Environmental Engineering Reference
In-Depth Information
T may be determined by the elimination of a from the equations of motion,
+
−
=
−
(m
1
m
2
)g
2
T
(m
1
m
2
)a
then
1
2
(m
1
(g
2
m
1
m
2
g
m
1
+
T
=
−
a)
+
m
2
(g
+
a))
=
m
2
.
Notice that if m
1
=
m
2
=
m then a
=
0
and T
=
mg.
2.3.3 Normal forces and friction
Although there are only four known fundamental forces in Nature (the electro-
magnetic, gravitational, strong and weak nuclear forces) it often seems like there
are many more. We speak of the force of the wind and the sea or the tension in
a rope. Each of these has their origins in the electromagnetic force, but it seldom
helps in everday life to think in such terms. In this section we turn our attention
to another essentially electromagnetic force that often plays a very important role
when it comes to understanding the dynamics of everyday things: friction.
When solid surfaces are brought into contact the interaction between them is
primarily electrostatic and depends on the structure of the two surfaces. No surfaces
are perfectly smooth, zooming in on them would reveal microscopic ridges and
valleys whose prominence and depth are determined by the material and the way
it was prepared, see Figure 2.18. We can quite generally express the force that
results when two surfaces are put into contact as the sum of components parallel
and perpendicular to the surface. The perpendicular component is known as the
normal force. It is the result of a microscopic compression of the layers of atoms
within the surface. It does not take much displacement of the layers of atoms to
support everyday objects on solid surfaces, and for the most part the compression
giving rise to the normal force goes unnoticed, i.e. things are solid. Experiments
with reflected laser beams from polished metal surfaces are able to measure this
compression. If we imagine pushing the two surfaces together, the amount of
compression increases. Usually, the contact area is a tiny fraction of the total
Normal force on
A
Surface
A
Friction on
A
Surface
B
Friction on
B
Normal force on
B
Figure 2.18 Illustration of two surfaces touching. The contact area is a tiny fraction of the
area of either surface.
