Chapter 2 Review of Forces and Moments - Brown University

The second law provides the definition of a force – if a mass m has acceleration a, the force F acting on it
is
F = ma
Of course, there is a big problem with Newton’s laws – what do we take as a fixed point (and orientation)
in order to define acceleration? The general theory of relativity addresses this issue rigorously. But for
engineering calculations we can usually take the earth to be fixed, and happily apply Newton’s laws. In
rare cases where the earth’s motion is important, we take the stars far from the solar system to be fixed.
2.1.2 Causes of force
Forces may arise from a number of different effects, including
(i) Gravity;
(ii) Electromagnetism or electrostatics;
(iii) Pressure exerted by fluid or gas on part of a structure
(v) Wind or fluid induced drag or lift forces;
(vi) Contact forces, which act wherever a structure or component touches anything;
(vii) Friction forces, which also act at contacts.
Some of these forces can be described by universal laws. For example, gravity forces can be calculated
using Newton’s law of gravitation; electrostatic forces acting between charged particles are governed by
Coulomb’s law; electromagnetic forces acting between current carrying wires are governed by Ampere’s
law; buoyancy forces are governed by laws describing hydrostatic forces in fluids. Some of these
universal force laws are listed in Section 2.6.
Some forces have to be measured. For example, to determine friction forces acting in a machine, you may
need to measure the coefficient of friction for the contacting surfaces. Similarly, to determine
aerodynamic lift or drag forces acting on a structure, you would probably need to measure its lift and drag
coefficient experimentally. Lift and drag forces are described in Section 2.6. Friction forces are
discussed in Section 12.
Contact forces are pressures that act on the small area of contact between two objects. Contact forces can
either be measured, or they can be calculated by analyzing forces and deformation in the system of
interest. Contact forces are very complicated, and are discussed in more detail in Section 8.
2.1.3 Units of force and typical magnitudes
In SI units, the standard unit of force is the Newton, given the symbol N.
The Newton is a derived unit, defined through Newton’s second law of motion – a force of 1N causes a 1
2
kg mass to accelerate at 1 ms − .
The fundamental unit of force in the SI convention is kg m/s 2
In US units, the standard unit of force is the pound, given the symbol lb or lbf (the latter is an abbreviation
for pound force, to distinguish it from pounds weight)
A force of 1 lbf causes a mass of 1 slug to accelerate at 1 ft/s 2