12.3 CHAPTER 12. FORCE,MOMENTUM AND IMPULSE
Friction forces
When the surface of one object slides over thesurface of another, eachbody exerts a frictionalforce
on the other. For example if a book slides across a table, the table exerts a frictional force onto the
book and the book exerts a frictional force ontothe table (Newton’s Third Law). Frictional forces act
parallel to surfaces.
A force is not always powerful enough to make an object move, for example a small appliedforce
might not be able to move a heavy crate. The frictional force opposing the motion of the crate is equal
to the applied force butacting in the opposite direction. This frictionalforce is called static friction.
When we increase the applied force (push harder), the frictional force will also increase until the ap-
plied force overcomes it. This frictional force can vary from zero (when no other forces are present
and the object is stationary) to a maximum thatdepends on the surfaces. When the applied force is
greater than the maximum frictional force, the crate will move. Once theobject moves, the frictional
force will decrease and remain at that level, which is also dependent on the surfaces, while the objects
are moving. This is called kinetic friction. In both cases the maximum frictional force is related to the
normal force and can becalculated as follows:
For static friction: Ff≤ μsN
Where μs= the coefficient of static friction
and N = normal force
For kinetic friction: Ff= μkN
Where μk= the coefficient of kinetic friction
and N = normal force
Remember that static friction is present when the object is not movingand kinetic friction while the
object is moving. For example when you drive at constant velocity in a car on a tar road you have to
keep the accelerator pushed in slightly to overcome the friction between the tar road and the wheels
of the car. However, while moving at a constantvelocity the wheels of the car are rolling, so thisis not
a case of two surfaces “rubbing” against each other and we are in fact looking at static friction.If you
should break hard, causing the car to skid to ahalt, we would be dealing with two surfaces rubbing
against each other andhence kinetic friction. The higher the value forthe coefficient of friction, the
more ’sticky’ the surfaceis and the lower the value, the more ’slippery’ the surface is.
The frictional force (Ff) acts in the horizontal direction and can be calculated in a similar wayto the
normal for as long as there is no movement. Ifwe use the same example as in Figure 12.8 andwe
choose to the rightwarddirection as positive,
Ff+ Fx = 0
Ff+ (+8) = 0
Ff =− 8
Ff = 8N to the leftExample 21: Forces on a slope
QUESTIONA 50 kg crate is placedon a slope that makes an angle of 30◦with the horizontal. The box
does not slide down theslope. Calculate the magnitude and direction of the frictional force