Newton’s 2nd Lawi
Purpose: You will conduct two experiments. The first will determine the relationship
between mass and acceleration and the second will determine the relationship between force
and acceleration. You will also be learning to make log-log plots and how these plots cab be
used to determine the relationship between two variables.
Background:
In both experiments, you will be making a graph with acceleration on the y-axis and the other
variable on the x-axis. You will then be asked to get the best-fit line to determine the
quantitative relationship between the different variables. It turns out that you can do this by
trial-and-error (which can be time consuming) or you can make a log-log plot which will give
you the relationship quite easily. That is, you will plot the log of acceleration versus the log of
the force (and log of acceleration versus the log of the mass). To assist you in understanding,
consider the general relationship below, where y is a general variable and x is a general
variable. (In this lab, y is acceleration and x is mass or force.)
y = axb
If we wish to understand how x and y are related to each
other (linear, quadratic, inverse, inverse squared, etc)
we will need to how the exponent, b. The easiest way to
do this is to take the log of both sides of the equation.
log (y) = log (axb)
log (y) = log (a) + log (xb)
By the product rule for logarithms, log (cd) = log (c)
+log (d)
log (y) = log (a) + b log (x)
By the power rule for logarithms, log (xp) = p
log (x)
y
= b
m
x
Given that you are making a log-log plot, that is log
(y) versus log (x), it follows that log (y) can be called
“y” in y = mx + b and that log (x) can be called x.
From this, one can see that the slope generated by a
best-fit line on a log-log plot yields the exponent and
that the coefficient is related to the y-intercept, given
by log (a).
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Materials: You will have available to you the following materials: a low-friction cart, a 1.0 m
track, a motion sensor, a pulley and string, a mass set and mass hanger, metal “bricks” to add
to the cart.
Procedure:
Part I
1. Set up the equipment so that there is a motion sensor at one end of the track and a cart
resting on the track. The string will connect the cart and the mass hanger and pass over
the pulley. Be sure to level the track and to center the pulley and string as much as
possible.
2. Turn on the Xplorer GLX and connect a motion sensor following the directions in the
Xplorer GLX handout. (Plug in the motion sensor into one of the ports at the top of the
GLX. Adjust the settings so that the sample rate unit is at samples/s, the sample rate is
at 20, and velocity is visible.)
3. You are ready to start the experiment. Note that you will have 4 individual masses.
Put one of the masses on the mass hanger and three of the masses in the cart. (We
want the total mass of the system to be constant throughout the experiment.) Be sure to
use masses that are small (say, 5-10 grams, 20 grams at most since the cart will really
start to move quickly and you will not get good data.
4. Hang the weight over the pulley and carefully let it go. The weight is applying the
force to cause the cart to move. Start to record data before you let go of the weight.
Calculate acceleration from the velocity-time graph. (You can use the GLX to find the
acceleration. Highlight the part of the graph during which acceleration is occurring
using the
keys. Then do a linear fit using
. You may have to readjust the
highlighted section by again using the arrow keys. If necessary swap cursors by
pressing
and scrolling to Swap Cursors. The equation of the line will be shown
on the screen.) Repeat the experiment 2 times (for a total of three trials) and be sure to
record your data for each trial.
5. Move one of the doughnut masses from the cart onto the hanger. Repeat the
experiment. Continue to repeat the experiment until all the doughnut masses are on
the hanger.
Part II
6. Now we will be testing the effect of mass on acceleration. Choose a weight to keep
constant on the hanger. Select a weight that is large enough to accelerate the cart but
small enough as to cause a small acceleration. You may have to experiment for a few
minutes to find a good weight. Change the mass of the cart by adding the metal bars so
that you have 4 different scenarios. For each scenario, perform 3 trials. (The metal
bars fit perfectly in the cart. The cart’s mass is approximately 0.50 kg, the long bars
are also approximately 0.50 kg, and the short bars are approximately 0.25 kg.)
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Data and Graphs:
1. Make a chart that shows total mass, force (weight) and acceleration for each trial.
Include a column in your chart for the average acceleration for each trial.
2. Graph average acceleration vs. weight of the hanging masses (force) for the constant
mass trials. Include a best fit line and be sure to display the equation of the line.
3. Graph log average acceleration vs. log weight. Include a best fit line and be sure to
display the equation of the line.
4. Graph acceleration vs. mass for the constant weight trials. Include a best fit line and
be sure to display the equation of the line.
5. Graph log acceleration vs. log mass. Include a best fit line and be sure to display the
equation of the line.
Analysis:
1. Using the graph of average acceleration vs. force, determine the relationship between
acceleration and force. How do you know? Now look at the log-log graph. What is
the slope of the log-log graph of average acceleration vs. force? How does the slope of
the log-log graph confirm the information that is determined by the acceleration vs
force graph?
2. Using the graph of acceleration vs. mass, determine the relationship between mass and
acceleration. How do you know? What is the slope of the log-log graph of
acceleration vs. mass? How does the slope of the log-log graph confirm the
information that is determined by the acceleration vs mass graph?
3. Draw a free body diagram for the weight. Write the equations for the sum of the
forces in the horizontal and vertical direction. Draw a free body diagram for the cart.
Write the equations for the sum of the forces in the horizontal and vertical direction.
(Neglect friction.)
4. How does the acceleration of the weight compare to the acceleration of the cart?
Explain.
5. Using the equations for force, calculate the accelerations of the weight and cart for
each experiment. How do these accelerations compare to the values you calculated
using the computer’s data? What do you think accounts for any discrepancies? (Note:
You need to calculate only for the averages.)
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You may use this data table or input your result into Excel or other software directly.
Part I
Total Mass (kg)
Acceleration (m/s^2)
Force (N)
Acceleration (m/s^2)
Total Mass (kg)
Trial 1
Trial 2
Trial 3
Average
Trial 1
Trial 2
Trial 3
Average
Trial 1
Trial 2
Trial 3
Average
Trial 1
Trial 2
Trial 3
Average
Part II
Force (N)
Trial 1
Trial 2
Trial 3
Average
Trial 1
Trial 2
Trial 3
Average
Trial 1
Trial 2
Trial 3
Average
Trial 1
Trial 2
Trial 3
Average
i
This lab meets the Massachusetts State Frameworks for Physics items 1.4 and 1.5.
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