5-27-98
Forces can come from various sources. Whenever two objects are touching, they usually exert forces on each other, Newton's third law reminding us that the forces are equal and opposite. Two objects do not have to be in contact to exert forces on each other, however. Let's start an examination of forces by looking at gravity, one example of a force between objects that do not have to be in contact for the force to exist.
Isaac Newton is probably best known for his study of gravity, seeing as just about everyone has heard the story about Newton being conked on the head by an apple. What Newton said was this: whenever there are two objects that have mass, they will exert a gravitational force on each other which is proportional to the product of the masses, and inversely proportional to the square of the distance between them. (Actually, inversely proportional to the square of the distance between the two centers of mass is more accurate.) If the first object has a mass we can call m1, and the second object has a mass we can label m2, and there is a distance r between them (between their centers of mass, that is), the magnitude of the gravitational force is given by:
You might be used to thinking of the gravitational force as F = mg. Where does this other, more complicated, equation fit in? F = mg is actually a special-case form of the other one, applying only to objects very close to the surface of the Earth. This value of g, 9.8 m/s^2, can be found by combining G, the mass of the Earth, and the radius of the Earth. If you set F = mg equal to the gravitational force equation, you get:
Plugging these numbers in, and the value of G, gives g = 9.80 m/s2.
Any two masses exert equal-and-opposite gravitational forces on each other. If we drop a ball, the Earth exerts a gravitational force on the ball, but the ball exerts a gravitational force of the same magnitude (and in the opposite direction) on the Earth. The force just makes a lot less difference to the Earth than it does to the ball because the Earth has such a large mass.
Mass and weight are often used interchangeably, but they are quite different. The mass of an object is an intrinsic property of an object. If your mass is 50 kg, you have a mass of 50 kg no matter where you go: on Earth, on the Moon, in orbit, wherever. Your weight, on the other hand, will vary depending on where you are. Your weight is the magnitude of the gravitational force you experience, and it has units of force, Newtons. Because the gravitational force you experience on the Earth is different from that you'd experience on the Moon or in orbit, your weight would be different even though your mass remains constant.
Many forces do come from objects being in contact with each other. A book rests on a table: the book exerts a downward force on the table, and the table exerts an equal-and-opposite force up on the book. We call this force the normal force, which doesn't mean that other forces are abnormal - "normal" is the technical physics word for perpendicular. We call it the normal force because the force is perpendicular to the interface where the book meets the table.
The normal force is just one component of the contact force between objects, the other component being the frictional force. The normal force is usually symbolized by N, although our textbook uses 
. In many cases the normal force is simply equal to the weight of an object, but that's because in many cases the normal force is the only thing counter-acting the weight...that is not always the case, however, and one should always be careful to calculate by applying Newton's second law.
The frictional force is the other component of the contact force between two objects. It always acts to oppose the relative motion between surfaces, and is parallel to the plane of the interface between objects. For the simple example of a book resting on a flat table, the frictional force is zero. There is no force trying to move the book across the table, so there is no need for a frictional force because there is nothing for the frictional force to oppose.
If we try to slide the book across the table, however, friction will come in to play. Let's say it takes a force of 5 N to get the book to start moving. If we push on the book with a force of less than 5 N, the book won't move, because the frictional force will exactly balance the force we apply. If we push with a 1 N force, a 1 N frictional force opposes us. If we exert a 2 N force, the frictional force matches us at 2 N, and so on. When a frictional force exists but there is no relative motion of the surfaces in contact (e.g., the book isn't sliding across the table), we call it a static frictional force. The static frictional force is given by the equation:
The coefficient of friction (static or kinetic) is a measure of how difficult it is to slide a material of one kind over another; the coefficient of friction applies to a pair of materials, and not simply to one object by itself.
Note that there is a less-than-or-equal-to sign in the equation for the static frictional force. The static force of friction has a maximum value, but when two surfaces are not moving relative to each other the static force of friction is always just enough to exactly balance any forces trying to produce relative motion.
What happens when one object is sliding over another, when there is relative motion between two surfaces? There will still be a frictional force, but because we're dealing with things in motion we call it the kinetic frictional force. There is a different coefficient of friction associated with kinetic friction, the kinetic coefficient of friction, which is always less than or equal to the static coefficient.
As with the static frictional force, the kinetic frictional force acts to oppose the relative motion of the surfaces in contact. One important difference between the two is that the kinetic friction equation has an equals sign: the kinetic force of friction is always equal to the kinetic coefficient of friction times the normal force.
Whenever we use a rope (or something equivalent, like a string) to exert a force on an object, we're creating tension in the rope that transmits the force we exert on the rope to the object at the other end of the rope. The tension force is usually labeled by T. To makes our lives simpler, we usually assume that the rope has no mass, and does not stretch. Using these assumptions, when we exert a certain T on our massless unstretchable rope, the rope exerts that same T on the object. The rope itself will feel like it's being pulled apart, because we'll be exerting a certain T in one direction and the object we're pulling on will be exerting an equal-and-opposite force at the other end.