Lab
Acceleration Down an Inclined Plane
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Introduction
We will be examining the acceleration of a cart rolling down an incline plane. The inclination of the plane will be very slight so that only a small component of the gravitational acceleration will cause the cart to move. We will use the LabPro motion detector to record the position and velocity of the cart at different points of time for one trial.
You will start by releasing a cart down an incline from a state of rest. If there is only one set-up, each group will go in turn until all groups have collected data.
The LabPro will collect the data and display it for your group.
In the table below, record the time, position, and velocity data for 8 unique times during the cart's descent.
data point
time
position
velocity
(sec)
(m)
(m/sec)
1
2
3
4
5
6
7
8
On graph paper, plot your data for the cart's
Position (m) verses Time (sec)
. Make sure to clearly label your axes with units and to include appropriate intervals that will use the majority of the graph paper.
This link
will provide you with graph paper that you can print if needed.
What is the shape of your graph?
hyperbolic
linear
parabolic
square root
Data Analysis
Since our x-axis represents time, what variable and unit would you place in the first column of the following chart to rectify your position-time data to be linear.
The methods to rectify, or linearize, a data set are listed below:
for a hyperbola (where y is inversely proportional to x) you would plot the re-calculated data as
1/x | y
.
for a parabola (where y is proportional to x
^{2}
) you would plot the re-calculated data as
x
^{2}
| y
.
for a square root (where y is proportional to the SQRT(x), you would plot the re-calculated data as
SQRT(x) | y
.
You can study the lesson and examples on rectifying data patterns on
this page
.
On graph paper plot your data in the above table (Question 6). Make sure to clearly label your axes with units and to include appropriate intervals which will use the majority of the graph paper.
Draw a line of best fit and calculate the line's slope. Make sure to include a unit with your numerical answer.
Knowing that s = ½at
^{2}
, what was the acceleration of your cart? Make sure to include a unit with your numerical answer.
Using graph paper, now plot a graph of
Velocity (m/sec) versus Time (sec)
using the original data collected from the LabPro in Question 3. Draw in a line of best fit.
What was the slope of your regression line? Be sure to include units with your numerical answer.
Refer to the following information for the next three questions.
Conclusions
Compare the slopes of your graphs for Question 10 and Question 8. The slope of your graph in Question 10 is ____ the slope of the graph in Question 8.
approximately half as large as
practically equal to
approximately twice as large as
Compared to the acceleration that you calculated in Question 9, the slope in Question 10 is
greater
the same
less
Determine a percent difference between the accelerations you obtained from your slopes in Question 10 and acceleration in Question 9.
A completed lab involves turning in all three graphs (Questions 4, 8, 10) as well as submit your results online.
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William A. Hilburn
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