Due To Gravity
Why does a skydiver accelerate as he leaps from the plane? The answer
to this question is relatively simple: gravity. Gravity acts on
all bodies in the universe, and each bodies' gravitional effects
are related. The body that the majority of the human population
is affected by is the planet earth. The gravitational acceleration
produced from earth is approximately 9.8 m/s^2, which changes slightly
as you move closer to or away from the earth's center of mass.
an instance for which a person named Joe prepairs for his first
skydiving experience. Joe gets on a plane with an instructor and
heads towards the sky.
First off, while Joe is in the plane, he does not constantly accelerate
downward, assuming the altitude of the plane remains constant. Why
might this be the case? Newton's Second Law states, "The acceleration
of an object is directly proportional to the net force acting on
it and inversely proportional to its mass" (Serway et al).
Therefore, we know that if there is no force acting on a body, the
acceleration of the body is equal to 0. Lets examine a free body
diagram of this situation.
Where M is equal to Joe's mass and G is equal to
Joe's acceleration from Gravity. Fplane is equal to the normal force,
which balances out the downward force of Joe.
One may now
clearly see why Joe does not accelerate downward while he remains
is in the plane. The normal force of the plane is acting against
the normal force of the gravity acting on Joe's 100 kilogram mass
(this is getting close to the maximum weight allowed for skydiving).
Since the sum of the forces in the y, or upward direction, is equal
to zero, there is effectively no force acting on Joe. Thus, the
acceleration of Joe must be zero.
Now that Joe
understands why he is remaining at a constant altitude, he's ready
to take his first jump. Joe is given the signal to jump from the
jump master, and he steps right off the edge of the plane. Joe is
now instantly accelerating in the downward direction. Joe's acceleration
will soon cause him to travel at a rapid rate. But exactly how fast
will he be traveling at a certain time? Without this knowledge,
Joe could easily splatter against the surface of the earth. In order
to calculate Joe's velocity at any time, T, we use the following
= Vi * T + .5 * g * t^2
Where X is the
change in distance, Vi is the initial velocity, t is time, and g
is the acceleration due to gravity. Since we know Joe's initial
velocity was 0, and the acceleration of gravity is always 9.8 m/s^2,
we can calculate how far Joe has traveled at any point in time.
the new free body diagram for this situation.
As you can see, the normal force is now absent from this diagram.
In its place is a difference force known as air resistance. Air
resistance, or drag force, is typically much smaller than that of
the normal force of a body, so Joe should continue to accelerate
downward. We did not take air resistance into account in the above