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ForcesUnit Packet

Unit 1

Physics

Cedar Ridge HS

2017-2018

Unit Checklist

Assignment Page # Completed?

Forces Vocabulary 6Activity: Measurement Olympics 8Forces Readingo Newton’s 1st Lawo Inertiao Balanced and Unbalanced Forceso Forces and Free-Body Diagramso Newton’s 2nd Lawo Newton’s 3rd Law

91215172124

Activity: Introduction to Newton’s Laws and Forces 30Practice: Free-Body Diagrams 34Practice: Net Force and Finding Acceleration 37Practice: Newton’s Law Word Problems 39Practice: Weight 42Vectors Reading 44Activity: Scalars and Vectors 54Practice: Vectors 59Test Review: Forces 60

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Unit 1 CalendarMonday Tuesday Wednesday Thursday Friday

August 22 A 23 B 24 A 25 B

28 A 29 B 30 A 31 B 1 A

4

No School

5 B 6 A 7 B 8 A

11 B 12 A 13 B 14 A 15 B

18 A 19 B 20 A 21 B 22 A

Unit 1 Learning Outcomes

Students will know...

The motion of an object remains constant unless acted on by an unbalanced force; unbalanced forces cause acceleration.

Inertia is the resistance to change in motion. Weight is the force of gravity acting on an object’s mass. Acceleration is directly proportional to the net force and inversely proportional to the mass of an

object. All forces exist in equal and opposite pairs. Forces acting on an object may be analyzed by free-body diagrams.

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1-Dimensional Motion Other

Velocity AccelerationGravity

g = 9.8 m/s2

Pythagoreana2 + b2 = c2

2-Dimensional Motion Solving 2 Dimensional Motion

Horizontal Motion

Vertical Motion

Horizontal Vertical

x = ? y = ?

vx = ? vy = 0 m/s

ax = 0 m/s2 ay = 9.8 m/s2

t = ?

Forces Momentum and Impulse

Elastic Collision: (m1 v1 i )+(m2 v2i )=(m1 v1 f )+(m2 v2 f )

Inelastic Collision: (m1 v1 i )+(m2v2i )❑=(m1+m¿¿2) v f ¿

Recoil: 0=m1 v1 f+m2 v2 f

Rotation Motion

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Formula Chart

Work - Power – Energy

Electrostatics Waves and Light

F e=kcq1q2d2

k c=8.99 x 109 N ∙m2

C2

Gravitation Force

Circuits

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Formula Chart

Unit 1 Vocabulary: Forces

Free-Body Diagram –A diagram showing all the forces acting on an object

Net Force –The combination of all the forces that act on an object, the resultant force

Resultant Vector – The vector that results from the sum of 2 or more vectors

Inertia – The resistance of a body to change its state of motion; mass is the measure of inertia.

Acceleration – The rate at which velocity is changing; the change may be in magnitude, direction, or both.

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Unit 1 Vocabulary: Forces

Normal Force – a force that acts on an object lying on a surface, acting in a direction perpendicular to the surface

Weight– The force on a body due to the gravitational attraction of another body (commonly Earth).

Tension– A force related to the stretching or pulling of an object such as found in a rope or stretched rubber band.

Gravitational Force– The mutual force of attraction between particles of matter

Frictional Force – The force that acts to resist the relative motion of objects or materials that are in contact.

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Measurement OlympicsPre-Lab Questions:

1. What is the measurement in cm? What about meters?2. What is the measurement on the triple beam balance in grams?

3. To what decimal do you measure in meters with a meter stick?

4. To what decimal do you measure in grams with a triple beam balance?Directions: As you complete each event, estimate how much before measuring. When measuring, be sure to use the correct precision.

Event Estimate Actual Score (Difference)Paper Plate Discus cm cmStraw Javelin Throw cm cmCotton Ball Shot Put cm cmSingle Handed Marble Grab g gHigh Jump m mLong Jump m mConclusion:

1. Why is it important to measure things accurately?~ 8 ~

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Forces1) Newton’s First Law of MotionNewton's first law of motion is often stated asAn object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Two Clauses and a ConditionThere are two clauses or parts to this statement - one that predicts the behavior of stationary objects and the other that predicts the behavior of moving objects. The two parts are summarized in the following diagram.

The behavior of all objects can be described by saying that objects tend to "keep on doing what they're doing" (unless acted upon by an unbalanced force). If at rest, they will continue in this same state of rest. If in motion with an eastward velocity of 5 m/s, they will continue in this same state of motion (5 m/s, East). If in motion with a leftward velocity of 2 m/s, they will continue in this same state of motion (2 m/s, left). The state of motion of an object is maintained as long as the object is not acted upon by an unbalanced force. All objects resist changes in their state of motion -

they tend to "keep on doing what they're doing."There is an important condition that must be met in order for the first law to be applicable to any given motion. The condition is described by the phrase "... unless acted upon by an unbalanced force." As the long as the forces are not unbalanced - that is, as long as the forces are balanced - the first law of motion applies. Suppose that you filled a baking dish to the rim with water and walked around an oval track making an attempt to complete a lap in the least amount of time. The water would have a tendency to spill from the container during specific locations on the track. In general the water spilled when: the container was at rest and you attempted to move it the container was in motion and you attempted to stop it the container was moving in one direction and you attempted to change its direction.

The water spills whenever the state of motion of the container is changed. The water resisted this change in its own state of motion. The water tended to "keep on doing what it was doing." The container was moved from rest to a high speed at the starting line; the water remained at rest and spilled onto the table. The container was stopped near the finish line; the water kept moving and spilled over container's leading edge. The container was forced to move in a different direction to make it around a curve; the water kept moving in the same direction and spilled over its edge. The behavior of the water during the lap around the track can be explained by Newton's first law of motion.

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 Everyday Applications of Newton's First LawThere are many applications of Newton's first law of motion. Consider some of your experiences in an automobile. Have you ever observed the behavior of coffee in a coffee cup filled to the rim while starting a car from rest or while bringing a car to rest from a state of motion? Coffee "keeps on doing what it is doing." When you accelerate a car from rest, the road provides an unbalanced force on the spinning wheels to push the car forward; yet the coffee (that was at rest) wants to stay at rest. While the car accelerates forward, the coffee remains in the same position; subsequently, the car accelerates out from under the coffee and the coffee spills in your lap. On the other hand, when braking from a state of motion the coffee continues forward with the same speed and in the same direction, ultimately hitting the windshield or the dash. Coffee in motion stays in motion.Have you ever experienced inertia (resisting changes in your state of motion) in an automobile while it is braking to a stop? The force of the road on the locked wheels provides the unbalanced force to change the car's state of motion, yet there is no unbalanced force to change your own state of motion. Thus, you continue in motion, sliding along the seat in forward motion. A person in motion stays in motion with the same speed and in the same direction ... unless acted upon by the unbalanced force of a seat belt. Yes! Seat belts are used to provide safety for passengers whose motion is governed by Newton's laws. The seat belt provides the unbalanced force that brings you from a state of motion to a state of rest. Perhaps you could speculate what would occur when no seat belt is used. Reading Comprehension: Answer the following questions based on the readings.

1. There are many more applications of Newton's first law of motion. Several applications are listed below. Perhaps you could think about the law of inertia and provide explanations for each application.

a. Blood rushes from your head to your feet while quickly stopping when riding on a descending elevator.

b. The head of a hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard surface.

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c. To dislodge ketchup from the bottom of a ketchup bottle, it is often turned upside down and thrusted downward at high speeds and then abruptly halted.

d. Headrests are placed in cars to prevent whiplash injuries during rear-end collisions.

e. While riding a skateboard (or wagon or bicycle), you fly forward off the board when hitting a curb or rock or other object that abruptly halts the motion of the skateboard.

2. Summarize Newton’s First Law of Motion.

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2) InertiaNewton's first law of motion states that "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force." Objects tend to "keep on doing what they're doing." In fact, it is the natural tendency of objects to resist changes in their state of motion. This tendency to resist changes in their state of motion is described as inertia.

Newton's conception of inertia stood in direct opposition to more popular conceptions about motion. The dominant thought prior to Newton's day was that it was the natural tendency of objects to come to a rest position. Moving objects, so it was believed, would eventually stop moving; a force was necessary to keep an object moving. But if left to itself, a moving object would eventually come to rest and an object at rest would stay at rest; thus, the idea that dominated people's thinking for nearly 2000 years prior to Newton was that it was the natural tendency of all objects to assume a rest position. Galileo and the Concept of InertiaGalileo, a premier scientist in the seventeenth century, developed the concept of inertia. Galileo reasoned that moving objects eventually stop because of a force called friction. In experiments using a pair of inclined planes facing each other, Galileo observed that a ball would roll down one plane and up the opposite plane to approximately the same height. If smoother planes were used, the ball would roll up the opposite plane even closer to the original height. Galileo reasoned that any difference between initial and final heights was due to the presence of friction. Galileo postulated that if friction could be entirely eliminated, then the ball would reach exactly the same height.Galileo further observed that regardless of the angle at which the planes were oriented, the final height was almost always equal to the initial height. If the slope of the opposite incline were reduced, then the ball would roll a further distance in order to reach that original height.

 

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Galileo's reasoning continued - if the opposite incline were elevated at nearly a 0-degree angle, then the ball would roll almost forever in an effort to reach the original height. And if the opposing incline was not even inclined at all (that is, if it were oriented along the horizontal), then ... an object in motion would continue in motion... .

Forces Don't Keep Objects MovingIsaac Newton built on Galileo's thoughts about motion. Newton's first law of motion declares that a force is not needed to keep an object in motion. Slide a book across a table and watch it slide to a rest position. The book in motion on the table top does not come to a rest position because of the absence of a force; rather it is the presence of a force - that force being the force of friction - that brings the book to a rest position. In the absence of a force of friction, the

book would continue in motion with the same speed and direction - forever! (Or at least to the end of the table top.) A force is not required to keep a moving book in motion. In actuality, it is a force that brings the book to rest.  

Mass as a Measure of the Amount of InertiaAll objects resist changes in their state of motion. All objects have this tendency - they have inertia. But do some objects have more of a tendency to resist changes than others? Absolutely yes! The tendency of an object to resist changes in its state of motion varies with mass. Mass is that quantity that is solely dependent upon the inertia of an object. The more inertia that an object has, the more mass that it has. A more massive object has a greater tendency to resist changes in its state of motion.Suppose that there are two seemingly identical bricks at rest on the physics lecture table. Yet one brick consists of mortar and the other brick consists of Styrofoam. Without lifting the bricks, how could you tell which brick was the Styrofoam brick? You could give the bricks an identical push in an effort to change their state of motion. The brick that offers the least resistance is the brick with the least inertia - and therefore the brick with the least mass (i.e., the Styrofoam brick).

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A common physics demonstration relies on this principle that the more massive the object, the more that object resist changes in its state of motion. The demonstration goes as follows: several massive books are placed upon a teacher's head. A wooden board is placed on top of the books and a hammer is used to drive a nail into the board. Due to the large mass of the books, the force of the hammer is sufficiently resisted (inertia). This is demonstrated by the fact that the teacher does not feel the hammer blow. (Of course, this story may explain many of the observations that you previously have made concerning your "weird physics teacher.") A common variation of this demonstration involves breaking a brick over the teacher's hand using the swift blow of a hammer. The massive bricks resist the force and the hand is not hurt. (CAUTION: do not try these demonstrations at home.)

Reading Comprehension: Answer the following questions based on the reading.

1. If a baseball were thrown in outer space, away from the forces of gravity and friction, what would the baseball do?

2. A 2-kg mass is moving at 4 m/s. How much force is required to keep it moving at this speed? Explain.

3. Two bricks are resting on edge of the lab table. Shirley Sheshort stands on her toes and spots the two bricks. She acquires an intense desire to know which of the two bricks are most massive. Since Shirley is vertically challenged, she is unable to reach high enough and lift the bricks; she can however reach high enough to give the bricks a push. Discuss how the process of pushing the bricks will allow Shirley to determine which of the two bricks is most massive. What difference will Shirley observe and how can this observation lead to the necessary conclusion?

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3) Balanced and Unbalanced ForcesInertia is the tendency of an object to resist changes in its state of motion. But what is meant by the phrase state of motion? The state of motion of an object is defined by its velocity - the speed with a direction. Thus, inertia could be redefined as follows:

Inertia: tendency of an object to resist changes in its velocity. 

An object at rest has zero velocity - and (in the absence of an unbalanced force) will remain with a zero velocity. Such an object will not change its state of motion (i.e., velocity) unless acted upon by an unbalanced force. An object in motion with a velocity of 2 m/s, East will (in the absence of an unbalanced force) remain in motion with a velocity of 2 m/s, East. Such an object will not change its state of motion (i.e., velocity) unless acted upon by an unbalanced force. Objects resist changes in their velocity.An object that is not changing its velocity is said to have an acceleration of 0 m/s/s. Thus, we could provide an alternative means of defining inertia:

Inertia: tendency of an object to resist acceleration.

Balanced ForcesBut what exactly is meant by the phrase unbalanced force? What is an unbalanced force? In pursuit of an answer, we will first consider a physics book at rest on a tabletop. There are two forces acting upon the book. One force - the Earth's gravitational pull - exerts a downward force. The other force - the push of the table on the book (sometimes referred to as a normal force) - pushes upward on the book. 

Since these two forces are of equal magnitude and in opposite directions, they balance each other. The book is said to be at equilibrium. There is no unbalanced force acting upon the book and thus the book maintains its state of motion. When all the forces acting upon an object balance each other, the object will be at equilibrium; it will not accelerate. Consider another example involving balanced forces - a person standing on the floor. There are two forces acting upon the person. The force of gravity exerts a downward force. The floor exerts an upward force. Since these two forces are of equal magnitude and in opposite directions, they balance each other. The person is at equilibrium. There is no unbalanced force acting upon the person and thus the person maintains its state of motion.

 

 

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Unbalanced ForcesNow consider a book sliding from left to right across a tabletop. Sometime in the prior history of the book, it may have been given a shove and set in motion from a rest position. Or perhaps it acquired its motion by sliding down an incline from an elevated position. Whatever the case, our focus is not upon the history of the book but rather upon the current situation of a book sliding to the right across a tabletop. The book is in motion and at the moment there is no one pushing it to the right. (Remember: a force is not needed to keep a moving object moving to the right.) The forces acting upon the book are shown below. 

The force of gravity pulling downward and the force of the table pushing upwards on the book are of equal magnitude and opposite directions. These two forces balance each other. Yet there is no force present to balance the force of friction. As the book moves to the right, friction acts to the left to slow the book down. There is an unbalanced force; and as such, the book changes its state of motion. The book is not at equilibrium and subsequently accelerates. Unbalanced forces

cause accelerations. In this case, the unbalanced force is directed opposite the book's motion and will cause it to slow down.  To determine if the forces acting upon an object are balanced or unbalanced, an analysis must first be conducted to determine what forces are acting upon the object and in what direction. If two individual forces are of equal magnitude and opposite direction, then the forces are said to be balanced. An object is said to be acted upon by an unbalanced force only when there is an individual force that is not being balanced by a force of equal magnitude and in the opposite direction. 

Reading Comprehension: Answer the following questions based on the reading.

1. What does it mean for the forces acting on an object to be balanced?

2. What does it mean for forces acting on an object to be unbalanced?

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4) Forces and Free-Body DiagramsA force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force. Forces only exist as a result of an interaction.

 Contact versus Action-at-a-Distance ForcesFor simplicity sake, all forces (interactions) between objects can be placed into two broad categories: contact forces, and forces resulting from action-at-a-distanceContact forces are those types of forces that result when the two interacting objects are perceived to be physically contacting each other. Examples of contact forces include frictional forces, tensional forces, normal forces, air resistance forces, and applied forces. These specific forces will be discussed in more detail later in Lesson 2 as well as in other lessons.Action-at-a-distance forces are those types of forces that result even when the two interacting objects are not in physical contact with each other, yet are able to exert a push or pull despite their physical separation. Examples of action-at-a-distance forces include gravitational forces. For example, the sun and planets exert a gravitational pull on each other despite their large spatial separation. Even when your feet leave the earth and you are no longer in physical contact with the earth, there is a gravitational pull between you and the Earth. Electric forces are action-at-a-distance forces. For example, the protons in the nucleus of an atom and the electrons outside the nucleus experience an electrical pull towards each other despite their small spatial separation. And magnetic forces are action-at-a-distance forces. For example, two magnets can exert a magnetic pull on each other even when separated by a distance of a few centimeters. These specific forces will be discussed in more detail later in Lesson 2 as well as in other lessons.Examples of contact and action-at-distance forces are listed in the table below.

Contact Forces Action-at-a-Distance Forces

Frictional Force Gravitational Force

Tension Force Electrical Force

Normal Force Magnetic Force

Air Resistance Force

Applied Force

Spring Force

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The NewtonForce is a quantity that is measured using the standard metric unit known as the Newton. A Newton is abbreviated by an "N." To say "10.0 N" means 10.0 Newton of force. One Newton is the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s. Thus, the following unit equivalency can be stated:

1 Newton = 1 kg • m/s2

 Force is a Vector QuantityA force is a vector quantity. As learned in an earlier unit, a vector quantity is a quantity that has both magnitude and direction. To fully describe the force acting upon an object, you must describe both the magnitude (size or numerical value) and the direction. Thus, 10 Newton is not a full description of the force acting upon an object. In contrast, 10 Newton, downward is a complete description of the force acting upon an object; both the magnitude (10 Newton) and the direction (downward) are given.Because a force is a vector that has a direction, it is common to represent forces using diagrams in which a force is represented by an arrow. Such vector diagrams were introduced in an earlier unit and are used throughout the study of physics. The size of the arrow is reflective of the magnitude of the force and the direction of the arrow reveals the direction that the force is acting. (Such diagrams are known as free-body diagrams and are discussed later in this lesson.) Furthermore, because forces are vectors, the effect of an individual force upon an object is often canceled by the effect of another force. For example, the effect of a 20-Newton upward force acting upon a book is canceled by the effect of a 20-Newton downward force acting upon the book. In such instances, it is said that the two individual forces balance each other; there would be no unbalanced force acting upon the book. Other situations could be imagined in which two of the individual vector forces cancel each other ("balance"), yet a third individual force exists that is not balanced by another force. For example, imagine a book sliding across the rough surface of a table from left to right. The downward force of gravity and the upward force of the table supporting the book act in opposite directions and thus balance each other. However, the force of friction acts leftwards, and there is no rightward force to balance it. In this case, an unbalanced force acts upon the book to change its state of motion.

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Types of ForcesPlease go to the following url and take notes on the types of forces: https://goo.gl/JR9V0W

Type of Force Symbol Description

Applied Force FAPP

Gravity Force

Normal Force

Friction Force

Air Resistance Force

Tension Force

Spring Force

Mass vs. WeightA few further comments should be added about the single force that is a source of much confusion to many students of physics - the force of gravity. As mentioned above, the force of gravity acting upon an object is sometimes referred to as the weight of the object. Many students of physics confuse weight with mass. The mass of an object refers to the amount of matter that is contained by the object; the weight of an object is the force of gravity acting upon that object. Mass is related to how much stuff is there and

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weight is related to the pull of the Earth (or any other planet) upon that stuff. The mass of an object (measured in kg) will be the same no matter where in the universe that object is located. Mass is never altered by location, the pull of gravity, speed or even the existence of other forces. For example, a 2-kg object will have a mass of 2 kg whether it is located on Earth, the moon, or Jupiter; its mass will be 2 kg whether it is moving or not (at least for purposes of our study); and its mass will be 2 kg whether it is being pushed upon or not.On the other hand, the weight of an object (measured in Newton) will vary according to where in the universe the object is. Weight depends upon which planet is exerting the force and the distance the object is from the planet. Weight, being equivalent to the force of gravity, is dependent upon the value of g - the gravitational field strength. On earth's surface g is 9.8 N/kg (often approximated as 10 N/kg). On the moon's surface, g is 1.7 N/kg. Go to another planet, and there will be another g value. 

Drawing Free-Body DiagramsPlease go to the following url and take notes on the types of forces: https://goo.gl/ab18Z7

You can find note pages after the readings. When you are finished, please answer the following questions.

Reading Comprehension: Answer the following questions based on the reading.

1. What is a free-body diagram?

2. Summarize the steps for drawing a free-body diagram.

Determining Net ForcePlease go to the following url and take notes on the types of forces: https://goo.gl/d5IPZl

When you are finished, please answer the following questions.

Reading Comprehension: Answer the following questions based on the reading.

1. How do you determine the net force from a free-body diagram?

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5) Newton’s Second LawNewton's first law of motion predicts the behavior of objects for which all existing forces are balanced. The first law - sometimes referred to as the law of inertia - states that if the forces acting upon an object are balanced, then the acceleration of that object will be 0 m/s/s. Objects at equilibrium (the condition in which all forces balance) will not accelerate. According to Newton, an object will only accelerate if there is a net or unbalanced force acting upon it. The presence of an unbalanced force will accelerate an object - changing its speed, its direction, or both its speed and direction.

 

Newton's second law of motion pertains to the behavior of objects for which all existing forces are notbalanced. The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object. The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object. As the force acting upon an object is increased, the acceleration of the object is increased. As the mass of an object is increased, the acceleration of the object is decreased.

 

 

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The BIG EquationNewton's second law of motion can be formally stated as follows:The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

This verbal statement can be expressed in equation form as follows:a = Fnet / m

The above equation is often rearranged to a more familiar form as shown below. The net force is equated to the product of the mass times the acceleration.

Fnet = m • a

In this entire discussion, the emphasis has been on the net force. The acceleration is directly proportional to the net force; the net force equals mass times acceleration; the acceleration in the same direction as the net force; an acceleration is produced by a net force. The NET FORCE. It is important to remember this distinction. Do not use the value of merely "any 'ole force" in the above equation. It is the net force that is related to acceleration. As discussed in an earlier lesson, the net force is the vector sum of all the forces. If all the individual forces acting upon an object are known, then the net force can be determined. If necessary, review this principle by returning to the practice questions in Lesson 2. Consistent with the above equation, a unit of force is equal to a unit of mass times a unit of acceleration. By substituting standard metric units for force, mass, and acceleration into the above equation, the following unit equivalency can be written.

1 Newton = 1 kg • m/s2

The definition of the standard metric unit of force is stated by the above equation. One Newton is defined as the amount of force required to give a 1-kg mass an acceleration of 1 m/s/s.

Reading Comprehension: Answer the following questions based on the reading.

1. Restate Newton’s Law.

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The Big MisconceptionPlease go to the following url and take notes on the types of forces: https://goo.gl/vLC4RE

When you are finished, please answer the following questions.

Reading Comprehension: Answer the following questions based on the reading.

1. What is the big misconception?

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Finding AccelerationPlease go to the following url and take notes on the types of forces: https://goo.gl/VsV4Rx

When you are finished, please answer the following questions.

Reading Comprehension: Answer the following questions based on the reading.

1. Describe a set of steps that would allow you to find acceleration in a problem.

Finding Individual ForcesPlease go to the following url and take notes on the types of forces: https://goo.gl/lxbk67

When you are finished, please answer the following questions.

Reading Comprehension: Answer the following questions based on the reading.

1. Describe a set of steps that would allow you to find an unknown force in a problem.

6) Newton’s Third LawAccording to Newton, whenever objects A and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body. There are two forces resulting from this interaction - a force on the chair and a force on your body. These two forces are called action and reaction forces and are the subject of Newton's third law of motion. Formally stated, Newton's third law is:For every action, there is an equal and opposite reaction.

The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object. The direction of the force on the first object is opposite to the direction of the force on the second object. Forces always come in pairs - equal and opposite action-reaction force pairs. 

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Examples of Interaction Force PairsA variety of action-reaction force pairs are evident in nature. Consider the propulsion of a fish through the water. A fish uses its fins to push water backwards. But a push on the water will only serve to accelerate the water. Since forces result from mutual interactions, the water must also be pushing the fish forwards, propelling the fish through the water. The size of the force on the water equals the size of the force on the fish; the direction of the force on the water (backwards) is opposite the direction of the force on the fish (forwards). For every action, there is an equal (in size) and opposite (in direction) reaction force. Action-reaction force pairs make it possible for fish to swim.Consider the flying motion of birds. A bird flies by use of its wings. The wings of a bird push air downwards. Since forces result from mutual interactions, the air must also be pushing the bird upwards. The size of the force on the air equals the size of the force on the bird; the direction of the force on the air (downwards) is opposite the direction of the force on the bird (upwards). For every action, there is an equal (in size) and opposite (in direction) reaction. Action-reaction force pairs make it possible for birds to fly.Consider the motion of a car on the way to school. A car is equipped with wheels that spin. As the wheels spin, they grip the road and push the road backwards. Since forces result from mutual interactions, the road must also be pushing the wheels forward. The size of the force on the road equals the size of the force on the wheels (or car); the direction of the force on the road (backwards) is opposite the direction of the force on the wheels (forwards). For every action, there is an equal (in size) and opposite (in direction) reaction. Action-reaction force pairs make it possible for cars to move along a roadway surface.

Reading Comprehension: Answer the following questions based on the reading.

1. Identify three force-pairs around you.

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All readings can be found at: http://www.physicsclassroom.com/Physics-Tutorial/Newton-s-Laws

Notes: Forces

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Notes: Forces continued

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Notes: Forces continued

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Notes: Forces continued

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Activity: Introduction to Newton’s Laws & Forces

To Begin: https://phet.colorado.edu/en/simulation/forces-and-motion-basics

Click on the “Motion” sim.

Part I - Newton’s First Law

Make sure the boxes that say “Force” and “Speed” are checked.

a. Apply a force of 50 N right to the box. Describe the motion of the box using physics vocabulary (i.e. velocity, acceleration, displacement). Refer to the speedometer in your answer.

b. Reset the scenario (don’t forget to check force, speed again). Apply a force of 50 N to the right for about 5 seconds then reduce the applied force to zero (the man should stop pushing). Don’t reset the scenario. Describe the motion of the box. Refer to the speedometer in your answer.

c. Apply a force of 50N to the left. Describe the motion of the box.

d. Explain the exact steps needed to make the box come to a stop.

Summary

Newton’s First Law of Motion States “An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.” Explain how your observations in a - d support this Law.

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Part II - Newton’s Second Law

a. Reset the sim, don’t forget to check force, speed again. Remove the box and place a garbage can on top of the skateboard. Using a timer, measure the amount of time it takes to reach maximum speed using a force of 50 N. Try this again with forces of 100N, and 200N.

Applied Force Time To Max Speed50 N100 N150 N200 N

b. Reset the sim, don’t forget to check force, speed again. Remove the box and place a garbage can on top of the skateboard. Using a timer with a refrigerator, and a crate. Record your findings

Object Time To Max Speed at 100 NGarbage CanRefrigeratorCrate

Summary

Newton’s Second Law states “The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.” Explain how your observations in both a and b support this Law.

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Part III - Friction’s Effects

The behavior of the skateboard in Part I and part II were not very realistic because friction was not present. At the bottom of the screen is a simulation that includes friction. Select this simulation.

a. Set friction to “none”. Notice how the screen changed. Why do you think the app designers did that?

b. Make sure that only Speed box is checked.i. Apply a force to get the box to about half of it’s maximum speed, then remove the force.ii. While the box is moving, move the friction slider to 1/2 way. What happened to the box?

Summary

Is friction a force? What evidence do you have?

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Part IV - Back to Newton’s Second Law

Reset the Friction app. Make sure Forces and Speed are checked.

a. Apply a force of 50 N. Describe the movement of the box.

b. Apply a force of 100 N. Describe the movement of the box.

c. Apply a force of 150 N. Describe the movement of the box.

d. Check the box that says “Sum of Forces” . Repeat procedure A, B, and C. What was different about c?

Summary

Newton’s Second Law states “The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.” Explain how your observations relate to the underlined portion of this Law (hint, you might want to look up the definition of the word “net”).

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Practice: Free-Body Diagrams

Free-body diagrams for four situations are shown below. For each situation, determine the net force acting upon the object. Then write a scenario for each situation.

Free-body diagrams for four situations are shown below. The net force is known for each situation. However, the magnitudes of a few of the individual forces are not known. Analyze each situation individually and determine the magnitude of the unknown forces.

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Draw a Free-Body Diagram for each of the following situations. Label each force that is present. State whether the object is balanced or unbalanced.

Situation Free-Body Diagram

1. A girl is suspended motionless from a bar which hangs from the ceiling by two ropes.

Balanced or unbalanced?

2. A book is at rest on a table-top.

Balanced or unbalanced?

3. An egg is free-falling from a nest in a tree. Neglect air resistance.

Balanced or unbalanced?

4. A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance.

Balanced or unbalanced?

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5. 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.

Balanced or unbalanced?

6. A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance.

Balanced or unbalanced?

7. A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder.

Balanced or unbalanced?

8. A force is applied to the right to drag a sled across loosely-packed snow with a rightward acceleration.

Balanced or unbalanced?

9. A car is coasting to the right and slowing down.

Balanced or unbalanced?

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Practice: Finding Net Force and Acceleration

For each of the following problems, give the net force on the block, and the acceleration, including units.

1) 2)

Net Force = ________ a = F/m = _______ Net Force = ________ a = F/m = _______

3) 4)

Net Force = ________ a = _______ Net Force = ________

a = __________

5)

Net Force = ________ a = _______

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12 N 26 N

7 kg

40 kg20 N

180 N

20 kg

190 N

70 N

100 kg30 N 200 N

40 kg300 N

60 N

For problems 6-9, using the formula net Force = Mass • Acceleration, calculate the net force on the object.

6) 7)

FNET = m•a = _____________ FNET = m•a = _____________

8) 9)

FNET = m•a = _____________ FNET = m•a = _____________

10) A student is pushing a 50 kg cart, with a force of 600 N. Another student measures the speed of the cart, and finds that the cart is only accelerating at 3 m/s2. How much friction must be acting on the cart?

FNET = m•a = _____________ = FApplied - FFriction

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a = 3 m/s2

9 kg a = 40 m/s2

5 kg

a = 4 m/s2

12 kg a = 6 m/s2

200 kg

a = 3 m/s2

Fapplied = 600 N

50 kgFfriction = ?

Practice: Newton’s Laws Word Problems

1. A little boy pushes a wagon with his dog in it. The mass of the dog and wagon together is 45 kg. The wagon accelerates at 0.85 m/s2. What force is the boy pulling with?

2. A 1650 kg car accelerates at a rate of 4.0 m/s2. How much force is the car's engine producing?

3. A 68 kg runner exerts a force of 59 N. What is the acceleration of the runner?

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4. A crate is dragged across an ice covered lake. The box accelerates at 0.08 m/s2 and is pulled by a 47 N force. What is the mass of the box?

5. Three women push a stalled car. Each woman pushes with a 425 N force. What is the mass of the car if the car accelerates at 0.85 m/s2?

6. A tennis ball, 0.314 kg, is accelerated at a rate of 164 m/s2 when hit by a professional tennis player. What force does the player's tennis racket exert on the ball?

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7. A 5 kilogram box is pushed with 10 N to the left, while friction pushes back against the box with a force of 2 N. What is the acceleration of the box?

8. A 5 kilogram box is pushed with 10 N to the left, while friction pushes back against the box . If the box accelerations at 0.5 m/s2, what is the force of friction?

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Practice: Weight

1. A locomotive’s mass is 18181.81 kg. What is its weight?

2. A small car weighs 10168.25 N. What is its mass?

3. What is the weight of an infant whose mass is 1.76 kg?

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4. What is the mass of a runner whose weight is 648 N?

5. A person has a mass of 80 kilograms. If they travel to an unknown planet with an acceleration due to gravity of 22 m/s2, what is their weight?

6. A 100 kilogram astronaut exploring Titan has a weight of 140 Newtons. What is the acceleration due to gravity on Titan’s surface?

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Vectors1) What is a vector?A study of motion will involve the introduction of a variety of quantities that are used to describe the physical world. Examples of such quantities include distance, displacement, speed, velocity, acceleration, force, mass, momentum, energy, work, power, etc. All these quantities can by divided into two categories - vectors and scalars. A vector quantity is a quantity that is fully described by both magnitude and direction. On the other hand, a scalar quantity is a quantity that is fully described by its magnitude. The emphasis of this unit is to understand some fundamentals about vectors and to apply the fundamentals in order to understand motion and forces that occur in two dimensions.Examples of vector quantities that have been previously discussedinclude displacement, velocity, acceleration, and force. Each of these quantities are unique in that a full description of the quantity demands that both a magnitude and a direction are listed. For example, suppose your teacher tells you "A bag of gold is located outside the classroom. To find it, displace yourself 20 meters." This statement may provide yourself enough information to pique your interest; yet, there is not enough information included in the statement to find the bag of gold. The displacement required to find the bag of gold has not been fully described. On the other hand, suppose your teacher tells you "A bag of gold is located outside the classroom. To find it, displace yourself from the center of the classroom door 20 meters in a direction 30 degrees to the west of north." This statement now provides a complete description of the displacement vector - it lists both magnitude (20 meters) and direction (30 degrees to the west of north) relative to a reference or starting position (the center of the classroom door). Vector quantities are not fully described unless both magnitude and direction are listed.

 Representing Vectors

Vector quantities are often represented by scaled vector diagrams. Vector diagrams depict a vector by use of an arrow drawn to scale in a specific direction.

Reading Comprehension: Answer the following questions based on the readings.

1. Draw a vector. Label the head and tail of the vector.~ 46 ~

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2) Vector Addition and the Resultant VectorA variety of mathematical operations can be performed with and upon vectors. One such operation is the addition of vectors. Two vectors can be added together to determine the result (or resultant). Observe the following summations of two force vectors:

These rules for summing vectors will be applied to free-body diagrams in order to determine the net force (i.e., the vector sum of all the individual forces) later in this unit. Sample applications are shown in the diagram below.

 

However, the addition of vectors are often done in complicated cases in which the vectors are directed in directions other than purely vertical and horizontal directions. For example, a vector directed up and to the right will be added to a vector directed up and to the left. The vector sum will be determined for the more complicated cases shown in the diagrams to the right.

There are a variety of methods for determining the magnitude and direction of the result of adding two or more vectors.

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The Pythagorean TheoremThe Pythagorean theorem is a useful method for determining the result of adding two (and only two) vectors that make a right angle to each other. The method is not applicable for adding more than two vectors or for adding vectors that are not at 90-degrees to each other. The Pythagorean theorem is a mathematical equation that relates the length of the sides of a right triangle to the length of the hypotenuse of a right triangle. To see how the method works, consider the following problem:Eric leaves the base camp and hikes 11 km, north and then hikes 11 km east. Determine Eric's resulting displacement.

This problem asks to determine the result of adding two displacement vectors that are at right angles to each other. The result (or resultant) of walking 11 km north and 11 km east is a vector directed northeast as shown in the diagram to the right. Since the northward displacement and the eastward displacement are at right angles to each other, the Pythagorean theorem can be used to determine the resultant (i.e., the hypotenuse of the right triangle).

The result of adding 11 km, north plus 11 km, east is a vector with a magnitude of 15.6 km. Use of Scaled Vector Diagrams to Determine a ResultantThe magnitude and direction of the sum of two or more vectors can also be determined by use of an accurately drawn scaled vector diagram. Using a scaled diagram, the head-to-tail method is employed to determine the vector sum or resultant. A common Physics lab involves a vector walk. Either using centimeter-sized displacements upon a map or meter-sized displacements in a large open area, a student makes several consecutive displacements beginning from a designated starting position. Suppose that you were given a map of your local area and a set of

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18 directions to follow. Starting at home base, these 18 displacement vectors could be added together in consecutive fashion to determine the result of adding the set of 18 directions. Perhaps the first vector is measured 5 cm, East. Where this measurement ended, the next measurement would begin. The process would be repeated for all 18 directions. Each time one measurement ended, the next measurement would begin. In essence, you would be using the head-to-tail method of vector addition.

The head-to-tail method involves drawing a vector to scale on a sheet of paper beginning at a designated starting position. Where the head of this first vector ends, the tail of the second vector begins (thus, head-to-tail method). The process is repeated for all vectors that are being added. Once all the vectors have been added head-to-tail, the resultant is then drawn from the tail of the first vector to the head of the last vector; i.e., from start to finish. Once the resultant is drawn, its length can be measured and converted to real units using the given scale. The direction of the resultant can be determined by using a protractor and measuring its counterclockwise angle of rotation from due East.A step-by-step method for applying the head-to-tail method to determine the sum of two or more vectors is given below.1. Choose a scale and indicate it on a sheet of paper. The best choice of scale is one that

will result in a diagram that is as large as possible, yet fits on the sheet of paper.2. Pick a starting location and draw the first vector to scale in the indicated direction. Label

the magnitude and direction of the scale on the diagram (e.g., SCALE: 1 cm = 20 m).3. Starting from where the head of the first vector ends, draw the second vector to scale in

the indicated direction. Label the magnitude and direction of this vector on the diagram.4. Repeat steps 2 and 3 for all vectors that are to be added5. Draw the resultant from the tail of the first vector to the head of the last vector. Label

this vector as Resultant or simply R.6. Using a ruler, measure the length of the resultant and determine its magnitude by

converting to real units using the scale (4.4 cm x 20 m/1 cm = 88 m).7. Describe the direction. The resultant is the vector sum of two or more vectors. It is the result of adding two or more vectors together. If displacement vectors A, B, and C are added together, the result will be vector R. As shown in the diagram, vector R can be determined by the use of an accurately drawn, scaled, vector addition diagram.

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To say that vector R is the resultant displacement of displacement vectors A, B, and C is to say that a person who walked with displacements A, then B, and then C would be displaced by the same amount as a person who walked with displacement R. Displacement vector R gives the same result as displacement vectors A + B + C. That is why it can be said that

A + B + C = R

The above discussion pertains to the result of adding displacement vectors. When displacement vectors are added, the result is a resultant displacement. But any two vectors can be added as long as they are the same vector quantity. If two or more velocity vectors are added, then the result is a resultant velocity. If two or more force vectors are added, then the result is a resultant force. If two or more momentum vectors are added, then the result is ...In all such cases, the resultant vector (whether a displacement vector, force vector, velocity vector, etc.) is the result of adding the individual vectors. It is the same thing as adding A + B + C + ... . "To do A + B + C is the same as to do R."

 As an example, consider a football player who gets hit simultaneously by three players on the opposing team (players A, B, and C). The football player experiences three different applied forces. Each applied force contributes to a total or resulting force. If the three forces are added together using methods of

vector addition (discussed earlier), then the resultant vector R can be determined. In this case, to experience the three forces A, B and C is the same as experiencing force R. To be hit by players A, B, and C would result in the same force as being hit by one player applying force R. "To do A + B + C is the same as to do R." Vector R is the same result as vectors A + B + C!!In summary, the resultant is the vector sum of all the individual vectors. The resultant is the result of combining the individual vectors together. The resultant can be determined by adding the individual forces together using vector addition methods.

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For instance, two displacement vectors with magnitude and direction of 11 km, North and 11 km, East can be added together to produce a resultant vector that is directed both north and east. When the two vectors are added head-to-tail as shown below, the resultant is the hypotenuse of a right triangle. The sides of the right triangle have lengths of 11 km and 11 km. The resultant can be determined using the Pythagorean theorem; it has a magnitude of 15.6 km. The solution is shown to the right.

This Pythagorean approach is a useful approach for adding any two vectors that are directed at right angles to one another. A right triangle has two sides plus a hypotenuse; so the Pythagorean theorem is perfect for adding two right angle vectors. But there are limits to the usefulness of the Pythagorean theorem in solving vector addition problems. For instance, the addition of three or four vectors does not lead to the formation of a right triangle with two sides and a hypotenuse. So at first glance it may seem that it is impossible to use the Pythagorean theorem to determine the resultant for the addition of three or four vectors. Furthermore, the Pythagorean theorem works when the two added vectors are at right angles to one another - such as for adding a north vector and an east vector. But what can one do if the two vectors that are being added are not at right angles to one another? Is there a means of using mathematics to reliably determine the resultant for such vector addition situations? Or is the student of physics left to determining such resultants using a scaled vector diagram? Here on this page, we will learn how to approach more complex vector addition situations by combining the concept of vector components (discussed earlier) and the principles of vector resolution (discussed earlier) with the use of the Pythagorean theorem (discussed earlier). 

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Addition of Three or More Right Angle VectorsAs our first example, consider the following vector addition problem:

Example 1:

A student drives his car 6.0 km, North before making a right hand turn and driving 6.0 km to the East. Finally, the student makes a left hand turn and travels another 2.0 km to the north. What is the magnitude of the overall displacement of the student?

Like any problem in physics, a successful solution begins with the development of a mental picture of the situation. The construction of a diagram like that below often proves useful in the visualization process.

When these three vectors are added together in head-to-tail fashion, the resultant is a vector that extends from the tail of the first vector (6.0 km, North, shown in red) to the arrowhead of the third vector (2.0 km, North, shown in green). The head-to-tail vector addition diagram is shown to the right.

As can be seen in the diagram, the resultant vector (drawn in black) is not the hypotenuse of any right triangle - at least not of any immediately obvious right triangle. But would it be possible to force this resultant vector to be the hypotenuse of a right triangle? The answer is Yes! To do so, the order in which the three vectors are added must be changed. The vectors above were drawn in the order in which they were driven. The student drove north, then east, and then north again. But if the three vectors are added in the order 6.0 km, N + 2.0 km, N + 6.0 km, E, then the diagram will look like this:

After rearranging the order in which the three vectors are added, the resultant vector is now the hypotenuse of a right triangle. The lengths of the perpendicular sides of the right triangle are 8.0 m, North (6.0 km + 2.0 km) and 6.0 km, East. The

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magnitude of the resultant vector (R) can be determined using the Pythagorean theorem.

R2 = (8.0 km)2 + (6.0 km)2

R2 = 64.0 km2+ 36.0 km2

R2 = 100.0 km2

R = √(100.0 km2)R = 10.0 km

In the first vector addition diagram , the three vectors were added in the order in which they are driven. In the second vector addition diagram (immediately above), the order in which the vectors were added was switched around. The size of the resultant was not affected by this change in order. This illustrates an important point about adding vectors: the resultant is independent by the order in which they are added. Adding vectors A + B + C gives the same resultant as adding vectors B + A + C or even C + B + A. As long as all three vectors are included with their specified magnitude and direction, the resultant will be the same. This property of vectors is the key to the strategy used in the determination of the answer to the above example problem.

Reading Comprehension: Answer the following questions based on the readings.

1. What is the head-to-tail method of vector addition?

2. Does the order in which vectors are added matter?

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All readings can be found at: http://www.physicsclassroom.com/class/vectors

Notes: Vectors

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Notes: Vectors continued

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Activity: Scalars and Vectors

Objective:To understand the differences between distance and displacement, and speed and velocity.Pre-lab questions:Answer the following questions.

1. Identify the following quantites as scalar or vector:• Distance• Displacement• Speed• Velocity• ForceIf you don't know the answers to these questions, please look them up. The following activity requires an accurate understanding of these terms.Preparation:You will measure long distances in this lab. They are too long to measure with a measuring tape or meter sticks. So, you will us the length of your stride as a unit, and then convert that to meters.

1. Choose one member of your team to be the official "strider."2. Use a measuring tape to measure 10 meters in the hallway.3. Your "strider" should walk those 10 meters, counting the number of steps.4. Write down how many steps it takes to cover 10 meters. Table 15. Do this two more times. Write down the number of steps each time.6. Average the three step-counts.7. Divide this average number of steps into 10 meters. That tells you how many meters each stride is.

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This is a map of CRHS first floor.

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1 2

3 4

Procedure1. Your team will measure the distance from position 1 to position 2 on the first floor.

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2. Walk from position 1 to position 2. Choose a route that turns at least one corner. Mark your route on the map. It can be as complicated as you like. Just remember to turn at least one corner.3. Measure the time that it takes to walk from position 1 to position 2 along your route.4. Count your steps along your route between position 1 and position 2.5. Convert your steps to meters. To do this conversion, use the conversion factor that you just calculated.

distance=¿ of steps xconversion factor

6. Do the same thing for position 2 to position 3, and position 3 to position 4. (Each time you must turn at least one corner!) Measure the time for each distance. Table 27. On your way back, you should count and record the displacement for each segment.8. Mathematically determine the distances and displacements from position 1 to positions 3 and 4. Remember that the displacement is the straight-line separation of the points. How will we figure this out? (Hint: Think of a giant right triangle.) Table 29. Calculate the average speed for each segment. Table 310. Calculate the average velocity for each segment. Table 3

Table 1: Number of StepsTrial Number of Steps123

Average number of steps = meters= 10

stepsaverage This is your conversion factor. Conversion factor = _______________________Table 2: Distance and Displacement for each segment

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Starting Ending Distance (m) Displacement (m) Time (s)1 22 33 41 31 4

Table 3: Calculated speed and velocity for each segmentStarting p Ending position Speed (m/s) Velocity (m/s)

1 22 33 41 31 4

ConclusionAnswer the following questions in complete sentences.1. For each segment, which is larger, distance or displacement?

2. Can you explain why this is so? (Hint: Compare the smallest possible value of distance to the displacement. Is it possible for distance to be less than the displacement?)~ 61 ~

3.a. Describe a pair of positions that would give you an average velocity of zero.b. Mark them on your maps.c. Explain why the velocity must be zero for these positions.d. Explain whether the speed would also be zero, or couldbe greater than zero.

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Vector Practice

Directions: Draw a vector diagram for each problem. Use your vector diagram to solve for the resultant vector (magnitude and relative direction).

1. Two people are pushing a disabled car. One exerts a force of 200 N east, the other a force of 150 N east. What is the net force exerted on the car? (Assume friction to be negligible.)

2. An airplane flies due north at 100.0 m/s through a 30.0 m/s cross wind blowing from the east to the west. Determine the resultant velocity of the airplane.

3. A mountain climbing expedition establishes a base camp and two intermediate camps, A and B. Camp A is 11,200 m east of and 3200 m above base camp. How far is Camp A from the base camp “as the crow flies?”

4. A plane flies with a velocity of 52 m/s east through a 12 m/s cross wind blowing the plane south. Find the magnitude and relative direction of the resultant velocity at which it travels.

5. The quarterback runs at 5 m/s to the right, while a wind blows at 1 m/s to the left. What is the overall resultant velocity?

6. An ambitious hiker walks 25 km west and then 35 km south in a day. Find the magnitude and relative direction of the hiker's resultant displacement.

7. I went for a walk the other day. I went four avenues east (0.80 miles), then twenty-four streets south (1.20 miles), then one avenue west (0.20 miles), and finally eight streets north (0.40 miles).

a. What distance did I travel?

b. What's my resultant displacement?

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Forces Test Review1. If an elephant exerts 1050 N of force to a mouse, how much force does the mouse

exert on the elephant?

2. If the elephant from problem 6 has a mass of 550 kg, what acceleration will the mouse cause to the elephant?

3. If the mouse from problem 6 has a mass of 0.38 kg, what will the mouse’s acceleration be?

4. If an object has a weight of 374 N on Earth, what is it mass?

5. What is the weight of a 3.0 kg object on the surface of the earth?

6. An object on earth has a mass of 4.0 kg and a weight of 39.2 N. If that object was put on an alien planet with an acceleration due to gravity of 17.3 m/s2, what would its weight be on that planet?

7. Mr. Miller has a mass of 62 kg and would weigh 105 N on the surface of planet X. What is the acceleration due to gravity on this planet?

8. Superman is flying with 8755 N of force, but air resistance is causing 1036 N of friction. What will Superman’s acceleration be if his mass is 107 kg?

9. Draw a free body diagram of a soccer ball in the air after it’s been kicked.

10.Four forces act on an object in four directions; north, south, east and west. If the object is moving at a constant velocity, what must the net force acting on the object be?

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11.Draw a FBD for a box in equilibrium.

12.Draw a FBD for a rock falling through the air. Include air resistance.

13.Draw a FBD for a car moving to the right, but slowing down because of friction.

14.Two forces, 5 N and 8N act on a point. How would you arrange these forces to get the greatest net force?

15.Two forces, 5 N and 8N act on a point. How would you arrange these forces to get the smallest net force?

16.Two men push a fridge across the room. One man pushes with a force of 70 N and the other man pushes with a force of 80N. If the fridge has a mass of 100 kg, what is the acceleration of the fridge?

17.A student is pushing a 40 kg cart, with a force of 200 N. Another student measures the speed of the cart, and finds that the cart is only accelerating at 3 m/s2. How much friction must be acting on the cart? Hint: Draw a diagram showing the cart, and the two forces acting on it.

18.A 30 N northward force and a 30 N westward force act concurrently on an object. What additional force must act upon the object to bring it into a state of equilibrium?

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