Force Main Page

Force notes.

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 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 measurementMass 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 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)(m1)(m2)/r2 

where G is the universal gravitational constant, m1 and m2 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-m2/kg2

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.


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 = Fg = GMEm/r2 

where 'Fg' = gravitational force, 'G' is the universal gravitational constant, 'ME' 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.


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 'μs'.

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 'μk'.

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 fs = μs

where  fs = force of static friction,  μs 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 fk = μk

where  fk = force of static friction,  μk 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.