March 13th, 2020
Purpose
The
purpose of this lab is to prove the acceleration due to gravity on earth is
9.81 m/s2 down. Therefore,
this will be examined by analyzing the motion path of a free fall eraser.
Testable
Question
Does
the eraser go through uniform acceleration while free falling?
Hypothesis/
Prediction/ Background Information
The acceleration due to gravity that the
eraser experiences will be constant, which is 9.81 m/s2 down because
gravity on earth causes the eraser to accelerate toward the centre of the
earth.
Variables
Control
variables: Mass
Independent
variable: Time
Dependent
variables: Velocity
Equipment
and Materials
-
1 Meter stick
-
1 Eraser
-
1 Smartphone to record video
-
Tracker software
Procedure
- Place the meter stick in the frame of the camera.
- Recording the motion path of the eraser while dropping the eraser straight down without initial velocity.
- Use Tracker to produce the velocity-time graph and table of the eraser’s motion.
- Obtain the values of velocity at every certain time interval from the table that is created by Tracker software and record them in the observation table.
- Record down the slopes of each certain time interval from the velocity-time graph in the observation table.
- Analyze the acceleration due to gravity and initial velocity from the equation which is vy = A × t + B.
Quantitative
Observations
Table: Time, Velocity, Acceleration for the Free Fall Eraser
|
Time
(s) |
Velocity
(m/s) |
Acceleration
(m/s2) |
|
0.000 |
|
|
|
3.333E-2 |
-0.300 |
|
|
6.667E-2 |
-0.675 |
-1.12E1 |
|
0.100 |
-1.050 |
-1.12E1 |
|
0.133 |
-1.423 |
-9.54E0 |
|
0.167 |
-1.686 |
-8.44E0 |
|
0.200 |
-1.985 |
-1.13E1 |
|
0.233 |
-2.439 |
-1.22E1 |
|
0.267 |
-2.798 |
-6.24E0 |
|
0.300 |
-2.855 |
-6.81E0 |
|
0.333 |
-3.252 |
|
|
0.367 |
|
|
*Let up to be positive.
Qualitative Observations
The initial velocity is not absolutely
zero. Before dropping down the eraser, there was some initial velocity down.
Figure 1: Before dropping the eraser Figure 2: The motion
path of the eraser
Analysis
Figure 3: Time vs. Velocity of the Free Fall Eraser
*Let up to
be positive.
*vy = A × t + B:
A is the slope which is the acceleration due to gravity, and B is the y-intercept of the graph which is the initial velocity of the eraser.
As
time increases, the value of the velocity decreases. But, the negative sign on
the graph means that the direction is going down. Therefore, as time increases,
the absolute value of the velocity also increases (which means that as time
increases, the velocity is faster). Furthermore, there is a linear relationship
between time and velocity, and the correlation between time and the absolute
value of velocity is positive.
Percentage Error:
|(Theoretical - Experimental)÷Theoretical|×100%
=|(-9.806-(-9.804))÷(-9.806)|×100%
= 0.02040%
Evaluation
The
hypothesis that was made before the lab is not completely supported by the
result. From the slope of each of the points, not every point of time has the
same acceleration, which means that the acceleration is not constant. However,
from the best fit line of the velocity-time graph, the slope which is the
acceleration of the free fall eraser’s whole motion is -9.804E0 m/s2.
That value is very close to the value of 9.81 m/s2 down.
Therefore, the differences between the accelerations due to gravity in every
point of time and the hypothesized value (i.e. 9.81 m/s2 down)
may be caused by the errors. The sources of these errors can come from the
initial velocity of the eraser, the air resistance, or the tracking points
which were not exactly the same as the eraser actually did.
Conclusion
While
an object is free-falling, the velocity increases along with the increase in
time. The slope of the best fit line that explains the variances of time and
velocity is 9.81 m/s2 down. However, errors actually exist, and that’s why
there are some distances from data points to the best line.
Citations
Acceleration
due to gravity. (2020, January 23). Retrieved March 12, 2020, from https://simple.wikipedia.org/wiki/Acceleration_due_to_gravity
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