Lab 6: Newton’s Second
Objective: To study accelerated motion under an applied force to test Newton’s Second Law of Motion.
Pre-lab Discussion
In this experiment we will measure the acceleration of a cart subject to an applied force and test the
theoretical predictions of Newton’s Second Law. A general diagram for this experiment is illustrated
here:
m1
m2
Treating the two masses as a single system with the pulley only serving to change the direction of the
applied force, we see that the applied force is equal to m2g. So F = ma becomes m2g = ( m1 + m2) a . In
this experiment we will first vary the applied force (while keeping the total mass constant) and then
vary the total mass (while keeping the applied force constant). We will be measuring accelerations in
each case.
Procedure
Part I: Acceleration With Fixed Total Mass
1. Obtain a dynamics cart, smart pulley, and mass set. Set up your kinematics track as shown below.
Level the track as carefully as possible.
2. Configure Data Studio to use a smart pulley. Display a velocity graph so that you can measure
accelerations by finding the slope of the graph.
3. Attach a string to the cart and a mass hanger (for m2) to the string. Use a string that is long enough so
that when the cart is next to the smart pulley and the string is over the pulley, the string touches the
ground. Weigh your dynamics cart. Place an extra 20 g on the mass hanger (so that m2 = 25 g), and
100 g of mass on the cart.
4. Pull the cart back so that mass m2 is as high off the floor as possible. Release the cart from a stationary
position and let it travel as far as it is able, while still accelerating. Do not let the cart hit the pulley!
Don’t let the mass hanger crash into the floor!
5. Obtain a “good” run and use your onscreen graph to measure its acceleration. Record all acceleration
values in your lab notebook in a data table that has three columns, m2 (kg), m2g (N), and a (m/s2).
6. Repeat this procedure for a hanging mass of 50 g, 75 g, 100 g, and 125 g. In each case, make sure the
total of the hanging mass and the mass on the cart is 125 g so that m1 + m2 = the cart mass + 0.125
kg.
7. Print a graph for each person in your group, showing the five runs you made.
Part II: Acceleration With Constant Driving Force
1.
2.
3.
In this part of the experiment we will vary the total mass of the system, keeping the driving mass
fixed. Use a mass of 50 g for m2. Do not place any masses on the cart. Measure the acceleration like
you did in Part I.
1
Record your data in a table with columns for (m1 + m2) (kg),
(1/kg), and a (m/s2).
(m1 + m2 )
Next, repeat the procedure with runs where you add 100 g, 200 g, and 300 g to your cart. Record all
results. Print a graph showing your four runs for each group member.
Data Analysis
1.
2.
3.
4.
5.
Launch the Vernier Graphical Analysis program. Make a graph of your a vs. m2g data from Part I. Use
proper axis labels and units. Use the program to draw a linear regression line on the graph. We know
that the equation that governs this experiment is m2g= ( m1 + m2) a . Re-arranging this so as to be in the
1
1
m2 g. The slope of the line should therefore be
form y = mx + b, we get a =
.
( m1 + m2)
( m1 + m2 )
1
Compare your measured slope with
by calculating the percentage error. Recall that
( m1 + m2 )
" Measured− Theoretical%
% error = $
'100.
#
Theoretical
&
Print one copy of the graph for each person in your group to be included in your lab report.
1
1
m g still
Use your data from Part II to make a graph of a vs.
. The equation a =
( m1 + m2 )
( m1 + m2) 2
1
applies, but now the independent variable is
and the slope is m2g, which was constant during
( m1 + m2 )
Part II. Measure your slope and calculate a percentage error.
Print one copy of this graph for each person in your group.
Questions
1.
2.
3.
Explain why you chose to use the graphical analysis method that you used to measure your
accelerations in Part I, Step 2.
How good was the linear fit in each of your two final graphs? How do you know this?
Evaluate the error in your experiment. Was it more than you would expect? Less? What are some
possible sources of this error?