Environmental Engineering Reference
In-Depth Information
2
Force, Momentum and
Newton's Laws
A force is something that pushes or pulls. The push or pull of a force may set
an object in motion, as is the case when we throw a ball, push a topic along the
surface of a table or drop something from a height. Alternatively, forces may be
used to stop objects already in motion; the friction between the brake-pads and the
wheels of a car and between the tyres of the car and the road surface can quickly
arrest the car's motion. In these dynamical situations the direction of the applied
force is crucial in achieving the desired effect: a stationary object starts to move
in the direction of an applied force; to stop a moving object we apply a force in
the opposite direction to the motion. This directional property suggests that forces
may be represented mathematically by vectors. Forces are often found in static,
rather than dynamic situations. Medieval cathedrals are impressive examples of
how gravitational forces can be balanced by the electrostatic forces between atoms
to create structures that are stable for many hundreds of years. To start this chapter
we shall seek to place these intuitive ideas on a firmer footing and establish a useful
definition of force. We shall do this first by looking at forces in static situations
and only once we have a definition of force will we strive to link forces to the
motion of things.
2.1 FORCE AND STATIC EQUILIBRIUM
How are we to define force? We wish to do so in a way that relies on as few other
concepts as possible and to this end we remove the complication of motion and
look at a case in which nothing is moving. Figure 2.1 shows a situation in which a
mass is held stationary on a very smooth horizontal surface between three stretched
springs. The springs each pull on the mass and we say that each spring exerts a
