PHYS 40A: Lab 2
1
PHYS 40A: Lab 2
Acceleration Due to Gravity
(Includes PreLab Assignment)
Objectives
These lab activities will focus on the concepts of the acceleration due to gravity
and recognizing and estimating error in measurements. You should read all the
steps in each part before you start. Work in your assigned groups and maintain a
collaborative and communicative team.
You will first setup the experimental system and have a brief introduction to
Capstone
, a data collection and analysis software. You will then determine
g
over
different fall distances, while considering sources of error and estimating their
influence on the measurement. Finally, you will explore equations of motion
graphically.
Introduction
An object dropped near the Earth’s surface will fall with a constant acceleration
due to gravity,
g
, which has a magnitude of approximately 9.8 m/s
2
.
The motion of an object in free fall is onedimensional motion with constant
acceleration. In general, an object moving with an initial velocity,
v
o
, and falling
with a constant acceleration, a, follows the kinematic equation:
! = $
%
& +
(
)
*&
)
(Eq. 1)
where
y
is the displacement of the object in time,
t
.
If we allow an object to drop from standstill (
v
0
=
0) at a predetermined height (
y
)
and measure the time of free fall (
t
), we can use Eq. (1) to calculate the
acceleration due to gravity.
Acceleration Due to Gravity
PHYS 40A: Lab 2
2
Air Resistance:
The force of an object due to its motion through air is proportional to its speed
squared (for moderate speeds) and to its crosssectional area,
A
. The constant of
proportionality,
k
, depends on the detailed shape of the object. Thus:
+
,
= $
)
.
(Eq. 2)
This relationship is appropriate for the air resistance for objects like cars, small
airplanes, and baseballs. At lower speeds, and in viscous media, the force
increases as
v
increases (linearly with speed). For high speeds in air, the relation
between air resistance and speed becomes more complicated due to turbulence.
For objects of similar shape (
i.e.
metal balls of different radii), the ratio of the
force due to air resistance to the force due to gravity is:
/
0
/
1
=
23
4
5
6
7
(Eq. 3)
The influence of air resistance on our measurement of g can be estimated both
from the variation of measured
g
values using the two balls with different
A
/
m
.
Sources of Error
:
In science, no measurement is EVER perfect. In a welldesigned experimental
procedure, a value that is measured can at best only be said to be near the true
value. We can never say that we know the result, only that it lies within a range of
uncertainty. This results in a measurement taking the form of:
Y
= (measured value ± uncertainty) =
v
±
u
The uncertainty is limited by the precision and accuracy of the measuring
instrument, human imperfection, other environmental factors, etc. The
uncertainty value corresponds to a 68% confidence interval. This means that if
you define your error well, 68% of the measurements you take will be within the
interval
v

u
to
v
+
u
of the quantity you are seeking to define,
Y
. In other words,