Free Fall 1/5
FREE FALL
OBJECTIVES:
The objectives of this experiment are to show that a freely falling
body has constant acceleration, g, and to determine a value for g.
BACKGROUND:
An object falling freely under the force of gravity in vacuum has an
acceleration that is constant. Therefore, as the object falls its
velocity increases at a constant rate. Any object that moves in a
straight line, with equal changes in velocity in equal intervals of
time, is said to be moving with uniform acceleration.
From an experimental point of view the easiest way to determine if
the acceleration of something is constant is to plot its velocity as a
function of time. If the plot is linear then the equation which governs
the plot is velocity = (acceleration)(time) + initial velocity (recall
the equation of a straight line y = mx + b). The slope of the plot is
the value of the acceleration while the intercept represents the
velocity of the object when the experiment began.
The definition for velocity(ignoring its vector nature) is,
Velocity
∆Position
∆Time
where ∆ means "change in". Equation 1 defines "average velocity
over an interval of time". A useful point to remember in situations
where the acceleration is constant is that the average velocity over
some interval of time is equal to the instantaneous velocity at the
mid point of the interval.
There are several ways to conduct a free fall experiment; we will
use two different methods and compare the results.
PART 1
In this part the motion of a steel ball is studied as it falls freely in a
vertically downward direction. This method uses a darkened room
with a strobe light flashing in the background. A photographic
record of the motion of the ball can be obtained by leaving the
shutter of a camera open during the flight of the ball. Each time the
strobe flashes an image of the ball is recorded on the film.
Free Fall 2/5
Figure 1 depicts the type of photograph obtained using this method. The
position of the ball is shown after successive equal intervals of time. The
increasing distance between successive images of the ball is indicative of
the fact that the ball is accelerating. In order to determine the velocity at
any point, for example point 4, measure the distance from the preceding
point to the following point (pts. 3 and 5 respectively) and divide by the
time elapsed (in this case the elapsed time would be twice the time
between flashes of the strobe). The velocity so obtained is the average
velocity over the interval from pt. 3 to pt. 5. This average velocity will be
greater than the instantaneous velocity at pt. 3 and less than the
instantaneous velocity at pt. 5, but exactly equal to the instantaneous
velocity at pt. 4. Hence, by calculating the average velocity for an interval
one obtains the instantaneous velocity at the time midpoint of the interval.
Figure 1
PART 2
In part 2 we toss a large rubber ball vertically into the air. Regardless of
the fact that the ball first travels upward and then downward the only force
acting on the ball after it is tossed is the force of gravity. If the acceleration
of the ball is constant then we should see a linear plot of velocity versus
time despite the change in direction.
The motion of the ball is tracked by a sonar system that can accurately
measure the location of the ball by measuring the time of flight of an ultra
sonic sound pulse reflected off the ball. Since the sound pulses are sent
at regular intervals of time, ∆ t is a constant.
PROCEDURE:
PART 1 - Strobe Photograph
All necessary equipment is assembled in the dark room. You will be
instructed in its operation and will obtain a photograph of the falling
sphere. Be sure to record the flash rate (flashes/minute) from the dial of
the strobe light. When a satisfactory photograph has been obtained
mount it on the digital cathetometer or a traveling microscope and
make the necessary distance measurements as follows:
1.
Align the vertical axis of the cathetometer with the images of
the falling sphere.
2.
Center the cross hairs on the second image (the first image
may not correspond to free fall motion).
Free Fall 3/5
3.
Zero the absolute scale on the y-axis. Therefore the position
of the second image of the sphere is zero.
4.
Center the cross hairs on the third image and record the
distance as the position y(1).
5.
Repeat step 4 for the remaining images (y2, y3,...).
6.
Using the meter stick in the photograph, determine the scale
factor by measuring the length of 10 cm. as it appears in the
photograph. Measure several 10 cm lengths, both light and
dark, and take the average as the scale factor.
PART II - Sonar Toss
The sonar apparatus will be set-up at the front of the lab. Practice
tossing the ball vertically upward such that it rises and falls in a
straight line above the sonar device. When you are ready, start the
program called "SR" in the "PHYSICS" subdirectory and proceed
as follows:
1.
Select "Collect Data" from the main menu and then select
"one target"from the next menu.
2.
Hit any key to begin collecting data. You should hear a
ticking sound while the sonar system is collecting data.
3.
Toss the ball into the air, allowing it to rise and fall, catching
it before it hits the sonar system (keep your arms to the side
so as not to interfere with the sonar beam).
4.
Once you are satisfied with the data use the "Load/Save
Data" entry in the main menu to save your data on your disk
(use the save data command).
Free Fall 4/5
ANALYSIS: We wish to construct a graph of velocity vs. time for each method.
In each case the first step is to construct a data table like the one
below:
Position
(cm)
Elapsed Time
(sec)
Velocity
(cm/sec)
Acceleration
(cm/sec^2)
Y1
0
(Y2-Y1)/∆T = V1
(V2-V1)/∆T = A1
Y2
T1
(Y3-Y2)/∆T = V2
(V3-V2)/∆T = A2
Y3
T1+T2
(Y4-Y3)/∆T = V3
(V4-V3)/∆T = A3
Y4
T1+T2+T3
(Y5-Y4)/∆T = V4
.....Yn
T1+.........+Tn
While the basic analysis is the same for each case, there are small
adjustments that must be made for each method.
PART I
The data from the photograph must be scaled from photograph
size back to real-life size. This is why there was a meter stick in the
photograph. When you have measured the length of 10 cm. on the
meter stick that appears in the photograph (let's call that the scale
factor) you can use that number to enlarge the position data from
the photograph back to life size. Simply divide each data entry
from the photograph by the scale factor (be sure to use the correct
units in your conversion). (Note: Use the scaled data in the
position column of the data table).
∆T is constant in this method therefore the elapse time is just a
running sum of ∆T's.
PART II
The calculations for PART II follow the same path as PART I with
the exception that no scaling is required. Obtain a printout of your
data from the “SR” program. Locate that portion of the data that
corresponds to the rise and fall of the ball.
For each method plot the instantaneous velocities against elapsed
time and determine the acceleration due to gravity from the slope
of the graph(use linear regression). In each case compare your
experimental value for g with the accepted value and compute the
percentage difference in your result.
Free Fall 5/5
Complete the following (be as brief as possible):
1.
How would you determine if air resistance is a problem in
this experiment?
2.
Why are the acceleration values in your data tables not
constant?
3.
For each case determine the initial velocity (Vo ).
Hand-in all data tables, graphs, and responses to questions as a
group.