The Force of Friction

Topics Covered:

• Definition

• Rough vs. Smooth Surfaces

• Factors Affecting Friction

• Mathematical Analysis of Friction

Friction is generally defined as the "force that opposes" motion.

When the applied force on an object is equal or less than the force of friction, the object will not move.  If the applied force is slightly bigger than the force of friction, the object will move in the direction of the applied force.  There are two types friction forces  acting on the object.

• Static friction: before the object starts to move

• Kinetic friction: while the object is moving

Static Friction is larger than Kinetic (moving) friction.

In our laboratory experiments we used graphical techniques to investigate the force of friction.

We used a spring scale attached to a block of wood. We placed different masses on the block of wood and pulled it a given distance of one meter at a constant speed (we tried our best to minimize error).  We recorded the force of gravity and the force applied as read from the spring scale.  This corresponds to the force of friction because the block of wood loaded with the masses is moving at constant speed. The spring scale needs to be a very sensitive one for this experiment; preferably one with a very flexible spring.

These are typical values we obtained for a wood block loaded with masses and dragged on a laboratory bench surface with a constant speed for a distance of 1 m.

 Let's graph this data.  We put the normal force F_N on the x-axis and the friction F_f on the y-axis.

We see that this is a straight line of the form y = kx (where k is the slope of the line).  Using the symbols corresponding to our data analysis we can derive a similar equation.  Therefore we can say:
F_f = k F_N. The constant k has a value of 0.4 (the slope of this line).  his value is known as the coefficient of friction and it is usually called  µ  (the lower case letter m  from the Greek alphabet,  pronounced "mu").

_{Therefore,  the equation for the force of friction is usually written as}
F_f = µ F_N

We also found that friction depends on several factors:

1. The weight of the object i.e. the force of gravity ( F_g). Recall that F_g = m x g

2. Friction also depends on the type of surface

3. The presence or the absence of a lubricant

Glass Surface Seen Under a Microscope	Sandpaper Surface Seen Under a Microscope	Sandpaper Surface with a few drops of oil Seen Under a Microscope

 Notice how relatively smooth a glass surface is when seen under a microscope compared to a piece of sand paper seen under a microscope.  The imperfections (bumps and grooves) are much more pronounced in sandpaper; therefore friction is higher on a rough surface (sand paper vs. glass).  Notice that adding a few drops of oil (a lubricant) to the sand paper makes the surface less rough.

Technicians have classified surfaces using a degree of roughness called  the Coefficient of static Friction  µ_s

The higher the Coefficient of friction, the rougher the surface .: the higher  the friction force.

Mathematically we can express the force of static friction as

F_f  ≤ µ_sF_N

Where:

• F_f  = Friction Force

• µ_s = coefficient of static friction

• F_N  = Normal Force

Recall that the normal force is calculated as the reaction force to the force of gravity at the perpendicular plane where a mass rests. i.e. F_N = m x g

Therefore,  in general we can say that :

F_f  ≤ µ_smg

Note: The force of friction dose not depend on surface Area.

To keep an object moving, one needs to keep applying an amount of force at least equal to the force of friction.  This type of friction if known as moving or kinetic friction.  The coefficient of moving friction is often symbolized as  µ_k.

Generally speaking,  static friction is higher than kinetic (moving) friction because it takes more effort (force) to start an object moving than to keep it moving at constant speed.

 i.e.  µ_k > µ_s

There are two possibilities to analyze the motion of an object on a surface that has friction:

1. If the object is moving at constant speed then the forces on the object are balanced and there is no acceleration
    (V = constant, a = 0)

2. If the object is moving at changing speed (a ≠ 0),  that means that the forces are not balanced and the object experiences an acceleration.
   Also see Newton's Laws Of  Motion  and  Free Body Diagrams

Example:
 A 200 Kg crate of bricks ( made of wood) is pulled along a rubber floor. The coefficient of friction is 0.38. How much force is needed to move the crate?

Given:              m = 200 Kg
                       g = 9.8 m / s²
                        µ = 0.35

Find: F_f

Solution:        F_f =  µ m g  

                            = ( 0.35)(200 Kg)( 9.8 m / s²)

                            = 686 Kg m /(s²)  =  686 N

  .: The minimum force required to get the crate moving is 686 N