Newtons Law's, Forces & Free Body Diagrams

Overall Expectations
By the end of this course, students will:

describe and apply concepts related to forces, Newton�s laws of motion,
work with free body diagrams in one and two dimensions,
determine the acceleration of an object when a balance or unbalanced force is applied to an object,
work with the equation F = ma, both as a scalar or vector

Forces in General

When we say that there is a force on an object we mean that there is a push or a pull on the object. Some outside agent is placing this push or pull on the object.

In the metric system forces are measured in units of Newtons. This unit is named after Isaac Newton. In the English system forces are measured in units of pounds. A Newton of force is much smaller than a pound of force. It takes about 4.5 Newtons to equal a force of one pound. So, if you usually state your weight in pounds, then you could figure your weight in the Newtons by multiplying those pounds by 4.5.

Forces are vectors. That is, they are quantities that have both size and direction. Forces can be symbolized with arrows, as can all vectors. The arrow in the picture below is meant to show a force with the size of 15 Newtons directed toward the left.

One must understand vectors to understand forces.

Why is "Net Force" Important?

"Net force" is a central idea of dynamics. Here's why:

Newton's Laws are the big deal in dynamics. Newton's First Law can be stated:

If the net force on an object is zero, its acceleration will be zero.

You will soon find out that Newton's Second Law says:

where F_net means "net force".

In order to use Newton's Laws, the first thing you need to know is "What is the net force".

Finding the Net Force:

In Physics 1, you will need to be able to calculate the net force on an object in the five situations shown below.

If no forces act on an object, the net force on the object is zero.

Although this happens in physics problems, it is very unlikely in practice that an object will have no forces at all acting on it.

If there is just one force on an object, then that force is the net force. In the diagram at left, the net force is 5 Newtons to the right.

For example in free fall, the net force on an object equals its weight - the one force pulling on it.

If 2 forces push or pull on an object in opposite directions, and the two forces cancel each other exactly, the net force is zero.

If two forces act on an object in opposite directions and they don't exactly cancel, what is left over is the net force (the difference in the forces).

In the diagram at left, the net force is 2 Newtons to the right.

If two(or more) forces act on an object in the same direction, the net force is the sum of the forces.

In the diagram at left, the net force is 10 Newtons to the right.

Two additional notes may be viewed at

1.Mechanics & Forces; Working with Net Forces Click here to view

2. Vectors in 4 parts; Introduction, Finding Components, Visualizing Components, & Component Method for Adding Vectors Click here to view

Newton's First Law of Motion

Inertia is defined as that property of matter that resists changes to its state of motion or when it is at rest. Inertia is a resistance to a change in motion, whereas friction is a resistance to that motion. Remember a body at rest will stay at rest, a body in motion will stay in motion, unless acted upon by some external force. This is not extremely obvious on Earth because all motion is subject to some from of friction which is an external force an will act in opposition to any appllied force or motion. The above statment is essentially Newton's First Law of Motion.

A force is either a push or a pull.
There are two categories of forces: contact or at-a-distance. At-a-distance forces are defined as fields. Gravity, magnetic and electric fields are forces that act at a distance.

Newton's Second Law of Motion

When a force acts on an object, this object will accelerate in the direction of the applied force. As long as the force is applied the object will accelerate. A bullet fired from a rifle will accelerate down the barrel of the rifle. Once it leaves the barrel, the applied force of the chemical explosion is not longer present and the bullet will now gradually slow down due to air resistance. Actually the bullet will either strike some object or fall to the ground long before air resistance will stop its motion. Gravity will act on the bullets vertical motion but will not effect its horizontal motion.
The mass of an object is also part of the equation. Throw a baseball then try to throw a bowling ball. Which can you throw farther? The applied force which cames from you arm muscles is the same in both cases. The baseball will achieve a greater acceleration and travel further. The only difference if the mass of each ball.
Newton's Second Law is stated on page 108 of the text, and so is the equation theat relates the three variables; mass, acceleration, and force. F = ma. Remember that F is actually the net force acting on the object.
Another example of this concept is the difference between mass and weight.

Gravity, Mass & Weight

Gravity: is the force of attaction exerted by the Earth of all matter on or near the Earth.
It is an action-at-a-distance force. Units are Newtons
Mass: is the amount of material that makes up or is that particular object of material. The units are kilograms (kg), the SI unit. Remember to switch grams to kilograms (x1000> when converting to Newtons, a force.
Weight: is the force of gravity acting on a particular object or mass. Units are Newtons. A misused term in the laymans world.

To convert mass into weight multiply the mass (in kg) by the acceleration due gravity (9.8 m/s²).
Example: What is the weight of a 6.7 kg bowling ball?
Answer: 6.70 kg X 9.8 m/s² = 65.66 or 65.7 N

The Law itself is simple and straight forward to use. Additions to a problem include

determining the net force acting on the object
resolving a force in the horizontal and vertical directions
when masses and forces are know, these can now be used with the seven equations of motion to determine velocity and distance of an object

How to solve Math Problems will be dealt with in class.
Emphasis is on Newton's Second Law: F = ma

Newton's Third Law of Motion

Forces always occur in pairs. The action force and the reaction force. Whenever one object exerts a force on another or second object, the second object exerts a force on the first object will an equal magnitude but in the opposite direction. So who wins this apparent pushing contest? Lets look at a couple of examples.

Take a slap shot with a hockey stick; what moves?
With skates on stand at the boards and push on them; what moves?
A rocket engine is ignited and rapidly expanding gases are thrust out the nozzle; both the gaes and rocket move, but in opposite directions
While sitting in a canoe, you paddle. The paddle pushes backwards and the canoe move forward; equal forces but opposite direction

You should be able to answer "what moves" but can you explain why and what commonality exist between each answer?
Newton's Third Law is stated on page 116 of the text.

First we must look at what is called a Free Body Diagram representing all the forces acting on an object. Please note that all forces are vectors. This will be dealt with accordingly.

Vectors will be discussed as a class activity. You need a ruler and a protractor.
You will be shown how to add vectors together so that you can complete and solve free body diagrams.

An object, either in motion or at rest on a horizonatal plane has four forces acting on it.

F_g is the force of gravity acting on the object in a downward direction.
F_m is the force of motion acting on this object and causing it to move with a given velocity in the same direction as the force. The object may or may not be accelerating.
F_f is the force of friction acting between the object and the surface it is resting on. This force is always opposite to the force of motion but can never cause the object to move in a backwards direction even though it may have a value that can exceed F_m.
F_n is the so called normal force. This is the force of the plane or surface acting upward on the block and if the object is not moving in the vertical plane, will equal the force of gravity of F_g. The normal force is always perpendicular to the surface. If the surface is horizontal F_n will equal F_g. If the surface is tilted then F_n will not equal F_g and always be less than F_g.

In this diagram the force of gravity F_g will not cause any horizontal motion.
The only applied force in this diagram is F_m. This would be the force that will produce motion in the object. F_f will oppose this motion and will cause the object to come to a stop once the applied force is removed.

Situations relating these four forces:

If F_g = F_n the object will niether move up or down.
If F_g > F_n the object will fall downward. Such an example would occur if placed your book on a piece of paper .
If F_g < F_n cannot occur because F_n is a reaction force and can never be greater than F_g Note, however, that if F_g is increased F_n will also increase.
If F_m = F_f the object will either be at rest or moving at a constant velocity. Note: at rest means the v = 0.0 m/s. In both cases there will be no acceleration.
If F_m > F_f the object will be accelerating in the direction of this force. When this situation occurs the horizontal force are considered to be unbalanced and the object moves in the direction of the greater force.
If F_m < F_f the object will definitely be at rest or slowing down if the object was origonal in motion. F_f will be studied on its own under the concepts of coefficient of friction.

For more information on Force, Newton's Laws of Motion, Friction, and Mass & Weight then just Click Here

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For a set of homework questions. This is a hand in homework assignment Physics Problems for College Bound Students
Click the Leaf for assignment

Due date is September 7 2008 or Feburary 6 2009
The homework section is divided into colour sections (blue, green,& pink). If you need addition help come at 8:00.
A short list of definitions and a formula page may be found at

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	If no forces act on an object, the net force on the object is zero. Although this happens in physics problems, it is very unlikely in practice that an object will have no forces at all acting on it.
	If there is just one force on an object, then that force is the net force. In the diagram at left, the net force is 5 Newtons to the right. For example in free fall, the net force on an object equals its weight - the one force pulling on it.
	If 2 forces push or pull on an object in opposite directions, and the two forces cancel each other exactly, the net force is zero.
	If two forces act on an object in opposite directions and they don't exactly cancel, what is left over is the net force (the difference in the forces). In the diagram at left, the net force is 2 Newtons to the right.
	If two(or more) forces act on an object in the same direction, the net force is the sum of the forces. In the diagram at left, the net force is 10 Newtons to the right.