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Velocity is important in that it distinguishes the direction the object is traveling. ... The SI unit for velocity is me

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Physical Science Forces of Motion

Forces of Motion Have you ever ridden in a car? Of course you have! Therefore, you already know basic principles of force, motion, and acceleration. In this module you will not just talk about speed as fast or slow, but will look at how to calculate speed. You will also learn how to calculate acceleration. Not only will you be calculating motion, you will be applying Newton's three laws of motion to everyday situations. For instance, why do you wear a seatbelt? Why should you wear a helmet when biking or skateboarding? How can knowing Newton's three laws help you be a better athlete? You will discover that applications of Newton's three laws are surrounding you in many different areas of your life. In addition, you will study different forces including gravitational forces. Upon completion of this module, you will know that mass and weight are not the same thing and why. You will also discuss how work can be made easier and more efficient as well as calculate how advantageous it is to use a simple machine to do work. You will see that this module is packed full of information that is applicable to your everyday life.

Essential Questions How can motion be observed, described, measured, and represented? How can each of Newton's 3 Laws be applied to everyday life? Why does your hand hurt after punching a wall when you are the object applying force? What is the relationship between mass and force? What is the difference between mass and weight? How can work be made easier and more efficient?

Key Terms Force – an action that can change the motion of an object. A push or a pull is an example of a force. Newton - the unit used to measure force Net Force – the combination of all of the forces acting on an object. Balanced Force – forces that are opposite in direction and equal in size, cause no change in motion, and the net force equals 0. Unbalanced Force - forces that are not opposite and equal. Forces that cause a change in motion. Motion - the act or process of changing position or place. Newton's 1st Law – states that an object at rest will stay at rest unless it is acted upon by an unbalanced force. An object in motion will continue to move in the same direction and with the same speed unless acted upon by an unbalanced force. Newton's 2nd Law – states that the acceleration, a, of an object is directly related to the net force, F, applied to the object and inversely related to the mass, m, of the object. Shown by F = ma Newton's 3rd Law - states that forces occur as equal and opposite pairs. For every action force there is an equal and opposite reaction force. Acceleration - is found by dividing the change in the velocity of the object by the change in time Velocity - a measure of speed in a given direction Speed – the distance an object moves per unit of time Inertia - the tendency of an object to resist a change in motion Mass – the amount of matter in an object Weight – the force due to gravity-Equal to the product of the object's mass and the acceleration of gravity (w = mg). At the surface of Earth, the acceleration of gravity is 9.80 m / s² which is the constant used in the equation for g. Gravitational force – is a force between any two objects. The strength of the force is related to the mass of the objects and the distance between them. Terminal velocity – occurs when the force of air resistance becomes large enough to balances the force of gravity. At this instant in time, the net force is 0 Newtons; the object will stop accelerating. Frictional forces – work against motion Work - is the transfer of energy when an applied force moves an object over a distance. For work to be done the force applied must be in the same direction as the movement of the object and the object must move a certain distance. (W = Fd) Joule – the unit used to measure work Simple Machines – machines that work with one movement. The 6 simple machines are lever, pulley, inclined plane, wedge, screw, and wheel and axle. Effort Force – the force applied to a simple machine Resistance Force – the force exerted by the machine Mechanical advantage – is the number of times a machine multiplies the effort force

What to Expect In this module, you will be responsible for completing the following assignments. Velocity and Acceleration Assignment Check Quiz Motion Lab or Motion Cartoon Forces Quiz A World Without Force Discussion Newton's Laws Lab or Newton's Laws Illustration Mechanical Advantage Assignment Check Quiz Forces and Motion Module Test

Motion Objects are in motion everywhere we look. Everything from a tennis game to a space-probe flyby of the planet Neptune involves motion. When you are resting, your heart moves blood through your veins. And even in inanimate objects, there is continuous motion in the vibrations of atoms and molecules. Questions about motion are interesting in and of themselves: How long will it take for a space probe to get to Mars? Where will a football land if it is thrown at a certain angle? But an understanding of motion is also key to understanding other concepts in physics. An understanding of acceleration, for example, is crucial to the study of force. In order to describe the motion of an object, you must first be able to describe its position—where it is at any particular time. More precisely, you need to specify its position relative to a convenient reference frame. Earth is often used as a reference frame, and we often describe the position of an object as it relates to stationary objects in that reference frame. For example, a rocket launch would be described in terms of the position of the rocket with respect to the Earth as a whole, whereas a bus driving by would be described with respect to you. If you are in a car that is moving in the same direction, then the bus will be moving at a different velocity with respect to you. If your car is moving in the same direction and same speed as the bus, the bus will appear to not move with respect to you. Of course, if you compare the speed with the ground, both of you will be moving at some velocity. Suppose you saw a person walking to the front of the moving bus. The person would be moving faster than the bus from your viewpoint. However, the person would not notice the speed of the bus while he walks to the front. As you can see in talking about motion, it is important to indicate your point of reference. To give you a good overview of the concepts we will be learning in this module, please watch the videos below. As you watch the videos, be sure to fill in the guided notes which can be found in the sidebar. Used by permission

Speed vs. Velocity Speed is not a new term to you. You commonly refer to how fast you were going in the terms of miles per hour. You might have heard speed and velocity used interchangeably, but they do differ from one another. Speed refers to how fast an object is moving in terms of distance moved and time taken to move in. Velocity is a measure of speed in a given direction. Velocity is important in that it distinguishes the direction the object is traveling. In physics, we use velocity because when comparing different object's motion it is important to know not only the magnitude but also the direction of the motion.

Calculating Velocity It is important that we can answer specific questions related to velocity. For instance, "How long does a foot race take?" and "What is the runner's speed?" can only be answered by making calculations. Velocity is calculated by using the following equation: v= Velocity equals the change in displacement of distance divided by the change in time. Whenever any calculations are performed it is important to include the units. Without units, the numbers are meaningless. The SI unit for velocity is meters per second or m/s, but many other units, such as km/h, mi/h (also written as mph), and cm/s, are in common use. There are a couple of things to be aware of when calculating velocity problems. 1) The problem could ask for you to find velocity, distance, or time. You will need to be able to rearrange the problem in order to find the missing variable. You can use algebra or you can use the triangle method. With the triangle method, you use the triangle given below and you cover up the variable you are trying to find. This allows you to know if you need to multiply or divide the remaining variables.

2) Watch the given units and the required units carefully. You need to make sure the units match. For instance, if the problem gives you a distance in miles but the final answer is asked for in meters then it will be important to convert before you plug the numbers into the equation. For example, look at this problem. A commuter train travels from Washington D.C. to Baltimore in 45 minutes. The distance between the two stations is approximately 41 miles. What is the average speed of the train in m/s? Convert 41 miles to meters: Convert 45 minutes to seconds: Plug calculated distance and time into the velocity equation: 1. Convert 41 miles to meters:

2. Convert 45 minutes to seconds:

3. Plug calculated distance and time into the velocity equation:

Check to ensure you have significant digits. Since there are 2 significant digits in each of the given numbers, then the answer should also have 2 significant digits. You should round your final answer to: 24 m/s Be sure to always include your units with your final answer.

Velocity Practice Problems 1. What is the velocity of a cheetah that travels north 118.0 meters in 6.0 seconds? Looking For:

Solution:

Velocity of cheetah



Given:

V = d = 118.0 meters = 19.7 m/s

Distance = 118.0 meters

t 6.0 seconds

Time = 6.0 seconds



Equation:

V = 19.7 m/s North

2. A bicyclist travels 60.0 kilometers in 3.5 hours towards Atlanta. What is the cyclist's average velocity? Looking For:

Solution:

Velocity of bicyclist



Given:



Distance = 60.0 kilometers

V = d = 60.0 km = 17 km/hr

Time = 3.5 hours

t 3.5 hr

Equation:





V = 17 km/hr towards Atlanta

3. How much time would it take for the sound of thunder to travel 1,500 meters if sound travels at a speed of 330 m/sec? Looking For:

Solution:

Time for thunder to travel



Given:

t = d = 1,500 m = 4.55 seconds

Distance = 1,500 meters

v 330m/sec

Velocity = 330 m/sec



Equation:

t = 4.55 seconds

4. How far can a person run in 15 minutes if he runs at an average speed of 16 km/hr? Looking For:

Solution:

Distance person can run



Given:



Time = 15 minutes

d = v x t = 16 km/hr x .25 hours =

Velocity = 16 km/hr

4 km

Equation:











*Must convert 15 minutes to hours in order to get the units the same.

d = 4 km

15 minutes x 1 hour = .25 hours 60 minutes

Distance versus Time Graphs Another way to visualize the motion of an object is to use a graph. Position vs. time graphs, also called distance vs. time graphs, are used to display a collection of data. The data, in this case, is the distance an object has travelled in a set amount of time. The graph shows the changes in velocity over time. Watch the following video explain how to interpret position versus time graphs. Be sure to answer the questions in the guided video notes to ensure you are taking away the important concepts from the video. Used by permission As you can see, graphs can give you a visual understanding of the motion of an object. Below is a summary of how to read distance versus time graphs.

Example: Journey to the Bus Stop The graph below shows Tom's journey to the bus stop is split into four sections. The straight lines indicate that Tom moves at a constant but different speed in each section. Look at each description related to each section of the graph.

A. In this section of the journey Tom walks away from home at a speed of 2 meters per second (100 meters ÷ 50 seconds). B. The negative slope here means a change in direction. At 100 meters from home Tom starts to walk towards home. He walks for 60 meters (100 meters - 40 meters) at a speed of 3 meters per second (60 meters ÷ 20 seconds). C. At the start of this section Tom changes direction. He is now walking away from home at a fast pace. His speed is 4 meters per second (Distance: 160 meters - 40 meters = 120 meters. 120 meters ÷ 30 seconds). D. Here the slope is zero. This means at 160 meters from home Tom stops. His distance does not change even though the time is continuing. It has taken him 100 seconds to get to this point.

Acceleration In everyday conversation, to accelerate means to speed up. The accelerator in a car can in fact cause it to speed up. The greater the acceleration, the greater the change in velocity over a given time. The formal definition of acceleration is consistent with this understanding of acceleration, but acceleration also includes any change of velocity, not just speeding up. To measure acceleration mathematically, the following equation should be used: a= or

a= This shows that acceleration is equal to the change in velocity divided by the time. To show a change in velocity you subtract the final velocity (vf) - the initial velocity (vi). The Δ is the Greek letter delta and stands for difference or change in . Whenever you solve an equation, you must include the correct units. Acceleration is velocity in m/s divided by time in s, the SI units for acceleration are m/s2, meters per second squared or meters per second per second, which literally means by how many meters per second the velocity changes every second. Since the definition for acceleration is any change in velocity, this change could occur in the form of speeding up (increasing the velocity), slowing down (decreasing the velocity), or changing directions. When an object is decelerating, it will have a negative acceleration.

Acceleration Practice Problems 1. An object speeds up from a velocity of 240 meters/second to 560 meters/second in a time period of 10 seconds. What is the acceleration of the object? Given:

Solution:

Final velocity = vf = 560 m/s

a = (vf - vi ) / t =

Initial velocity = vi = 240 m/s

(560 m/s - 240 m/s) / 10 sec =

Time = 10 seconds

320 m/s / 10 sec =

Equation:

32 m/s2

a =

a = 32 m/s2 2. While traveling along a highway a driver slows from 24 m/sec to 15 m/sec in 12 seconds. What is the automobile's acceleration? Given:

Solution:

Final velocity = vf = 15 m/s

a = (vf - vi ) / t =

Initial velocity = vi = 24 m/s

(15 m/s - 24 m/s) / 12 sec =

Time = 12 seconds

-9 m/s / 12 sec =

Equation:

- 0.75 m/s2

a=

a = - 0.75 m/s2 *Note since the car is slowing down (decelerating) there is a negative acceleration.* 3. A cart rolling down an incline for 5.0 seconds has an acceleration of 4.0 m/sec2 . If the cart has a beginning speed of 2.0 m/sec, what is its final speed? Given:

Solution:

Initial velocity = vi = 2.0 m/s

a = (vf - vi ) / t =

Time = 5.0 seconds

4.0 m/s2 = (vf - 2.0 m/s) / 5.0 sec =

Acceleration = 4.0 m/s2

4.0 m/s2 x 5.0 s= vf - 2.0 m/s

Equation:

20 m/s = vf - 2.0 m/s 20 m/s + 2.0 m/s = vf

a=



vf = 22 m/s

Calculating Motion Assignments Velocity and Acceleration Assignment Check Quiz At this time you are ready to take the Velocity and Acceleration Quiz. Be sure you review the pages prior to this quiz to ensure you know the material before taking the quiz.

Motion Assignment Choose one of the following assignments to complete: Motion Lab You will be conducting an activity to answer the following question: By which method can you walk the fastest (backwards, without feet leaving the floor, regular walking)? You will be collecting data and making calculations. Look at the full directions given in the document in the sidebar. Motion Cartoon You will create a cartoon or animation explaining the difference between speed and velocity. You can draw the cartoon by hand, ensuring that it is neat and legible. You can upload pictures of your work. You can also create a cartoon or animation using various websites given. Look at the full directions given in the document in the sidebar.

Forces What is a Force? A force is simply a push or a pull. A force can cause a change in motion. A force is a vector quantity, meaning that it has both magnitude (size or numerical value) and direction. Knowing the size of the force and the direction of the force is very important, as it will determine the motion of the object. Let's use a game of tug of war to explain this concept of forces. When each team is pulling with an equal force in opposite directions, then neither team can cause the other team to move. Forces that are equal in size, but in opposite directions are called balanced forces. Balanced forces do not cause a change in motion.

However, if one team is able to pull with a greater force than the other team, the there will be a change in motion. Forces that cause a change in motion are called unbalanced forces. Unbalanced forces can occur in the same direction or in opposite directions. Unbalanced forces are not equal and opposite.

More than one force can act on an object at one time. Looking back to the game of tug of war, each team member experiences the applied force of the other people in the game as well as the force of gravity holding them to the ground. The combination of all of the forces acting on an object is the net force. The net force determines the motion of the object. For balanced forces, the net force is zero indicating that there is no motion.

When more than one force is acting on an object, forces that are in the same direction are added together and forces in opposite directions are subtracted. Suppose you and a friend need to move a piano. To do this, you push on one end and your friend pulls on the other end. Your added forces are enough to move the piano. This is because your forces are in the same direction. Another example is two dogs playing tug of war. Since the dogs are pulling in opposite directions, the forces are subtracted. The net force is the difference between the two forces in the direction of the larger force.

To review balanced and unbalanced forces, please watch the video below. You will be shown 5 different scenarios and will determine if the forces acting on the object are balanced or unbalanced. Source

Types of Forces All forces can be placed into two basic categories: distant forces and contact forces. As you can imagine, contact forces are those forces in which the interacting objects have some sort of physical contact. Distant forces, on the other hand, are those forces in which the two interacting objects do not have physical contact but are still pushing or pulling on each other at a distance.

Distant Forces Force

Definition

Gravitational Force

Gravity is a force that attracts objects toward other massively large objects such as the Earth or moon. On Earth, all objects experience a downward force due to gravity to the center of the Earth.

Fg Electromagnetic A force that acts between charged particles and is the combination of all electrical and magnetic forces. The Force electromagnetic force can be attractive or repulsive.

Contact Forces Force Applied Force

Definition An applied force is a force applied by another object such as a person, machine, and lots others. For example, if you push a book across a table then you are applying a force with your hand to push the book.

F app Normal Force

Also called the support force because it supports the weight of an object on a surface. For example, the table supports a book resting on a table.

Fn Friction Force Ff

A force that opposes the motion of an object caused by the force exerted by the surface as an object moves across it. There are three types of frictional forces: sliding friction, rolling friction, and static friction. Sliding friction occurs when one solid surface slides over another solid surface. Rolling friction occurs when an object rolls across a solid surface. Static friction occurs between the surfaces of two objects that touch but do not move against each other. Static friction must be overcome for one of the objects to move.

Air A type of frictional force that opposes the motion of an object as it moves through the air. For example, if a book fell off a table Resistance then gravity would be pulling it down and air resistance would be pushing slightly up on the book. Force F air Tension Force

A force that is transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends.

F tens Spring Force

A force exerted by a compressed or stretched spring upon any object that is attached to it. An object that compresses or stretches a spring is always acted upon by a force that restores the object to its rest or equilibrium position.

F spring

Free Body Diagrams A free body diagram is a visual representation used to analyze the forces acting on a body. The purpose of a free body diagram is to show all the forces acting on an object as well as indicate the magnitude and direction of each of the forces. The size of the arrow reflects the magnitude of the force. The direction of the arrow shows the direction that the force is acting. The object is usually represented by a box as seen in the example.

To review free body diagrams and see examples, please watch the videos below. Used by permission How well do you understand free body diagrams? Test your knowledge by completing the interactive activity below. Source

Gravitational Forces Let's look a little closer at gravity. It is important to note that every object in the universe attracts every other object in the universe. However, the force of gravity is a weak force and is dependent on both the mass of the object and the distance between the objects. Gravity is most clearly seen with very large massive objects such as the Earth. It is important to know that the more massive the objects the more gravitational force each will experience. In addition, the closer the objects are to each other the more gravity they will experience. Whereas, the further the objects are apart the less gravitation force they will experience.

Acceleration Due to Gravity It's a good thing this mountain climber's safety gear is working, because it's a long way down to the ground! If he were to fall, he'd be moving really fast by the time he got there. The higher any object starts falling from above Earth's surface, the faster it's traveling by the time it reaches the ground. Do you know why? The reason is gravity. As stated above, gravity is a force that pulls objects down toward the ground. When objects fall to the ground, gravity causes them to accelerate. Gravity causes an object to fall toward the ground at a faster and faster velocity the longer the object falls. In fact, its velocity increases by 9.8 m/s2, so by 1 second after an object starts falling, its velocity is 9.8 m/s. By 2 seconds after it starts falling, its velocity is 19.6 m/s (9.8 m/s + 9.8 m/s), and so on. The acceleration of a falling object due to gravity is illustrated in the picture below.

In summary when an object is dropped, it accelerates toward the center of Earth. Galileo was instrumental in showing that, in the absence of air resistance, all objects fall with the same acceleration (which is denoted by a constant g). Consider an object with mass falling downward toward Earth. It experiences only the downward force of gravity. Knowing the gravitational acceleration constant and the mass of the object can provide us with the weight. To calculate weight, the following equation is used: w = m x g (On Earth, the gravitational constant (g) is 9.8 m/s2) What if you were to drop a bowling ball and a soccer ball at the same time from the same distance above the ground? The bowling ball has greater mass than the basketball, so the pull of gravity on it is greater. Would it fall to the ground faster? No, the bowling ball and basketball would reach the ground at the same time. The reason? The more massive bowling ball is also harder to move because of its greater mass, so it ends up moving at the same acceleration as the soccer ball. This is true of all falling objects. They all accelerate at the same rate due to gravity, unless air resistance affects one object more than another. For example, a falling leaf is slowed down by air resistance more than a falling acorn because of the leaf's greater surface area. When the net external force on an object is its weight, we say that it is in free-fall. That is, the only force acting on the object is the force of gravity. In the real world, when objects fall downward toward Earth, they are never truly in free-fall because there is always some upward force from the air acting on the object. However, in true free-fall (neglecting air resistance) all objects accelerate to the Earth at a constant rate of 9.8 m/s2. Now, the value of g decreases the farther away from the center of Earth an object gets. This means the weight of an object would decrease if it was placed on top of a mountain or put into space. What happens in the presence of air resistance, as is most commonly the case on Earth? When an object accelerates towards the Earth due to gravity, air resistance is opposing the motion. Eventually the downward pull of gravity equals the upward force of the air resistance. When this occurs, there is a balanced net force which means that the object is no longer accelerating. The object will remain going at a constant speed towards the Earth. This final, constant velocity is called terminal velocity. Source

Weight vs. Mass Mass and weight are often used interchangeably in everyday language. However, in science, these terms are distinctly different from one another. Mass is a measure of how much matter (how much "stuff") is in an object. Mass is typically measured in the kilograms. Weight, on the other hand, is a measure of the force of gravity acting on an object. Weight is equal to the mass of an object (m) multiplied by the acceleration due to gravity (g). On earth's surface gravitational field strength is a constant of 9.8 m/s2. Like any other force, weight is measured in terms of Newtons. Assuming the mass of an object is kept intact, it will remain the same, regardless of its location. However, because weight depends on the acceleration due to gravity, the weight of an object can change when the object enters into a region with stronger or weaker gravity. For example, the acceleration due to gravity on the Moon is 1/6 that of the gravity on Earth. If you measured your weight on Earth and then measured your weight on the Moon, you would find that you "weigh" much less, even though you do not look any skinnier. This is because the force of gravity is weaker on the Moon. In other words, a 180-pound man would only weigh 30 pounds on the Moon. In fact, when people say that they are "losing weight," they really mean that they are losing "mass" (which in turn causes them to weigh less).

Forces Quiz At this time you are ready to take the Forces Quiz. Be sure you review the pages in this lesson to ensure you know the material before taking the quiz.

Newton's Laws of Motion Issac Newton's (1642-1727) laws of motion were just one part of the monumental work that has made him legendary. The development of Newton's laws marks the transition from the Renaissance into the modern era. This transition was characterized by a revolutionary change in the way people thought about the physical universe. For many centuries natural philosophers had debated the nature of the universe based largely on certain rules of logic with great weight given to the thoughts of earlier classical philosophers such as Aristotle (384-322 BC). Among the many great thinkers who contributed to this change were Newton and Galileo. In this lesson, we will explore each of Newton's three laws of motion. To begin, watch the following video which will highlight each of Newton's three laws of motion. Be sure to use the Guided Video Notes in the sidebar to assist you in taking notes while watching the video. Used by permission

Newton's 1st Law of Motion To introduce the concepts of Newton's 1st Law, watch the following video created by the European Space Agency. By watching the video you will learn what Newton's 1st Law states as well as see many examples of Newton's 1st Law in action. Used by permission Newton's 1st Law of Motion states that an object at rest will stay at rest unless it is acted upon by an unbalanced force. An object in motion will continue to move in the same direction and with the same speed unless acted upon by an unbalanced force. This law is often referred to as the Law of Inertia. Inertia is that tendency of an object to either stay at rest or to stay in motion. You have experienced Newton's 1st Law many times in your lifetime. A good example is why we wear seat belts. What happens when you are driving down the road and then you have to slam on the breaks? Your body lurches forward. Why is this? It's because of inertia. Your body is in motion within the car in motion. When the brakes (an unbalanced force) are applied to the car, the car stops but your body wants to stay in motion. You need something applied to your body to stop the motion just as the brakes stop the car. Seatbelts safely provide an outside force that can stop or slow down your body when the car stops or slows down. For more explanation and application examples of Newton's 1st Law, view the following interactive activity. Source

Newton's 2nd Law of Motion We are now ready to look at Newton's 2nd Law. Let's begin by watching the following video created by the European Space Agency. Used by permission Newton's 2nd Law of Motion mathematically states the cause and effect relationship between force and acceleration. It states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. In other words, this equation tells us that an object subjected to an external force will accelerate and that the amount of the acceleration is proportional to the size of the force. The greater the force, the greater the acceleration will be. The amount of acceleration is also inversely proportional to the mass of the object; for equal forces, a heavier object will experience less acceleration than a lighter object.

You have seen this law in effect since you were a baby. To exemplify this law, let's think about a grocery cart. With the same amount of stuff (mass) in your cart, if you push your cart with a large force then the cart will have a large acceleration. However, if you push your cart with a small force then the cart will have a small acceleration. Continuing, if we change the mass but use the same force then we will also see an effect on the acceleration. If you have an empty cart and apply a force then it will accelerate much quicker than if you have a totally full cart applying the same force.

Newton's 2nd Law Equation:

Fnet = m * a You will be required to find all of the variables given in the equation. If you would like help rearranging the equation, then use the given triangle below.

Let's look at a couple example problems: How much force is needed to accelerate a truck with a mass of 2,000 kilograms at a rate of 3m/sec2? Looking For:

Solution:

Force

F net = m * a

Given:



Mass = 2,000 kg

F net = 2000 kg * 3 m/s2

Acceleration = 3 m/s2



Equation:

F = 6,000 N

F net = m * a

What is the mass of an object that requires 15 N to accelerate it at a rate of 1.5 m/sec2? Looking For:

Solution:

Mass



Given: m =

Force = 15 N



Acceleration = 1.5 m/s2 Equation:

m =

=10 kg

m = 10 kg

Problem 1

Problem 2:

Problem 3:

Problem 4:

Problem 5:

Problem 6:



Newton's 3rd Law of Motion We have made it to the last law of Newton's three laws of motion, Newton's 3rd Law. Newton's 3rd Law states that for every action there is an opposite and equal reaction. It is important to note that this is not a cause/effect type relationship. This is looking at whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts. You have experienced this whenever you have stubbed your toe or thrown a ball. To demonstrate and explain Newton's 3rd Law, please watch the following video created by the European Space Agency. Used by permission As you have learned from the video above, this law shows that forces always occur in pairs, and one body cannot exert a force on another without experiencing a force itself. We sometimes refer to this law loosely as "action-reaction," where the force exerted is the action and the force experienced as a consequence is the reaction. Examples:



A World Without Force Discussion We have talked a lot about forces in this unit (gravity, friction, applied, support, air resistance, etc). Imagine a world in which there are no external forces to stop motion. Think about what life might be like under such circumstances. Write a short story describing this world, and a particular event that takes place in that setting. Describe any problems that arise. Use your imagination! Your story must be at least 10 sentences. Ask them clarifying questions related to their story; were there any loop holes in their story, etc.

Newton's Laws Assignment Choose one of the following assignments to complete: Newton's Laws of Motion Lab You will be conducting 4 activities to demonstrate Newton's three laws of motions. You will need coins, a toy car, a cup, ruler/meterstick, and notecard or playing card to complete these activities. Look at the full directions given in the document in the sidebar. Newton's Laws Illustration You will create a cartoon or animation illustrating each of Newton's Three Laws. You can draw the cartoon by hand, ensuring that it is neat and legible. You can upload pictures of your work. You can also create a cartoon or animation using various websites given. Look at the full directions given in the document in the sidebar.

Work What Does it Mean to Do Work? The teens in the picture on the left are having fun playing basketball. The teen in the picture on the right is working hard studying for an exam. It's obvious who is doing work—or is it? Would it surprise you to learn that the teens who are working are the ones who are having fun playing basketball, while the teen who is studying isn't doing any work at all?

The scientific definition of work differs from its everyday meaning. Certain things we think of as hard work, such as writing an exam or carrying a heavy load on level ground, are not work as defined by a scientist. The scientific definition of work looks at the force exerted on an object and the distance the object moves. Specifically, in order to do work the force applied to an object must be in the same direction as the movement of the object and the object must move a certain distance. Therefore, if the object does not move then no matter how much force is exerted; no work has been done. Also, if a force is exerted perpendicular to the movement of the object, then no work has been done either. The teens who are playing basketball in the picture above are using force to move their bodies and the basketball, so they are doing work. The teen who is studying isn't moving anything, so she isn't doing work. Let's look at two more examples below, of work versus not work. Work

Not Work

Calculating Work We can mathematically solve to see how much work has been done. The equation for work is as follows: W = F * d From the equation of work, we see that the units used are for force and distance. Thus, in SI units, work is measured in newton-meters. A newton-meter is given the special name joule (J). This equation shows that the greater the force that is used to move an object or the farther the object is moved, the more work that is done. You will be required to find all of the variables given in the equation. If you would like help rearranging the equation, then use the given triangle below.

Let's look at a couple example problems: How much work is done on a 10-newton block that is lifted 5 meters off the ground by a pulley? Looking For:

Solution:

Work

W = F * d

Given:



Force = 10 N

W = 10 N * 5 m

Distance = 5 m



Equation:

W = 50 J

W = F * d

You did 150 joules of work lifting a 120-newton backpack. How far did you lift the backpack? Looking For:

Solution:

Distance



Given: d =

Work = 150 J



Force = 120 N Equation:

d =

= 1.25 m

d = 1.25 m Complete the practice problems below: Problem 1:

Problem 2:

Problem 3:

Problem 4:

Problem 5:

Problem 6:



Mechanical Advantage Simple machines are devices used to help make work easier or get done faster. How do machines help us perform work? Simple machines help to multiply our effort force or help to change the direction in which we apply the force. You should be familiar with the six types of simple machines as seen below learned in earlier science courses throughout your life. If you need to familiarize yourself with them again, use the extra resources in the side bar.

To introduce this concept of mechanical advantage, please watch the following video. Used by permission As you saw in the video, mechanical advantage is a numerical value that indicates how beneficial it is for you to use the machine. In other words, mechanical advantage provides the ratio of resistance to effort force magnitudes for any simple machine. The higher the mechanical advantage means the more the machine multiples the effort force. If the mechanical advantage is less than one it means that you are having to exert more force than if you were not to use the machine, but you have to exert the force over less distance. It is also important to realize that the total amount of work is the same regardless of if you use the simple machine or not. For a machine to do work, an effort force must be applied over a distance. If you exert less force, then you will have to apply that less force over a greater distance. Thus, it might seem "easier" as you are exerting less effort force but you are having to go over a greater distance. Let's look at an example to help explain this concept. In the picture below, you will see two men loading barrels onto a platform. One man is using an inclined plane while the other man is lifting straight up onto the platform. Both men are doing the same amount of work. One man is using less force over a greater distance while the other man is using more force over a smaller distance.



Whether or not you realize it, you utilize mechanical advantage on a daily basis. Maybe the lid of a pickle jar is tightly shut, so you use a flat-edged screwdriver as a lever to pry it open. Maybe one of your grandparents uses a wheelchair, so instead of taking the stairs up to the shopping center, you wheel him or her up the wheelchair ramp. Mechanical advantage means putting a smaller force into a simple machine to output a larger one. It certainly makes our lives easier, but it actually gives us a little less extra output than we would expect. This is because factors such as friction and machine wear over time and cause a loss of energy. Actual mechanical advantage takes these factors into account, while ideal mechanical advantage does not.

Calculating Mechanical Advantage In order to understand how to mathematically calculate mechanical advantage, there are a couple of terms that are important to know. The force applied to a simple machine is called the effort force, Fe. It can also be called input force, but for this course we will focus on calling it the effort force. The force exerted by the machine is called the resistance force, Fr. The resistance force is the load or the weight of the object being moved. Resistance force can also be called the output force. The distance in which the effort force is applied over is called the effort distance, de. The distance in which the resistance of the object moves is called the resistance distance, dr. The mechanical advantage is determined by using one of two equations:

Did you notice that the force unit involved in the calculation, the newton (N) is present in both the numerator and the denominator of the fraction and the distance units in the other equation are present in both the numerator and the denominator? These units cancel each other, leaving the value for mechanical advantage unitless. It is important that you be able to identify the effort force, resistance force, effort distance, and resistance distance on various types of simple machines. Please look at the pictures below to see where each variable is labeled on the simple machine.

Lever

1st and 2nd class levers help to multiple the effort force, but 3rd class levers are used to multiply the distance. Therefore, 3rd class levers will give a mechanical advantage that is less than 1. A mechanical advantage less than one doesn't mean a machine isn't useful. It just means that instead of multiplying force, the machine multiplies distance. For example, a broom is a 3rd class lever. A broom doesn't push the dust with as much force as you use to push the broom, but a small movement of your arm pushes the dust a large distance.

Inclined Plane



Pulley The mechanical advantage of a moveable pulley is equal to the number of ropes that support the moveable pulley. When calculating the mechanical advantage of a moveable pulley, count each end of the rope as a separate rope. You can also use the IMA and AMA equations to calculate the mechanical advantage, but using the number of support ropes is a shortcut.

Click on Quiz Group below to complete the activity.

Source Let's look at a couple of example problems: You need to push a grand piano with the weight of 4900 N onto a stage that is 3 m above the ground. If you can only apply a maximum force of 1000 N, what is the mechanical advantage? What is the minimum distance from the stage that you should begin building your ramp? Looking For:

Solution:

Mechanical Advantage

Step 1:

Effort Distance MA =

Given:



MA = F e = 1000 N

MA = 4.9

F r = 4900 N



dr = 3 m

Step 2:

Equation:

MA =





Actual Mechanical Advantage=

(AMA)

4.9 =

Ideal Mechanical Advantage=

(IMA)

= 4. 9 x 3 m = 14. 7 m

For a broom, your upper hand is the fulcrum and your lower hand provides the effort force. Given the picture below, calculate the mechanical advantage of using the broom. Looking For:

Solution:

Mechanical Advantage



Given:



MA = MA = MA = 0.25

dr = 1.2 m de = 0.3 m Equation:

Actual Mechanical Advantage =

Ideal Mechanical Advantage =

(AMA)

(IMA)

A block-and-tackle pulley is used to lift an object weighing 2000 N using an effort force of 500 N. Determine the mechanical advantage of the pulley. Looking For:

Solution:

Mechanical Advantage



Given:



MA = MA = F r = 2000 N



F e= 500 N

MA = 4

Short Cut: The number of support ropes = 4 Equation:

Actual Mechanical Advantage =

Ideal Mechanical Advantage =

(AMA)

(IMA)

Suppose you need to remove a nail from a board by using a claw hammer. What is the input distance for a claw hammer if the resistance distance is 2.0 cm and the mechanical advantage is 5.5? Looking For:

Solution:

Effort Distance Given:

MA =

MA = 5.5



dr = 2.0 cm

5.5 =

Equation:





5.5 x 2.0 cm = Actual Mechanical Advantage =

Ideal Mechanical Advantage =

(AMA)

(IMA)

= 11 cm

Complete the practice problems below: Problem 1:

Problem 2:

Problem 3:

Problem 4:

Problem 5:

Problem 6:



Mechanical Advantage Assignment Check Quiz At this time you are ready to take the Mechanical Advantage Assignment Quiz. Be sure you review the pages in this lesson to ensure you know the material before taking the quiz.

Module Wrap Up Module Checklist Velocity and Acceleration Assignment Check Quiz Motion Lab or Motion Cartoon Forces Quiz A World without Force Discussion Newton's Laws Lab or Newton's Laws Illustration Mechanical Advantage Assignment Check Quiz Forces and Motion Module Test

Review In this module you have performed a lot of math calculations to demonstrate motion and how motion is related to force, mass, and distance moved. You have applied Newton's three laws to everyday situations by explaining inertia, F= m* a, and equal and opposite forces. You have learned that mass and weight are not interchangeable terms but have distinct meanings. Lastly, you saw that a quantity could be assigned to show how beneficial using a machine could be to a person. To help you review for the Forces and Motion Module test, you should review your notes taken from every lesson. Be sure to be familiar with each vocabulary term and apply the definition to real world situations. Also, remember that you can use the Physical Science Formula Sheet on your test. Any equation not provided on the formula sheet must be memorized. You should also be sure that you know the SI units associated with each variable covered in this module. Complete the three matching activities below.



Final Assessment Forces and Motion Module Test It is now time to complete the Forces and Motion Test. Once you have completed all self-assessments, assignments, and the review items and feel confident in your understanding of this material, you may begin.

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