubles, find the truck’s skidding distance in terms of Dx. (Hint: Increasing the mass increases the normal force.)

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**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 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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**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 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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**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 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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**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 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

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**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 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?

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**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 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

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Extended Response 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 mk between the sled and the snow is 0.040, what is the sled’s acceleration? Show your work.

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Extended Response 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 mk between the sled and the snow is 0.040, what is the sled’s acceleration? Show your work. Answer: 0.71 m/s2

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**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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**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. Answer: Plans should involve measuring forces such as weight, applied force, normal force, and friction.

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