# Newton's Second Law of Motion

Isaac Newton’s Second Law of Motion (F=ma) explains the relationship between force and acceleration in motion. The application of force on an object causes an acceleration of that object. Yet, force is not the only factor in the movement, or acceleration of an object. The two main influences on the acceleration of an object are net force and mass. For example, net force is directly proportional to acceleration while mass is inversely proportional to acceleration. In other words, net force- the force that has overcome friction and accelerates an object- is directly linked to acceleration; the more force you have, the faster an object goes.Other factors such as the friction, air or fluid resistance, and pressure effect the acceleration as well. All of these factors do not work against or in accordance with acceleration in the same way. Friction works in opposition to acceleration. Friction involves two objects that are in direct contact with on another but are moving in different directions. Involved with friction is air and fluid resistance. Fluid resistance, such as liquids or gases, focuses on when the object is moving in the opposite direction of a fluid flow or through a dense area of fluid. Air resistance involves movement through the air. The most noticeable effect of air resistance is when and object travels into a strong breeze or wind. And finally pressure, pressure refers to an applied force. With pressure you will find that the overall weight of and object doesn’t change no matter how you stand or lay it but you will fill more pressure from that same object depending on the force per surface area. The weight of the object has not changed but you that area of application the force feels greater. That is the pressure increase. In Newton’s Second Law, the areas such as free falling verse vacuum suction are also compared with the falling of objects. [4][7] [8] [9] [10]

## Vocabulary

1. Acceleration – the change in velocity per certain time interval; how quickly motion changes
2. Force – is the cause of acceleration; any influence that tends to accelerate an object
3. Net Force – the combination of all the forces that act on an object
4. Inversely – when two values change in opposite directions, so that if one is doubled the other is reduced to one half, they are said to be inversely proportional to each other
5. Friction – the force that acts to resist the relative motion (or attempted motion) of objects or materials that are in contact
6. Fluids – anything that flows; in particular, any liquid or gas
7. Air Resistance – friction, or drag, that acts on something moving through air
8. Free- Body Diagram – a diagram showing all the forces acting on an object
9. Pressure – force per square area where the force is normal to the surface; measured in pascals
10. Pascal – the SI unit of pressure. One pascal of pressure exerts a normal force of one Newton per square meter
11. Terminal Speed – the speed at which the acceleration of a falling object is zero because friction balances the weight
12. Terminal Velocity – terminal speed together with the direction of motion (down for fall objects)
13. Free Fall – motion under the influence of the gravitational force only
(Courtesy of Conceptual Physics by Prentice Hall, 2006. Boston Massachusetts.)

## Newton's First Law Leads to Newton's Second Law

Newton’s First Law of Motion is sometimes called the law of inertia. Newton’s First Law was a restatement of Galileo’s concepts of motion; however Galileo only explained how things move. Newton explained why things move. Newton’s First Law states can be broken into two statements.
"An object at rest will remain at rest until acted upon by a force".
"An object in motion will remain in motion in a straight line at a constant speed until acted upon by a force".
When a force acts upon an object in motion, the movement (speed and/or direction) of the object changes. The affect of a force on a moving object may cause the object to either increase its speed or decrease its speed. A change in motion is called acceleration.
When determining the force acting on an object under Newton’s First Law of Motion, the force evaluated is the net force. The net force is the result of all forces acting on an object. Under Newton’s First Law, when the net force is zero, an object in motion remains in motion. Similarly, when the net force is zero an object at rest remains at rest.
Under Newton’s First Law, a moving object’s inertia is related to speed of the object as caused by the net force acting upon it and the mass of the object. The greater the speed of a moving object, the more inertia it has. The mass of an object is the amount of material contained in an object. An object’s mass depends on the number and kinds of atoms contained in the object. The greater the mass of a moving object, the more inertia it has.
In his First Law, Newton explained the affect of a net force, greater than zero, upon an object at rest. In his Second Law, Newton explains the affect of a force upon a moving object and the relationship between acceleration, force, and the mass of an object. [7] [8]

## Acceleration and Force versus Mass

Newton’s Second Law explains that the acceleration of an object is effected by the net force applied to the object and the mass of the object.

What exactly is acceleration? Well, acceleration is simply the movement of an object.

Force is the cause of acceleration. Net force is measured in units called Newton. One or more forces may be applied to an object to make it move. The net effect of the forces acting on an object is called the net force. Net force also influences the direction of the acceleration. An object accelerates in the same direction as the net force acting on the object. The net force acting on an object is directly proportional to that object’s acceleration, which means the greater the net force, the greater the acceleration.

The mass of an object is also a key factor determining the effect of force upon an object. Mass is one of the obstacles that inhibits motion and acceleration. Mass is inversely related to acceleration, so if the force is constant then as the mass of an object increases acceleration decreases. Therefore, unlike force where if you double the force the resulting acceleration also doubles, if you double the mass of an object you will reduce the acceleration by half. This relationship between acceleration and mass can be written as: acceleration ~ 1/ mass.

It may be useful to your understanding of the relationship between force, mass and acceleration to be familiar with the formula:

Force equals mass times acceleration or F = ma.

You have applied this formula if you have ever pushed two people of different masses on the swings and noticed that if you pushed both people with the same force, the person with the lesser mass swung higher than the person of greater mass. The reason is the acceleration of an object being pushed is effected by the mass of the object itself. As a result, if the same force is applied to two objects, the object with the lesser mass will have a greater resulting acceleration than the object with the greater mass. [9] [10]

 Image courtesy of "How Stuff Works"

 Image courtesy of "How Stuff Works"

 Image courtesy of "How Stuff Works"

## Friction

Friction is a force that acts on materials that are in contact with one another to effect motion. The kind of materials in contact affects how much friction occurs. For example, friction is greater if you were to slide a hockey puck over sandpaper than if you slid the puck over glass. Friction, like mass, works to decrease the acceleration
 Image courtesy of "BYU Biomechanics"
of an object. Friction can be caused by contact with solids, fluids, or air.
Friction caused by solids acting against each other is the form of friction that the most people think of because it is the type of friction that is most commonly seen or noticed in our own daily lives. Yet, fluid friction and air resistance also play a big role in our lives. For example, many of our means of transportation are designed to reduce the amount of fluid friction and air resistance acting against them because friction slows down movement and opposes acceleration.
Fluid friction applies to objects moving through a body or current of liquid or gas. If you have ever tried to run through a body of water or against a water current, you should have noticed the effects of fluid friction. The friction caused by moving through water causes you to apply more energy, exert more force, to maintain your speed or motion. This is caused by the fluid friction acting against your motion. Air resistance, a kind of fluid friction, applies to objects moving through the air or against an air current. Air resistance is most commonly noticed when walking into the wind. Have you ever felt as though you were walking in place when you were trying to walk into a strong wind? The air resistance is working against the force applied by your legs opposing motion and reducing acceleration.
When friction forces become so great that they equally counter the applied force, the acceleration of the object is zero, meaning the object moves at constant speed despite the applied force. [4] [6] [20]

## Pressure

Pressure is a familiar concept to many people. If you carry a book in your hand, you could feel the pressure from the weight of the book on your hand. The force of gravity pulls the book and creates pressure you feel on your hand. No matter what position the book is held, it has the same weight or applied force. However, the book may feel heavier or lighter based on the area of the book in contact with your hand because the weight may be spread over a different area of contact. Meaning, if the contact area is smaller, the book would cause more pressure on that area of your hand, which many people would mistakenly say makes the book feel heavier. Pressure and force, however, aren’t the same thing, because pressure is quantity of force per contact area.

Pressure = force / area of application or P = F/A. Pressure is expressed as force per area ( Newtons per square meter), also called pascals.

So, if a person stood on his or her feet holding a chair the pressure on the ground would be the force caused by gravity (the weight of the person and the chair) divided by the area of your feet contacting the floor. If however, a person sat on a four-legged chair the pressure would be the force (weight of the person and the chair) divided by the area of the bottom of the chair legs on the ground. In the latter experiment, even though the force or weight has not increased, the pressure on the ground would probably increase because the area in contact with the ground is probably smaller. These experiments demonstrate that pressure is inversely related to area. That is, as area decreases,
 Image courtesy of "Pressure is Force per Unit Area"
pressure increases. However, if a heavier person (force caused by gravity) sat on the same chair, the pressure would increase because, if the contact area remains the same, the increase in force (weight) results in an increase in pressure. Consequently, the more force applied to the contact area, the more pressure and visa–versa. [5] [18]

## Free Fall

Newton’s Second Law changed the understanding of the affect of gravity on free falling objects. Free falling objects are dropped so that the only force acting upon the object is gravity. These experiments where perform so that little or no significant air resistance would affect the free falling objects. Aristotle believed that if 10 kg object and a 1 kg object were
 Multimedia courtesy of "The Physics Classroom"
dropped that the 10 kg object would fall ten times faster than the 1 kg object because it weighed ten times as much. Through experiments, the most famous included dropping objects off the Tower of Pisa, Galileo demonstrated that a 10 kg object and a 1 kg object dropped simultaneously from the same height would land simultaneously, or as nearly as observations were possible in his day. However, Galileo did not explain why.
 Image courtesy of"http://www.ltc.arizona.edu/images/services_graphics_illustration.jpg"

Newton’s Second Law explains Galileo’s observations. Newton’s Second law of Motion states that acceleration equals force over mass (a = F/m). As applied to the experiment, the force is gravity and the mass of the two objects are 10 kg and 1 kg, respectively. An object in free fall is being affected by only gravity. Gravity is a force that can be measured in Newtons (N). The gravitational pull on a 1 kg object is 9.8 N and the pull on a 10 kg object is 98 N, so Aristotle was correct that the force on a 10 kg object is ten times as much as a 1 kg object. However, Aristotle did not take into account that the mass of the 10 kg object was ten times greater. Newton’s Second Law addressed this fact by showing that acceleration is the result of force (gravity) divided by mass. The 10 kg object had ten times as much force acting on it but it also had ten times as much mass to move. Through Newton’s Second Law of Motion a = F/m, Newton explains Aristotle’s theory that gravity pulls ten times as much on a 10 kg free falling object as a 1 kg object and also Galileo’s observations that the fall at the same acceleration. [4] [7] [8]

## Falling and Air Resistance

 Image courtesy of "Motion and Force"

Objects falling in a vacuum always fall at the same rate. Objects falling through the air under normal conditions, or in the real world, often do not. The acceleration of a falling object (not in a vacuum) is affected by air resistance. As discussed earlier, air resistance is a kind of fluid friction which applies to objects moving through the air or against an air current. When an object falls through the air, there two main forces acting on the object. One in the direction of the fall (gravity) and one against gravity (air resistance) and the object’s acceleration. Air resistance reduces the net force applied to a falling object, since gravity is typically labeled the positive force and air resistance is the negative force acting on it. The amount of air resistance on a falling object is dependent to the shape
 Multimedia courtesy of "The Physics Classroom"
and weight of the object, and the density of the fluid or air.
When talking about density and fluid friction or air resistance, the density refers to the density of the fluid or air the object is moving through. For example, an object falling through air will have much less fluid resistance and will fall faster than one falling through water because water is denser. Hence, fluid resistance is actually a force of friction.
With regard to shape, the larger the surface area of an object opposed by the air resistance, the more air that must be pushed out of the way. So, larger falling objects have more air resistance opposing gravity which slows the object’s fall.
Lastly, the weight of the falling object affects the resistance and thus its acceleration. A falling object builds up air resistance as it falls which resistance offsets its weight. When the air resistance equals the object’s weight, the net force becomes zero, as does its acceleration. Consequently, the acceleration of the falling object stops and the object then falls at a constant speed, known as its terminal velocity.
If you were to compare the rate of fall of a feather and a coin in the natural world, you would find that the lighter feather with greater surface area falls much slower than the heavier coin with less surface area because the feather reaches terminal speed first and its acceleration terminates while the coin continues to accelerate and therefore lands first. [4] [7] [8]

## Newton's Second Law Leads to Newton's Third Law

In his First Law of Motion, Newton explained that objects at rest remain at rest until acted upon by a force. Accordingly, once acted upon by a force, an object will continue in motion in the same direction until acted upon by another force. In his Second Law of Motion, Newton continued with the moving object and explained that a force acting upon an object causes acceleration and acceleration is a change in motion. Under the Second Law, Newton explained why a force acting on a moving object causes acceleration and the interrelationship of the force with the object. He also showed that the force is directly proportional to the resulting acceleration and is inversely proportional to the objects mass. Finally in his Second Law of Motion, Newton provided a method for measuring acceleration, force and the mass of the object. In his Third Law, Newton turned to look at the interaction between the accelerating object, the force that affected it, and the objects the accelerating object affects. In his Second Law, Newton explained that when one object acts or applies force upon a second object what acceleration occurs to the second object. In his Third Law, Newton explained how the second object (accelerated object) affected the first object (the object applying force).
Newton’s Third Law of Motion is sometimes called the “law of action and reaction.” An action may be a push or a pull. Newton’s Third Law states that if one object applies a force on a second object then there is interaction between the objects. Newton refers to this interaction in terms of action and reaction. In his Third Law, Newton explains that the object that acts upon a second object is also acted upon by the second object. The action by the second object upon the first object is equal in force to the action of the first object. People commonly summarize Newton’s Third Law by saying for every action there is an equal and opposite reaction. Each objects actions or reaction can be analyzed using the formula: “a = F/m” from Newton’s Second Law. [4] [7] [8] [9]

## Isaac Newton - Biography

 Image courtesy of "Newton"

Famous mathematician and physicist, Isaac Newton was born Christmas Day, December 25, 1642, however after the present day calendar was changed in the 19th century his birth was refigured as January 4, 1643, the date that is now commonly used as his birth date. Isaac Newton was born approximately a year after the death of Galileo. Isaac Newton died March 20, 1727. To give a historical prospective, Newton lived during the times of the Salem Witch trials, the exploration by Marquette and Jolliet of the Mississippi River for France, the reign of King Louis XIV, and the days of Rembrandt, Bach and Handel.
In 1661, Isaac Newton attended before entering Cambridge University. In 1665 and 1666, Isaac Newton was forced to return home because the plague had infested London. During those years, he was away from Cambridge, Newton concentrated on mathematics and physics formulating his theories of optics, integral and differential calculus, and gravity. There is a famous story about Isaac Newton sitting in his garden and a falling apple. Although most writers do not believe the apple fell on his head, many report that the falling apple inspired Newton to explore why the apple fell.

In 1668, Newton invented, designed, and assembled the first reflective telescope, which gave a sharper image of distant planets and bodies. Many believe Newton’s greatest scientific contributions were to calculus, physics and celestials mechanics. Newton wrote Principia and explained the motion of projectiles, pendulums, free-falling objects and celestial bodies. Newton studied optics and discovered that white light was made up of many colored lights. He later wrote Opticks, in 1704, chronicling his discoveries thoughts and theories on light.

In his own time, Newton’s life was marred by and his inventions and discoveries challenged by critics such as including other prominent scientists and inventors. Arguments raged over Newton’s ideas and disputes persisted over credit for his theories.

In 1705, Isaac Newton was the first scientist to be knighted when Queen Anne honored him. Upon his death, in 1727, Sir Isaac Newton became the first scientist to be buried at Westminster Abbey. [1] [2] [11] [15] [16] [17]

## Extra Media for Understanding

For extra understanding, view this short video/ slideshow about Newton's Laws.

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# References

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1. Sir Isaac Newton - http://www.lucidcafe.com/library/95dec/newton.html
2. Chapter 3. Acceleration and Free Fall - http://www.lightandmatter.com/html_books/1np/ch03/ch03.html#Section3.1
3. Air Pressure - http://wright.nasa.gov/airplane/pressure.html
4. Physics Tutorial – Frictional Forces - http://www.staff.amu.edu.pl/~romangoc/M4-frictional-force.html
5. Newton’s 2nd Law Notes Overview - http://www.batesville.k12.in.us/physics/Phynet/Mechanics/Newton2/Newton2Intro.html
6. The Physics Classroom - http://www.physicsclassroom.com/class/1dkin/u1l5a.cfm
7. How Stuff Works? - http://science.howstuffworks.com/newton-law-of-motion3.htm
8. Newton’s Second Law Definitions - http://www.grc.nasa.gov/WWW/K-12/airplane/newton2.html
9. Motion and Force - http://library.thinkquest.org/12632/images/parachute.jpg
10. The Physics Classroom (Media) - http://www.physicsclassroom.com/mmedia/newtlaws/efar.gif
11. A Brief Biography of Isaac Newton - http://courses.science.fau.edu/~rjordan/bios/Newton/Newton_bio.htm
12. Sir Isaac Newton Biography - http://www.who2.com/ask/sirisaacnewton.html
13. Pressure is Force per Unit Area - http://www.school-for-champions.com/Science/pressure.htm
14. BYU Biomechanics - http://neon.byu.edu/~seeleym/exsc362(seeley)/images/runnerforce.gif
15. Conceptual Physics by Prentice Hall, 2006. Boston Massachusetts.