Physics for Geologists, Second edition

16 Force
Figure 2.1 The sum of the forces acting on a static body must be zero. The
normal reaction is equal to the component of weight normal to the
surface; and the frictional resistance is equal to the component of
weight down the surface.
Normal
reaction
Figure 2.2 A triangle of forces.
of these must be zero. As long as the frictional resistance can equal the
component of weight down the slope, the book will remain stationary.
When the sum of forces equals zero, the relationship can be expressed in
another way called Lami's Theorem, or the triangle or polygon of forces.
If three forces in the same plane act at a point in a stationary object (such
as the centre of mass), then three lines drawn parallel to these forces with
lengths proportional to the magnitude of each force form the three sides of
a triangle. So the book on an inclined surface (Figure 2.1) is acted on by the
weight of the book, the normal reaction, and the frictional resistance, and
this can be represented by a triangle of forces, as in Figure 2.2.
When it slides, there is no longer a triangle of forces because the shear
component of weight, T, is greater than the frictional resistance, t.
If more than three forces act on a body at rest, a polygon of forces results.
Coriolis force
Why does the carousel attendant at the fun fair have to lean over in order
to walk radially outwards from the centre? Why do the ocean currents in
the same hemisphere circulate the same way, but those in opposite hemi-
spheres the opposite way? Why does a cyclone or typhoon in the Southern
Hemisphere rotate clockwise when viewed from above, but anti-clockwise
in the Northern Hemisphere?
Copyright 2002 by Richard E. Chapman