Frictional resistance to the relative motion of two solid objects is usually proportional to the force which presses the surfaces together as well as the roughness of the surfaces. Since it is the force perpendicular or "normal" to the surfaces which affects the frictional resistance, this force is typically called the "normal force" and designated by N. The frictional resistance force may then be written:
Ffriction =m N
m = coefficient of frictionmk = coefficient of kinetic frictionms = coefficient of static friction
The frictional force is also presumed to be proportional to the coefficient of friction. However, the amount of force required to move an object starting from rest is usually greater than the force required to keep it moving at constant velocity once it is started. Therefore two coefficients of friction are sometimes quoted for a given pair of surfaces - a coefficient of static friction and a coefficent of kinetic friction.
Frictional resistance forces are typically proportional to the force which presses the surfaces together. This force which will affect frictional resistance is the component of applied force which acts perpendicular or "normal" to the surfaces which are in contact and is typically referred to as the normal force. In many common situations, the normal force is just the weight of the object which is sitting on some surface, but if an object is on an incline or has components of applied force perpendicular to the surface, then it is not equal to the weight.
Friction and Surface Roughness
In general, the coefficients of friction for static and kinetic friction are different.
Coefficients of Friction
Friction is typically characterized by a coefficient of friction which is the ratio of the frictional resistance force to the normal force which presses the surfaces together. In this case the normal force is the weight of the block. Typically there is a significant difference between the coefficients of static friction and kinetic friction.
Static frictional forces from the interlocking of the irregularities of two surfaces will increase to prevent any relative motion up until some limit where motion occurs. It is that threshold of motion which is characterized by the coefficient of static friction. The coefficient of static friction is typically larger than the coefficient of kinetic friction.
The difference between static and kinetic coefficients obtained in simple experiments like wooden blocks sliding on wooden inclines roughly follows the model depicted in the friction plot from which the illustration above is taken
This difference may arise from irregularities, surface contaminants, etc. which defy precise description
When two surfaces are moving with respect to one another, the frictional resistance is almost constant over a wide range of low speeds, and in the standard model of friction the frictional force is described by the relationship below. The coefficient is typically less than the coefficient of static friction, reflecting the common experience that it is easier to keep something in motion across a horizontal surface than to start it in motion from rest.
Static friction resistance will match the applied force up until the threshold of motion. Then the kinetic frictional resistance stays about constant. This plot illustrates the standard model of friction.
The experimental procedure described below equates the vector component of the weight down the incline to the coefficient of friction times the normal force produced by the weight on the incline.
The Accomplishments of Newton
We shall concentrate on three developments
1) Newton's Three Laws of Motion
2) The Theory of Universal Gravitation
Newton's First Law of Motion:
I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
This we recognize as essentially Galileo's concept of inertia, and this is often termed simply the "Law of Inertia".
Newton's Second Law of Motion:
II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.
Newton's Third Law of Motion:
III. For every action there is an equal and opposite reaction.
What Really Happened with the Apple?
The apple is accelerated, since its velocity changes from zero as it is hanging on the tree and moves toward the ground. Thus, by Newton's 2nd Law there must be a force that acts on the apple to cause this acceleration. Let's call this force "gravity",
Sir Isaac's Most Excellent Idea
Now came Newton's truly brilliant insight: if the force of gravity reaches to the top of the highest tree, might it not reach even further; in particular, might it not reach all the way to the orbit of the Moon!
If we increase the muzzle velocity of an imaginary cannon, the projectile will travel further and further before returning to earth. Newton reasoned that if the cannon projected the cannon ball with exactly the right velocity, the projectile would travel completely around the Earth, always falling in the gravitational field but never reaching the Earth, which is curving away at the same rate that the projectile falls. That is, the cannon ball would have been put into orbit around the Earth. Newton concluded that the orbit of the Moon was of exactly the same nature
the Moon continuously "fell" in its path around the Earth because of the acceleration due to gravity, thus producing its orbit.
By such reasoning, Newton came to the conclusion that any two objects in the Universe exert gravitational attraction on each other, with the force having a universal form: