**Force Main Page**

**Forces in General**

Classical mechanics involves the study of the motion of objects and of the forces that act upon those objects.

The force acting on an object by gravity is considered to be the weight of the object. A force can cause an object to accelerate, deform, or gain heat.

When people think of forces, if they think of them, they usually consider a force to be a push or pull exerted upon something. When you kick a football your foot exerts a force on the football that distorts the football and may cause it to accelerate away from you.

**Types of Forces**

There are two main categories of force. They are contact forces and field forces. Contact forces involve pushing or pulling on an object, or hitting or throwing an object. Field forces include the force due to gravity and electromagnetic forces.

**Contact Forces**

Collisions between automobiles involves contact forces. Each automobile exerts a force on the other. Hitting a golf ball with a golf club involves contact forces. The club applies a force to the ball and the ball applies a force to the club. Pushing or pulling a lawnmower involves contact forces. Hammering a nail into a board involves contact forces.

The early scientist developed a fairly good understanding of the contact forces that they could study. They did not have a good understanding of field forces.

**Field Forces**

When you drop your plate of food while carrying it to the table, it will fall to the floor or to the ground where the plate will probably break and distribute your food all over the most expensive items nearby. It fell to the ground because of what we call gravity. There is no visible contact between gravity and the plate, however just because you cannot see the force does not mean that it is not there. This invisible force is a field force.

The force we call weight is caused by the gravitational attraction between our mass and the mass of Earth.

Michael Faraday is credited with the concept of a force field. He lived from 22 September 1791 until 25 August 1867.

**Types of Force Fields**

There are currently considered to be four force fields. They are listed below starting with the strongest force.

1) Strong nuclear force

2) Electromagnetic forces

3) Weak nuclear forces

4) Gravitational forces

**Mass**

**Mass** can be thought of as being a measure of the resistance to the effects of
a ** force** on the motion of the object.
**Mass** is usually measured in
** kilograms**
in the ** SI system of
measurement**. **Mass** is a
** scalar quantity**.
It is measured in slugs in the U. S. Customary system of measurement. The
U. S. Customary unit of pounds is not a unit of **mass**.
The common conversion that a **kilogram**
is about 2.2 pounds is valid only on **Earth**.

**Inertia**

**Inertia** is the tendency of an object to continue in its current state of
motion. Moving objects have inertia. Stationary objects have
inertia. Neither moving or stationary objects have a tendency to change
from their current state of motion.

**Newton's Laws of Motion**

There are three laws of motion that are known as Newton's laws of motion.
These laws involve **inertia**,
**mass**, **acceleration**,
and the fact that forces are like shoes since they occur in pairs.

**Newton's First Law of Motion **

Up until about 1600 A.D. most scientists thought that the natural state for
objects was for them to be at rest. ** Galileo** thought otherwise and created
experiments that led to the conclusion that once an object is in motion it tends
to stay in motion. **Sir
Isaac Newton** continued this study and got credit for coming
up with the law now known as Newton's first law of motion.

Simply stated this law tells us that an object in motion will remain in motion and an object at rest will remain at rest unless acted upon by an outside force.

When the net force exerted upon an object is **zero**,
the object continues in its original state of motion. If at rest it will
remain at rest. If in motion it will remain in motion.

**Newton's Second Law of Motion**

When a net force acts on an object the **acceleration**
of the object is **directly
proportional** to the force acting on it, and the **acceleration**
of the object is inversely proportional to the **mass**
of the object.

This is usually written as an equation.

∑F = ma

**Newton's Third Law of Motion**

**Units of Force**

Force is measured in a variety of units.

The SI unit of force is the newton which uses the symbol N.

The CGS system of force is the dyne witch used the symbol dyn

The English system of force is the pound witch uses the symbol lb or #.

Other units have been used but he units listed above are the most common.

**Gravitational Force**

**Newton's Law of Universal Gravitation**

The force of attraction between two objects is directly proportional to the product of the masses of the objects and inversely proportional to the square of the distance between the objects.

It is usually written as

F = (G)(m_{1})(m_{2})/r^{2}

where G is the **universal
gravitational constant**, m_{1} and m_{2} are the
respective masses involved, and r is the distance between the centers of the
masses.

**Universal Gravitational Constant**

The **universal
gravitational constant** is used in Newton's law of universal
gravitation. This constant has its own symbol, the upper case 'G'.
In 1797 English scientist **Henry
Cavendish** was the first to attempt a determination of the value of
'G'. His experiment consisted of two large and two small lead balls with
the two small balls on a rod. The rod was suspended and it turned as the
large balls were moved closer to the small balls. Since the value of 'G' is very
small, great care must be taken in its measurement. Outside forces may
have a large impact on the results.

G = 6.67 x 10-11 N-m^{2}/kg^{2}

There has been some suspicion that the value of the **universal
gravitational constant** may be changing at a very slow rate of
change. Estimates indicate a possible change of 1 part in 10 **billion**
per year. The estimates are that the value is decreasing. Since we
normally only use 'G' to 3 significant digits we can probably ignore this small
change for a few more million years.

**Weight**

The weight of an object is the magnitude of the force of gravity on the **mass**
of the object. The weight of an object can change depending upon the
location of the object but its mass will remain the same.

Weight is a force.

Weight and **mass**
are not the same even though they are often considered to be the same by the
ignorant.

The weight of an object is equal to its **mass**
times the **acceleration
due to gravity**. Weight is expressed in **newtons**
in the **SI
system of measurement**, and in pounds in the U. S. customary system.

This is shown by the equation

w = mg

where m is the ** mass** and g is the **acceleration
due to gravity**. If on another heavenly body the value of 'g' will
probably be different. The **acceleration
due to gravity on other heavenly bodies** has been determined for most of
our solar system.

Weight can also be calculated using the equation

w = F_{g} = GM_{E}m/r^{2}

where 'F_{g'} = **gravitational
force**, 'G' is the **universal
gravitational constant**, 'M_{E}' is the **mass
of Earth**, 'm' is the **mass**
of the object, and r is the distance between the centers of the objects.
For an object on the Earth's surface the ** distance** is considered to be Earth's **radius**.
When working with these equations pay close attention to the units of
measurement.

**Equilibrium **

An object that is at rest or moving at a constant velocity is considered to
be in a state of equilibrium. When an object is in equilibrium the sum of
the forces acting on the object is **zero**.

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**Friction Main Page**

**Friction Forces **

The forces of friction are very important to life on our planet. Friction can cause a resistance to motion and friction can also be an aid to motion. Friction occurs when an object is in contact with another object or when an object is moving through another substance. A football encounters friction from the air as it moves through the air. Since this friction opposes motion it will cause the football to slow down. Friction is the force that holds a nut onto a bolt. Friction between your feet and the ground allows you to walk. It is difficult to accelerate on ice because the force of friction is very low.

**Coefficients of Friction**

There are two ** coefficients of
friction**. They are the ** coefficient of
static friction** and the ** coefficient of kinetic
friction**.

The ** coefficients of friction** are **dimensionless**.

The coefficient of friction between one pair of surfaces will be different
from that between another pair of surfaces, depending upon the material that are
in contact. The **coefficients
of friction vary depending upon the material**.

**Coefficient of Static Friction **

The symbol used for the ** coefficient of
static friction** is 'μ_{s}'.

The ** coefficient of
static friction** is a measure of the resistance needed to
get the object to start moving. It is greater than the ** coefficient of kinetic
friction**. You should remember that objects at rest tend to remain at
rest so this tendency must be overcome to get an object into motion.

**Coefficient of Kinetic Friction**

The symbol used for the ** coefficient of kinetic
friction** is 'μ_{k}'.

The ** coefficient of kinetic
friction** is a measure of the resistance needed to
keep an object moving once it is moving. This is lower than the value of
the ** coefficient of
static friction**.

**Force of Static Friction**

The force of static friction between two surfaces is f_{s} = μ_{s}n

where
f_{s} = force of static friction, μ_{s}
is the
** coefficient of
static friction**, and n is the normal force that presses
the two surfaces together.

**Force of Kinetic Friction**

The force of kinetic friction between two surfaces is f_{k} = μ_{k}n

where
f_{k} = force of static friction, μ_{k}
is the
** coefficient of kinetic
friction**, and n is the normal force that presses
the two surfaces together.

**Terminal Speed or Velocity**

When an object is falling through the air it encounters friction caused by
the effects of the air on the object. As long as the force of friction on
the object is less than the force due to gravity, the object will undergo **acceleration**.
The force of friction will increase as the object accelerates until the force of
friction is the same as the force causing it to accelerate in the downward
direction. Once the two forces are equal, but in opposite directions, the
acceleration will cease because the net force acting on the object is now **zero**.
With no net force there can be no additional acceleration so the maximum
velocity has been reached. This maximum velocity is called the terminal
velocity. If you fall out of an airplane with no parachute you will
probably hit the ground at a speed of less than 150 miles per hour since by that
time you will have reached the terminal velocity.

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