Newton’s Second Law of Motion
The second law states that the net force acting on a body is proportional to the acceleration observed. The constant of proportionality is the mass, so the law looks like
It is important to note that the left hand side is the net (unbalanced) force acting on the object and that this is a vector sum. If the net force is in the same line as the motion (at least partly), then the result of the net force is that the object speeds up or slows down. If the net force is perpendicular to the motion, the the object changes direction (also an acceleration). Notice that there is one vector on the left (force) and one vector on the right (acceleration). The net force must be in the same direction as the acceleration.
One important application of Newton’s Second is weight. Your weight is the gravitational force pulling on the mass of your body. If gravity is the only force acting, then according to Newton’s Second
W = mg ,
where we have denoted SF by the weight W and the acceleration as the acceleration due to gravity at the Earth’s surface.
Dynamic Equilibrium means that the net force is zero (SF = 0) but the velocity is not zero. A common example is a car driving at constant speed.
Dissipative forces are those that always oppose motion or even the tendency of motion. Two examples are friction and air resistance. Careful measurements show that friction results from the microscopic irregularities of the surface of an object. When brought into contact with another object, the mutual catching and interlocking of these rough surfaces cause friction. Thus the amount of friction present depends on the normal force pressing the surfaces together and the types of surfaces themselves. These dependencies are symbolized
F = mN
Here N is the normal force (perpendicular to the surface) and m is the coefficient of friction for the contact surfaces. The coefficients are generally numbers less than one. We considered two types of friction: static (no motion) and kinetic (moving). Static friction is a variable force. It is as big as it needs to be to prevent motion. If there is no applied force on the object, there is no static friction. The amount of static friction is equal to the applied force until the applied force becomes big enough to cause the object to move. Once motion has begun, kinetic friction becomes the frictional force. We can express the frictional force in the same way, but the coefficient m is generally less than the static coefficient. This leads to the common experience that once the object begins to move, it becomes easier to move. Kinetic friction is almost constant for most normal speeds.
Air resistance depends on the velocity of the falling object and the surface area exposed to the direction of travel. So a sheet of paper held flat and dropped falls very slowly (large surface area), but the same sheet dropped edge on falls rapidly (small surface area). The dependence on velocity is also common, if you have “caught the wind” with you hand as your car moves down the road. You don’t feel much at low speeds, but at highway speeds, the force of air resistance can be quite large.
If we consider a sky diver, we see that the air resistance starts very small, since she is not falling very fast at first. As the speed increases, so does the air resistance. Using Newton’s Second we have the weight pointed down and air resistance (opposing the motion) pointed up. It is possible for the two forces to be equal in magnitude. When that happens, the net force is zero and thus the acceleration is zero. From that point on she falls with constant speed (terminal velocity).