FREE FALL
The simplest real-life example of motion under almost constant acceleration is the
motion of objects in the earth’s gravitational field, near the surface of the earth and
ignoring any effects due to the air (mainly air resistance). With these effects
ignored, an object can fall freely, that is, it can fall experiencing only acceleration
due to gravity. Near the surface of the earth, the gravitational acceleration has a
constant magnitude of about 9.8 m/s^2 (or, for our purposes, about 10 m/s^2 ); this
quantity is denoted g (for gravitational acceleration). And, of course, the
gravitational acceleration vector, g, points downward.
Hammers and Feathers
At a given location on the
earth and in the absence
of air resistance, all
objects fall with the same
uniform acceleration.
Thus, two objects of
different sizes and
weights, such as hammers
and feathers, dropped
from the same height will
hit the ground at the same
time.Since the acceleration is constant, we can use the Big Five with a replaced by +g
or −g. To decide which of these two values to use for a, make a decision at the
beginning of your calculations whether to call “down” the positive direction or the
negative direction. If you call “down” the positive direction, then a = +g. If you
call “down” the negative direction, then a = −g. Just to make things easier, you
should default to referring to the direction of the object’s displacement as positive.
In each of the following examples, we’ll ignore effects due to air resistance.
- A rock is dropped from an 80-meter cliff. How long does it take
to reach the ground?
Here’s How to Crack It
Since the rock’s displacement is down, we call down the positive direction, so a =