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**Preview Section 1 Changes in Motion Section 2 Newton's First Law**

Section 3 Newton's Second and Third Laws Section 4 Everyday Forces

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**What do you think? What is a force?**

Are any forces acting on your book as it rests on your desk? If so, describe them. Make a sketch showing any forces on the book. What units are used to measure force? Can forces exist without contact between objects? Explain. 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. Many students will be able to answer these fairly well. They may have some trouble describing the forces acting on the book. They probably know pounds as a unit of force, but they may not know that the newton is the SI unit of force.

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**Forces Forces can change motion.**

Start movement, stop movement, or change the direction of movement Cause an object in motion to speed up or slow down One common misconception is that “forces cause motion.” Forces actually cause a change in motion, or more specifically, a change in velocity (an acceleration). This will be covered in more detail in the next sections, in the context of Newton’s laws.

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**Forces Contact forces Field forces**

Pushes or pulls requiring physical contact between the objects Baseball and bat Field forces Objects create force fields that act on other objects. Gravity, static electricity, magnetism Pictured is a contact force, the bat and the ball, as well as a field force, the static electric field around charged balloon exerting a force on small pieces of paper. Ask students to identify other examples of contact forces.

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**Units of Force The SI unit of force is the newton (N).**

Named for Sir Isaac Newton Defined as the force required to accelerate a 1 kg mass at a rate of 1 m/s2 Approximately 1/4 pound Other units are shown below. 1 N = pounds (roughly 1/4 pound) Have students determine their approximate weight in newtons to reinforce the size of the unit. When talking about problems, use both units to help them become more comfortable. For example, a N car is about a 2500 lb car.

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**Force Diagrams Forces are vectors (magnitude and direction).**

Force diagram (a) Shows all forces acting during an interaction On the car and on the wall Free-body diagram (b) Shows only forces acting on the object of interest On the car Students often have trouble isolating the forces acting on an object to draw a free-body diagram for the object. The free-body diagram of the car is analyzed in more detail in the next slide.

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**Free-Body Diagrams Three forces are shown on the car.**

Describe each force by explaining the source of the force and where it acts on the car. Is each force a contact force or a field force? For simplicity, all forces are shown acting on the center of the object. Remind students that, when adding vectors, they can be moved parallel without changing the results. Even though the upward force acts on each of the 4 tires, the total is shown acting on the center of the car. Even though the wall strikes the front bumper, that force can be moved to the center of the car without changing the resultant. Gravity (the pull of Earth’s field) acts on every particle in the car but is shown as a single downward force at the center.

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**Now what do you think? What is a force?**

What forces act on your book as it rests on your desk? Make a sketch showing any forces on the book. Are they contact forces or field forces? What SI unit is used to measure force? What equivalent basic SI units measure force? Answers: A force is a push or a pull between two objects. There are two forces acting on the book: the force of gravity downward (field force) and the force of the desk pushing upward (contact force). Forces are measured in newtons (N), a derived unit equivalent to kg•m/s2 .

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**What do you think? Imagine the following two situations:**

Pushing a puck across an air hockey table Pushing a book across a lab table What should your finger do in each case to maintain a constant speed for the object as it moves across the table or desk? (Choose from below.) A quick push or force, then release the object Maintain a constant force as you push the object Increase or decrease the force as you push the object Explain your choice for the puck and the book. 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. Answers will vary. If you have an air track or table or a low-friction cart, you should have the students try their ideas. Hopefully they will see that the continuous push is only needed if there is an opposing force of friction. If not, you can come back to these questions after working through Newton’s 1st law. Students might insist that you need to keep pushing the air hockey puck because it will slow down ever so slightly due to the slight amount of friction. Ask them questions about why this is true. Be very accepting of all answers because there may be a wide variety of beliefs.

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Newton’s First Law Experimentation led Galileo to the idea that objects maintain their state of motion or rest. Newton developed the idea further, in what is now known as Newton’s first law of motion: Discuss Galileo’s experiment with balls rolling down and then back up inclines. Each ball returned to its original height even if the angle of incline was changed. He theorized that the ball would roll forever if the track was horizontal because it would never reach the starting height. A short version of this law would be as follows: Fnet = 0 <-----> v = constant If net force is zero, the velocity is constant and, if the velocity is constant, the net force is zero. It sounds simple, but students have a difficult time with this law because they do not “see” the force of friction when they look at moving objects.

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**Newton’s First Law Called the law of inertia Inertia**

Tendency of an object not to accelerate Mass is a measure of inertia More mass produces more resistance to a change in velocity Which object in each pair has more inertia? A baseball at rest or a tennis ball at rest Answer: the baseball A tennis ball moving at 125 mi/h or a baseball at rest Students may choose the moving tennis ball if they confuse inertia (mass) with momentum (mass times velocity). Emphasize that inertia depends only on mass, and so the baseball has a greater inertia in both cases.

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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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**Now what do you think? Imagine the following two situations:**

Pushing a puck across an air hockey table Pushing a book across a lab table What should your finger do in each case to maintain a constant speed for the object as it moves across the table or desk? (Choose from below.) A quick push or force, then release the object Maintain a constant force as you push the object Increase or decrease the force as you push the object Explain your choice for the puck and the book. Have students revisit these two examples, and discuss them both in terms of Newton’s first law.

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What do you think? If a net force acts on an object, what type of motion will be observed? Why? How would this motion be affected by the amount of force? Are there any other factors that might affect this motion? 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. Hopefully, students will follow Newton’s first law (balanced forces produce no acceleration) with the idea that unbalanced forces produce accelerations. They may posit that a greater force will produce a greater acceleration. They may also use the idea of inertia from the previous section to realize that a greater mass corresponds to a smaller acceleration. On the other hand, it may be difficult for some students to let go of the idea that a force is necessary to maintain constant motion. Revisit this misconception with examples throughout this presentation.

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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? Two football players, Alex and Jason, collide head-on. They have the same mass and the same speed before the collision. How does the force on Alex compare to the force on Jason? Why do you think so? Sketch each player as a stick figure. Place a velocity vector above each player. Draw the force vector on each and label it (i.e. FJA is the force of Jason on Alex). 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. This question will likely produce a wide variety of responses. Some students may believe that the forces are always equal. Many will believe they are equal for the first example but not so for the second and third examples (next slide).

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What do you think? Suppose Alex has twice the mass of Jason. How would the forces compare? Why do you think so? Sketch as before. Suppose Alex has twice the mass and Jason is at rest. How would the forces compare?

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**Forces always exist in pairs.**

Newton’s Third Law Forces always exist in pairs. You push down on the chair, the chair pushes up on you Called the action force and reaction force Occur simultaneously so either force is the action force Emphasize that the action and reaction forces occur at the same time.

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Newton’s Third Law For every action force there is an equal and opposite reaction force. The forces act on different objects. Therefore, they do not balance or cancel each other. The motion of each object depends on the net force on that object.

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Hammer Striking a Nail What are the action/reaction pairs for a hammer striking a nail into wood? Force of hammer on nail = force of nail on hammer Force of wood on nail = force of nail on wood Which of the action/reaction forces above act on the nail? Force of hammer on nail (downward) Force of wood on nail (upward) Does the nail move? If so, how? Fhammer-on-nail > Fwood-on-nail so the nail accelerates downward This example is continued on the next slide.

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**Hammer Striking a Nail What forces act on the hammer?**

Force of nail on hammer (upward) Force of hand on hammer (downward) Does the hammer move? If so, how? Fnail-on-hammer > Fhand-on-hammer so the hammer accelerates upward or slows down The hammer and nail accelerate in opposite directions. Use this example to stress the fact that the action and reaction forces do not cancel each other because they act on different objects. The best way to handle this is by drawing free body diagrams of each object next to each other. The free-body diagram for the nail is show on the previous slide. Ask students to draw the free-body diagram for the hammer. Then students can visualize the action-reaction forces and see that they do not balance each other. Each object accelerates or maintains constant motion based on the forces acting on that object.

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**Action-Reaction: A Book on a Desk**

Action Force The desk pushes up on the book. Reaction Force The book pushes down on the desk. Earth pulls down on the book (force of gravity). The book pulls up on Earth. Have students observe a book sitting on a desk for this slide. After students see the action force on the slide, they should be able to state the reaction force before you show it to them. Often students think the reaction force for the desk pushing up on the book is Earth pulling down on the book. Remind them that these forces act on the same object, the book, so they are not an action-reaction pair.

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**Action-Reaction: A Falling Book**

The book pulls up on Earth. What is the result of the reaction force? Unbalanced force produces a very small upward acceleration (because the mass of Earth is so large). Action Earth pulls down on the book (force of gravity). What is the result of the action force (if this is the only force on the book)? Unbalanced force produces an acceleration of m/s2. Now, remove the book from the desk and allow it to fall to the floor. Ask students if the forces on the book are still balanced. What is the result of this unbalanced force? Acceleration. Have students calculate the acceleration of Earth. Assume the book’s mass is 2.0 kg, so the force on the book is (2.0 kg)(-9.8 m/s2) or 19.6 N downward. Therefore, the upward force on Earth is also 19.6 N. The mass of Earth is about 6 x 1024 kg, so students can calculate the upward acceleration and see how small it will be. You could also choose a falling distance and have students calculate the time required to fall the distance Earth would move upward during that time (using the equations from Chapter 2).

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Now what do you think? If a net force acts on an object, what type of motion will be observed? Why? How would this motion be affected by the amount of force? Are there any other factors that might affect this motion? Acceleration or a changing velocity will result. Increase the force will increase the acceleration. Increasing the mass will decrease the acceleration.

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Now what do you think? Two football players, Alex and Jason, collide head-on. For each scenario below, do the following: Sketch each player as a stick figure. Place a velocity vector above each player. Draw the force vector on each and label it. Draw the acceleration vector above each player. Scenario 1: Alex and Jason have the same mass and the same speed before the collision. Scenario 2: Alex has twice the mass of Jason, and they both have the same speed before the collision. Scenario 3: Alex has twice the mass and Jason is at rest. The forces are equal in all three scenarios. In this first case, the accelerations will also be the same because the forces are equal and the masses are equal. In the other two cases, the accelerations will differ because the masses are not the same.

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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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Now 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. Mass is the amount of matter in an object while weight is the force of gravity. On the surface of Earth, weight = 9.81 x mass. Friction is a force. Friction is affected by the normal force and by the nature of the surfaces in contact with each other.

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