Forces

We all have a fairly deep intuitive understanding of what forces are and what effect they have on objects. We are constantly using our muscles to exert forces: we pull up on a coffee cup to get it to our mouths, we push against a car stuck in a ditch in order to get it moving and we exert a force to stop a basketball as we catch it. We know that sometimes, the force has the desired effect but sometimes it is inadequate (such as when the car is stuck too deep in mud or the basketball is thrown at us too fast). So a force is something whose purpose is to cause a change in motion. It can cause an object to increase its velocity, or to decrease its velocity depending on the circumstances. In fact, if the velocity is initially zero (eg car) or the force is in the same direction of the velocity, then the velocity will increase, whereas if the force and velocity are in opposite directions, then the velocity will decrease. Forces, like velocities, therefore have both a magnitude and a direction. The magnitude of the force (how hard we push) has something to do with how effective the force is in causing the desired motion, whereas the direction of the force will determine the direction of the resulting change in motion (if any).

Although many things can cause forces (our muscles, car engines, springs, the gravitational pull of the Earth), in Nature there are only four fundamentally distinct types of forces. In fact in our daily lives we only directly experience two of these forces: electromagnetic forces and gravitational forces. Electromagnetic forces we usually experience as two very different phenomena. Electric, or electrostatic forces, cause the sometimes painful sparks that we feel when touching a metal object after walking across a wool carpet in bare feet. Magnetic forces cause the magnet in a compass to point towards the North Pole. It was Maxwell who first showed that electrostatic and magnetic forces are two different manifestations of one and the same phenomenon, so they are now often referred to by their common name: electromagnetic forces. Electromagnetic forces hold the electrons in orbit around the nuclei in atoms, and, as the name suggests, they also provide the basis for many of the modern ``electronic'' gadgets (radios, TVs, microwaves, computers) that we currently take for granted. Our most direct experience with electromagnetic forces comes from the fact that they are responsible for holding together the molecules that make up solid objects. Thus electromagnetic forces are also the source of the ``repulsive'' contact forces we feel when we touch or hit solid objects. Electromagnetic forces keep you from falling through the chair that you are sitting on while you read this.

The other force most important to our daily lives is gravity. It is what pulls us towards the Earth and keeps us from drifting off into space. It also keeps the Earth and other planets in orbit around the Sun. So your ability to sit motionless on the chair while reading this is caused by a balance between gravity, which is trying to pull you down, and the electromagnetic forces that hold the molecules of the chair together and keep you from ``bursting'' through it.

There are two other fundamental forces that we do not directly experience. The so called ``strong'' force holds the nucleus of the atom together. It is very short range, and cannot be felt even by the electron orbiting the nucleus. However, under the right conditions, the energy of the nuclear force can be unleashed with startling consequences, as in the case of nuclear bombs, and nuclear power plants. The fourth force is called the weak force. It is primarily responsible for the reactions in the Sun that give rise to the radiation (heat and light) that keeps us alive on Earth.

Thus, it should be clear that even though we only have direct experience with electromagnetic and gravitational forces, life on Earth depends in a crucial way on the presence, and delicate balance between, all four forces.

In this Section we are concerned with the effect that forces have on macroscopic objects. We have already implicitly defined a force as something that has the ability to cause motion, or more specifically a change in the motion of an object (i.e. it can get things moving or slow things down). Forces are vector quantities: they have both a magnitude and a direction. A more complete definition of a force is difficult to give. Forces, as stated above, are really defined in terms of the effects that they have on material objects, and these effects are described by Newton's laws, which are the subject of the next sub-Section.