# Forces and Fields

Q:     "What factors affect the magnitude of friction, and is the co-efficient of friction always a constant value for a given surface?"

A:     Friction is a physical phenomenon that occurs at the atomic scale, at the interface between two materials, when atoms from one material make "bonds" with atoms of the other material over the gap space that separates them. When we say that two objects are "in contact with each other", in reality this only means that the surface atoms of the two objects "are very close". Atoms can never really touch each other.

When atoms come very close to each other, attractive electrostatic forces between the electrons of one of them and the nuclei of the other may result in the formation of "bonds". The strength of these bonds depends obviously on the nature of the atoms that bond. If now the two objects move with respect to each other, these bonds will have to be broken, and energy will have to be consumed for this purpose. The energy consumed to break such bonds is thought of as being equivalent to the "work" done by a "force" that breaks the bonds. This "force" is the "force of friction".

The more two objects are pressed against each other, the shorter the gap between them will be, and the larger the number of pairs of atoms that make bonds across the separation gap will be; therefore, the larger the work needed to be done to separate the objects will be. We view this, as if the larger the force of friction will be. A proportionality relationship between the pushing force, F, and the resulting force of friction, f, defines the coefficient of friction "": f is equal to times F".

For example, if an object of mass m is placed on top of another object, the force that pushes the objects against each other is the weight of the upper object (mg, where g is the acceleration of gravity) resting on the second object. The heavier the upper object, the larger the force of friction. In this case, the equation that defines the coefficient of friction is: "f is equal to times mg".

In science and engineering, very often objects are approximated with "point masses", disregarding their shape, volume, and mass distribution. In this case, obviously, as seen from the equation above, the coefficient of friction depends only on the force that keeps the two objects pressed against each other, and on the nature of the objects. Numerical values for coefficients of friction can be found tables, in various science and engineering reference publications and handbooks. Notice that the coefficient of friction is always given for couples of materials (i.e. steel and plastic, glass and wood, leather and linoleum, etc.), never for a single material.

In a refined model in which "real objects" are considered instead of "point masses", the coefficient of friction between two objects will obviously depend on the area of contact, too, since the larger the contact area, the larger the number of atoms that "see" each other over the gap of separation space.

Q:     How does change in friction affect the motion of an object on a plane supporting surface?

A:     The force of friction always opposes the motion.  Therefore it is always subtracted from any force applied on the object, and it result in slowing down the object

 Note if  = 0 then cos = 1 and N = mg so we have horizontal displacement.

Example:     A player hits a hockey puck. (Click for an in-depth example).

Q:    What causes friction?

A:    Friction is the result of an interaction process between two objects "in contact."   Atoms belonging to one object are so close to atoms belonging to the second object that they form bonds.  When the two objects move relative to each other, these bonds are being broken, which requires energy to be provided to the system.  Thus, friction is the result of an interaction process at the atomic scale.  The physico-chemical properties of each of the two objects determine the magnitude of the bonds formed and therefore the magnitude of the external energy needed to break these bonds.

Example:

When one object slides over the top of another bonds form between the surface atoms of the two objects.  As the objects approach each other bonds are formed.  Then, as the two objects move away from each other, the bonds are broken.

## References

### Equations

 Drag Force D = C A v2 Terminal Speed Centripetal Acceleration Centripetal Force

# Mechanics List of Topics

 Measurements Newton's Laws Potential Energy and Conservation of Energy Rotation of Rigid Bodies Elasticity Vectors Forces and Fields Linear Momentum Angular Momentum Mechanical Oscillations Motion of Point-Mass Objects in One Dimension The Gravitational Field Collisions Torque Mechanical Waves Motion of Point-Mass Objects in Two and Three Dimensions Kinetic Energy and Work Circular Motion of Point-Mass Objects Equilibrium Sound

ครั้งที่

เรื่องการทดลองเสมือนจริง