Name____________________
Newton’s Second Law of Motion Lab
Date________________Blk___
Overview
The purpose of this investigation is to validate Newton’s Second Law of
Motion. In part A the lab cart will be accelerated by various net forces while
keeping mass constant. In part B the lab cart will be accelerated by a constant
net force while its mass is varied. The goal is to determine the relation between
acceleration and force and the relation between acceleration and mass. The
force on the lab cart is controlled and provided by gravity acting on a weight at
the end of a string that passes over a pulley at the end of a lab table.
Force, mass, and acceleration all must be measured in order to complete
this lab. Force data is collected by calculating the weight of the calibrated
masses added to the end of the string. Mass data is collected with an electronic
balance. Acceleration data is collected by a sonic ranging device working in
connection with Logger Pro 3 software.
Part A – Acceleration vs. Force
In this section of the lab the cart will be loaded with three masses. Then various
combinations of mass will be removed from the cart and placed on the end of a string
passing over a pulley. By doing this the amount of net force will be varied while keeping
constant the total amount of mass being accelerated. It is important to note that the pull
of gravity on the dangling mass causes not only the cart and its contents to accelerate,
but also the string itself and the mass or masses attached to the end of the string. Put
another way, the weight on the end of the string causes all of the mass to accelerate (and
it all accelerates at the same rate).
Procedure
1. Set up the track with one end hanging slightly over the edge of the table. Attach the
pulley to this end. Attach the sonic ranger at the other end. Do not over tighten any
of the nuts, screws, etc.
2. Load the cart with the following masses: 20 g, 50g, 100 g. Attach one end of a
string to the cart. Pass the other end over the pulley at the end of the track. Give the
free end of the string a slight tug so that the cart and string are set into motion. Adjust
the feet of the track so that the cart goes slightly downhill toward the pulley and does
not accelerate once it is set into motion. (i.e. With just enough tilt in the track the cart
will move downhill with constant velocity.) At this point, because the cart is not
accelerating it should be true that all forces acting on the cart are balanced and there
is no net force acting on it.
3. Important note: The slight slope of the track is a way to counteract friction. Once a
proper slant has been determined do not change it. In so doing it follows that
any additional weight added to the end of the string will be the net force acting to
cause the acceleration. In other words, gravity alone is the force causing the
acceleration.
4. Complete the mass of cart, string, and added weights data table using the electronic
balance. The values in this table must remain the same for each trial.
5. For the first trial, remove the 20 g mass from the cart and hang it on the end of the
string. Leave the 50 g and 100 g masses on the cart.
6. You should release the cart and let it accelerate after you hear the steady clicking of
the sonic ranger. Someone must catch the cart! (Before it hits the pulley or runs off
the table.)
7. You should now be looking at a graph of velocity vs. time that clearly shows the cart
at rest, the cart accelerating, and the cart being caught. You may need to change the y
axis of the graph from position to velocity. If the graph is not a clear constant
acceleration, you need to repeat the experiment – simply click on the Collect button
to repeat. You may need to adjust the direction the ranger is pointing if it is getting
errant reflections (normally it works best when tilted slightly upward).
8. You now need to get the acceleration of the cart. To do this click and drag across the
region of the graph that you want to measure (the part where the cart was
accelerating). Highlight only the linear portion.
9. Now we want to do a best fit or linear regression. Click on the tool bar button labeled
Analyze.
10. If all seems well with the regression, then record the results in the data table, making
sure to include units in the spaces provided. The line of best fit should match the data
very closely! The correlation coefficient is an indicator of how well the data matches
the best fit: the closer R is to 1 the better the match. The computer labels this as
Correlation; it is also often called simply R. It should be possible to get values of R
of at least 0.990 – if it is less than this, then try again if you feel like you have enough
time.
11. For the next trial remove the 20 g mass from the string and put it back on the
cart. Remove the 50 g mass from the cart and place it on the end of the string. You
now have changed the force pulling the cart without changing the mass being
accelerated. Collect, graph, scrutinize and record acceleration data as before.
12. Repeat this process with 70 g, 100 g, 120 g, and 150 g of mass on the end of the
string. Do this by transferring a mass or masses between the end of the string and the
cart – thus keeping constant the total amount of mass being accelerated.
Part B – Acceleration vs. Mass
In this section of the lab the cart will begin with no mass loaded onto it. Then under the
influence of the same net force each time, increasing amounts of mass will be loaded onto
the cart.
Procedure
1. Use the same cart and the same track setup. Remove all masses from the cart and the
end of the string.
2. Attach a 50 g mass to the end of the string and pass it over the pulley. This same
mass will be used to provide the same net force for each trial. Record this value in
the mass table.
3. Use the program to collect, graph, scrutinize, and record acceleration data just as
explained in part A.
4. Repeat the process with 250 g, 500 g, 750 g, 1000 g, and 1250 g of mass placed on
top of the cart. Do not change the mass pulling the cart. In this way you are
changing the mass being accelerated without changing the amount of force.
Analyses – Part A
1. Complete the bottom table on the data sheet for part A: Determine the net force in
Newtons by finding the pull of gravity (i.e. the weight) acting on the mass added to
the end of the string for each trial. (Remember – by tilting the track, all other forces
were set to balance one another.) Acceleration is simply copied from the regression
results.
2. Use these results to construct a force vs. acceleration graph. For this graph only, plot
the independent variable (force) on the y-axis. Determine the best fit and equation.
Analyses – Part B
1. Complete the bottom table on the data sheet for part B: Total mass being accelerated
includes the cart, the string, and all other masses that accelerated with the cart,
including the one on the end of the string. Calculate the reciprocal of
this. Acceleration is simply copied from the regression results.
2. Use these results to construct an acceleration vs. mass graph. Draw the best
fit. Determine the equation assuming this to be a hyperbola of the form: y = k/x. Use
each datum to solve for a value of k and then take the mean of the k values and use it
for the best-fit equation and curve. You may instead use your graphing calculator to
find the equation of the line.
3. Also construct a “curve straightening” graph of acceleration vs. mass –1. On this
graph the x-variable is the reciprocal of the total mass being accelerated. Determine
the best fit and equation.
A complete report (50 pts): (5 or 6 pages in this order)

Completed data/results tables. (8)

Force vs. Acceleration graph. (10)

Acceleration vs. Mass graph. (10)

Acceleration vs. Mass –1 graph. (10)

On separate paper, answers to the questions using complete sentences. (12)
Questions (2 ea)
1. Show the work for the following calculated values that appear in the tables: (a) the
net force for the 20 g trial, (b) the total mass for the very last trial in part B, and (c)
the reciprocal mass for the very last trial in part B.
2. Discuss whether or not your graphs confirm and/or support the types of relations
described in Newton’s 2nd Law and explain how so. Be specific in referring to your
results and graphs. Remember to address both aspects of the 2nd Law: how
acceleration is related to force and how it is related to mass.
3. Consider the total mass accelerated as shown in the data table for part A. This is the
mass that was accelerated by the pull of gravity acting on the hanging weight. This
value should be the same as one of the constants, slopes, or y-intercepts found on
your graphs. (a) The total mass from Part A should be equal to which constant, slope,
or y-intercept? (b) Calculate the absolute value of the difference between these two
values. (This is a little like finding the absolute error – however, neither value is a
“true” or “accepted” value.)
4. Consider the weight that was pulling the cart in part B. This weight should be the
same as one of the constants, slopes, or y-intercepts found on your graphs. (a) The
weight of the mass on the end of the string should be equal to which constant, slope,
or y-intercept? (b) As in the previous question calculate the absolute value of the
difference between the values.
5. (a) What would be the effect on the graphs and/or equations if you did not correctly
compensate for friction? (i.e. What would happen if the track is slanted
incorrectly?) (b) Is there any evidence of this in your results? Explain both answers
and be specific!
6. Discuss error in this lab. (Things to discuss: indications and signs of error – random
and/or systematic, the probable and significant cause(s) of the error that is apparent in
the results. The goal of discussing error is to explain satisfactorily why the results of
your lab are not quite exactly what was expected. Be as specific as possible. You
will have unexpected results in almost any lab – but what are the particulars
in this one. Your task is to write a discussion that is intelligent, thoughtful, and
insightful!)
Part A – Acceleration vs. Force
Mass of cart and string
Combined mass of the three calibrated
weights
Total mass being accelerated
Trial
Results of CBR/Logger Pro linear regression of velocity-time
graph:
Slope
y-intercept
Corr. Coeff.
(
)
(
)
(no units)
20 g
50 g
70 g
100 g
120 g
150 g
Trial
20 g
50 g
70 g
100 g
120 g
150 g
Net Force (N)
Acceleration (m/s2)
Part B – Acceleration vs. Mass
Mass of cart and string
Mass at end of string
Mass added to cart
(g)
0
Results of CBR/Logger Pro linear regression of velocity-time
graph:
Slope
y-intercept
Corr. Coeff.
(
)
(
)
(no units)
250
500
750
1000
1250
Total mass
being accelerated:
m (kg)
Reciprocal of total mass
being accelerated:
1/m (kg –1)
Acceleration obtained
from regression:
a (m/s2)