## A Brief History: Sir Isaac Newton Edit

**Born:** December 25, 1642 in Lincolnshire, England

**Died:** March 31, 1727 in Kensington, London

**Sir Isaac Newton** was one of the greatest and most influential English mathematicians and scientists of his time. He laid the foundation for differential and integral calculus. His work on optics and gravitation made him one of the greatest scientists in the world. Furthermore, his three laws of motion helped advance the study of physics to what we know today.

## Introduction: Isaac Newton's Second Law of Motion Edit

In order to understand Isaac Newton's Second Law of Motion, you must know the basic principles of **Force**. Once the fundamental rules have been established, you will be able to grasp his Second Law of Motion. Force is defined as a push or a pull in a given direction. Since a force has both magnitude (the "strength" of the force) and direction, it is a vector quantity. The SI unit for force is represented by the letter **F**.

### Measuring Forces Using a!Edit

You may wonder-how do you measure a force? This can be answered quite simply: by using Hooke's Law. We can measure the magnitude of a force by recognizing that an applied force will stretch or compress a spring.

Knowing that this was true, an English scientist named Robert Hooke was able to show that the magnitude of a force (**F**) is directly proportional to the stretch or compression of a spring (**x**) within certain limits. Hooke's Law is defined by:

1) **x** - strech or compression of a spring

2) **k** - the spring constant

**F = kx**

Under the SI system of measurement, **x** is measured in meters (**m**) and **F** is measured in Newton’s (**N**). One Newton is equal to about 1/4 pound of force or **One Newton** = **1kg** x **m/s^2**. The constant of proportionality, **k**, is known as the spring constant. Its unit is the Newton per meter (**N/m**), and it is related to the spring stiffness; the greater the constant, the stiffer the spring.

### General Idea of Newton's Second LawEdit

Newton's Second Law of Motion can be stated as follows:

The acceleration of an object 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.

In terms of an equation, the net force is equated to the product of the mass multiplied by the acceleration.

**F**(**net**) = **m** x **a**

The above equation can be interpreted as:

**N** = **kg** x **m/s^2** = (**kg x m**)/**s^2**

## The Concept of the *Law of Nature* Edit

We know that Newton's First Law of Motion predicts the behavior of objects for which all existing forces are balanced. The first law states that if the forces acting upon an object are balanced, then the acceleration of that object will be:

**0 m/s^2** or **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 by changing either its speed, its direction, or both.

With this knowledge, we can thus explore Newton's Second Law or the "Law of Nature". Newton's second law pertains to the behavior of objects for which all existing forces are not balanced. It states that the acceleration of an object is dependent upon two the net force acting upon the object and the mass of the object.

The acceleration of an object (or the rate at which an object changes its velocity) depends directly upon the net force (also defined as the unbalanced force: **F**(**net**)) acting upon the object, and inversely upon the mass of the object. Therefore, the acceleration is directly proportional to the net force. 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.

### A Helpful Way to Remember **F**(**net**) = **m** x **a**Edit

**F**(**net**) = (k) **m** x **a** is a great example of how a variation in one quantity might effect another quantity. Whatever *change* is made of the net force, the same *change* will occur with the acceleration. For instance if the net force doubles, triples or quadruples, the acceleration will do the same. Likewise, whatever *change* is made of the mass, the opposite or inverse *change* will occur with the acceleration. If you double, triple or quadruple the mass, then the acceleration will be one-half, one-third or one-fourth its original value.

In conclusion, Newton's second law provides the explanation for the behavior of objects under unbalanced forces. The law states that unbalanced forces cause objects to accelerate with an acceleration which is directly proportional to the net force and inversely proportional to the mass.

## A Brief Summary Edit

Newton's second law of motion explains how an object will change velocity if it is pushed or pulled upon.

**1.** If you do place a force on an object, it will accelerate. For example if you change its velocity, then it will change its velocity in the direction of the force.

**2.** Acceleration is directly proportional to the force. For example, if you are pushing on an object, causing it to accelerate, and then you push the object twice as hard, the acceleration will be two times greater.

**3.** Acceleration is inversely proportional to the mass of the object. For example, if you are pushing equally on two objects, and one of the objects has five times more mass than the other, it will accelerate at one fifth the acceleration of the other.

Here's an animation to help you understand the *concept* of Isaac Newton's second law better:

## Normal Force, Frictional Force, and the Coefficient of Kinetic Friction Edit

*In physics, there are three types of forces: Normal Force, Frictional Force, and the Coefficient of Kinetic Friction.*

### Normal Force (N)Edit

**Normal Force (N):** When an object is at rest on a horizontal surface (a desk for instance), it has weight, but it is *not* accelerating. For this reason, the weight of the object is not an unbalanced force...it is zero! Thus, another force must be present on the object to balance the effects of gravity. Since this second force is perpendicular to both the object and the surface it is called a **normal force**. The equation is as follows:

**F**(**gravity**) = **m** x **g**

This is an example of the location of the force of gravity (pointing downward) and the normal force (pointing upward) on a flat surface while a person is sledding. It represents **F(g)** = **F(n)**

### Force of Friction (N)Edit

**Force of Friction F(f):** Consider the following situation: A 5.0 kg object is pulled across a floor with an applied force of 20. Newton’s. The acceleration of the object is measured to be 3.0 m/s^2. This situation is illustrated in the diagram below:

Something just doesn't seem right here: *F* doesn’t equal *m* times *a*! However, since we know from Newton's second law that *ma* has to equal the unbalanced force **F**(net). In this situation, **F(net)** is equal to 15 Newton’s (5.0 kg x 3.0 m/s^2), *not* to the applied force of 20. Newton’s. You may wonder where the 5.0 Newton’s went. There is another force present here called: friction. **Frictional forces** are always present when two surfaces come into contact with each other. The direction of a frictional force on an object is always *opposite* to the direction of the object's motion. The symbol for **frictional force** is **F(f)**. Now we can complete the diagram by adding in the 5.0 Newton frictional force:

The equation is as follows:

**F**(**net**) = **F**(**applied**) - **F**(**friction**)

### Coefficient of Kinetic Friction (μ)Edit

**Coefficient of Kinetic Friction (μ):** The coefficient of kinetic friction is one way of predicting how much friction will be produced on an object because of its contact with another surface. The frictional force of an object in motion is directly proportional to the normal force present on the object. that determines the amount of friction. This varies tremendously based on the surfaces in contact. There are no units for the coefficient of either static or kinetic friction, but the gravitational constant is **9.8 m/s^2**.

The equation is as follows:

**F**(**friction**) = **µ** x **F**(**normal**)

We can calculate µ by measuring the frictional force on an object and then dividing this value by the normal force present on the object.

Consider the following example: As illustrated in the diagram below, a 5.0 kg object slides across horizontal surface. If a 5.0 Newton frictional force is present, calculate the coefficient of kinetic friction between the two surfaces.

The first step to this problem is to calculate the weight of the object, as shown above, which is **49 N**. Since this surface is horizontal and the object is not falling downward, the weight is balanced by the normal force, which is also **49 N**.

We can calculate **μ** from the relationship **μ** = **(F(f))** / **(F(N))** = **5.0 N** / **49 N** = **0.10**

Just Remember: **μ** does not have units. Also, as **μ** increases, so does the frictional force on the object.

## Finding Acceleration Edit

By learning about calculating acceleration, we will know how to determine the acceleration if the magnitudes of all the individual forces are known. The three major equations which will be useful are: the equation for net force **F(net)** = **m** x **a**), the equation for gravitational force **F(g)** = **m** x **g**), and the equation for frictional force **F(f)** = **µ** x F(n).

In order to determine the acceleration of an object, you must know the mass and the net force of the object. If mass (**m**) and net force **F(net)** are known, then the acceleration is determined by:

**a** = (**F(net)**)/ **m**

Consider the following example: An applied force of 50 N is used to accelerate an object to the right across a frictional surface. The object encounters 10 N of friction. Use the diagram to determine the normal force, the net force, the mass, and the acceleration of the object. (Neglect air resistance.)

The first step to solve this problem is to solve for the mass by using the formula for the force of gravity **F(g)** = **m** x **g**. Since you know the force of gravity and the gravitational constant, you can therefore solve for the mass. Also, since there is no vertical acceleration, the normal force is equal to the gravity force. Then you add up all of the net forces to then find your acceleration.

We calculate acceleration by knowing:

**F(n)** = **F(g)** = **80 N**
**m** = **8 kg**
**F(net)** = **50N - 10N** = **40 N**

Getting to the Acceleration using all the information:
**a** = **F(net)** / **m** = **(40 N)** / **(8 kg)** = **5 m/s^2**.

## Practice Problems & Solutions Edit

All the questions are from [1]

Check Your Understanding of Newton's Second Law...

**1.** What acceleration will result when a 12-N net force applied to a 3-kg object? A 6-kg object?

**2.** A net force of 16 N causes a mass to accelerate at a rate of 5 m/s^2. Determine the mass.

**3.** An object is accelerating at 2 m/s^2. If the net force is tripled and the mass is doubled, then what is the new acceleration?

**4.** An object is accelerating at 2 m/s^2. If the net force is tripled and the mass is halved, then what is the new acceleration?

Here are the Answers...

**1.** A 3-kg object experiences an acceleration of **4 m/s^2**. A 6-kg object experiences an acceleration of **2 m/s^2**.

**2.** F(net) = (m)(a)
16 N = (m)(5 m/s^2)
**m** = **3.2 kg**

**3.** The original value of 2 m/s^2 must be multiplied by 3 (since a and F are directly proportional) and divided by 2 (since a and m are inversely proportional). Therefore it is **3 m/s^2**.

**4.** The original value of 2 m/s^2 must be multiplied by 3 (since a and F are directly proportional) and divided by 1/2 (since a and m are inversely proportional. Therefore it is **12 m/s^2**.

## References Edit

The links below were applied to during the creation of this Wiki page:

**1.** Barron's Regents Review Book

**2.** [2]

**3.** [3]

**4.** (http://www.usoe.k12.ut.us/curr/science/sciber00/8th/forces/sciber/newton2.htm]

**5.** [4]

**6.** Glencoe Physics: Principles and Problems

**7.** Notes from Mr. GK’s Physics class on Isaac Newton’s Three Laws of Motion

## ResourcesEdit

For more help on Newton's Second Law of Motion you can go to the following websites or buy certain books:

**1.** Barron's Regents Review Book. This specific Barron’s Regents Review Book is a great source to go to for multiple practice problems on Newton's three laws of motion and beyond. It is a great learning tool. I highly recommend this for physics in general.

**2.** www.glenbrook.k12.il.us This website is a useful tool for information on everything you would want to possibly know about physics. It has great practice problems. I highly recommend this website.

**3.** [5] This website gives you step by step factions of Newton's second law and it has great animations. I highly recommend this website.

**4.** [6] I personally really like this website because it gives you a great history of who Isaac Newton was and general information about the three laws and wonderful explanations!! But this is very general in relation to Newton's second law.

**5.** [7] This website is a great reference for the SAT II in physics. It gives you in-depth information without overwhelming you and plenty of practice for the SAT II or even physics in general.

**6.** Actual Physics Regents Test If you don't want to buy a book to study for physics...no worries! This website has real Regents Exam tests and solutions to help your understanding of physics. It is a great resource to use to sharpen your skills in physics as a whole. After all, you only get better if you practice, practice, practice.