Download Notes - SFA Physics and Astronomy

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


F  ma
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 F 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 (F = 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 = N
Here N is the normal force (perpendicular to the surface) and  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  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).