1.

Newton’s 2nd Law

INTRODUCTION
The purpose of this experiment is to verify Newton’s Second Law for a one
dimensional system. A measured force is applied to a low friction cart and the resulting
acceleration is measured.

THEORY
The following equation is Newton’s Second Law:

 
∑ F = ma (1)

The sum of the forces, F, acting upon a mass, m causes the mass to accelerate with
acceleration a, where F and a are vectors. Since our system is one dimensional and there
is only one force (the vertical forces cancel out), this reduces to

𝐹𝐹 = 𝑚𝑚𝑚𝑚.

In this lab, the acceleration must be measured from a velocity-time graph. Since
acceleration is defined as the change in the velocity per unit time, then the slope of the
velocity-time graph equals the acceleration.

SETUP
1. Open PASCO Capstone software. Turn on the Smart Cart, open the Hardware Setup
in Capstone, and connect through Bluetooth to the Smart Cart.
2. Use adjustable feet on both ends to level the track. Give the cart a little push in one
direction to see if it coasts to a stop or accelerates and then push it in the direction to
see if the cart coasts to a stop equally in both directions.
3. Clamp the pulley to the other end of the track. Place this end over the edge of the
table. Attach the elastic end-stop to prevent damage to the pulley.
4. Tie a loop in one end of a one meter length of string. Attach the notch of the mass
hanger to the loop. Add 5 g to the hanger for a total of 10 g (including the 5 g
 hanger.) Tie a loop in the other end of the string and attach the loop to the hook of
the Smart Cart. Hang the mass hanger over the pulley. Adjust the string so the mass
is just above the floor when the cart plunger strikes the end-stop.
5. Level the string by adjusting the pulley.
6. In PASCO Capstone, Set the sample rate of the Smart Cart Position Sensor and the
Smart Cart Force Sensor to 40 Hz.
7. Create a graph of velocity vs. time.
8. Create a table with two columns. Create a User-Entered Data Set called “a 1 ” with
units of m/s2. Create another User-Entered Data Set called “a 2 ” with units of m/s2.
9. Create a new page in Capstone and make a graph of Force vs. Time. Create a table
with two columns. Create a User-Entered Data Set called “F 1 ” with units of N.
Create another User-Entered Data Set called “F 2 ” with units of N.

Fig. 1. Centripetal force.

EQUIPMENT
1. 250 g Stackable Masses, hanger with braided string
2. Smart Cart Blue
3. Dynamics Track Feet
4. Elastic Bumper
5. Super Pulley with Clamp
6. 1.2 m Dynamics Track
PROCEDURE A
1. In Capstone, select the Smart Cart Force Sensor in the Sampling Control Bar at the
bottom of the page. Remove the string from the Smart Cart Force Sensor hook and
press the "ZERO" button in the Sampling Control Bar (next to the sample rate) in
Capstone. Then replace the string.
2. Pull the cart back as far as possible without allowing the mass hanger to contact the
pulley.
3. Start recording and release the cart.
4. Click STOP after the cart strikes the end-stop.
5. The graph should look like the picture below. The region of interest in this example
is the accelerated region between 2.0 s and 3.5 s. Delete bad data runs by clicking on
the Delete Last Run at the lower right of the screen.

6. Click on the Data Summary button on the left toolbar. Double-click on the run you
just made in any box and re-label it 10 g Run 1. Then close the Summary.
7. Repeat the above steps 2-6 four more times using masses of 20 g, 30 g, 40 g, and 50
g on the end of the string. Label them 20 g Run 1, etc. Do not repeat step 1!!!!

ANALYSIS
1. Create a table and create a user-entered data set called a1 with units of m/s2 in the
first column and another user-entered data set called a2 with units of m/s2 in the
second column.
2. On the toolbar at the top of the velocity graph, click the black triangle of the Run
Select tool, and select the “10 g Run 1”.
3. Click the Selection Tool (graph toolbar) and drag the handles on the selection box to
select the initial accelerated portion of the run where the data is clean (no spikes)
 and linear. Write down the time range you have selected. You will use this in step 10
below.
4. Select a Linear Fit.
5. Record the slope (m) from the Linear Curve Fit box in line 1 of the “a1” column in
the table. You want a precision of 2 decimal places. You may adjust that using the
Gear Icon in the Curve Fit box. First right click anywhere in the Linear box. Then
click on the Curve Fit Properties and select 2 Fixed Decimals.
6. Repeat the above steps for the “20 g Run 1”, entering the acceleration in line 2, and
so on for all five runs.
7. Create a new page in Capstone and make a graph of force vs. time.
8. Create a second table and create a user-entered data set called f1 with units of N in
the first column and another user-entered data set called f2 with units of N in the
second column.
9. On the toolbar at the top of the graph, click the Run Select tool, and select the “10 g
Run 1”.
10. Click the Selection Tool and drag the handles on the selection box to select the same
time range you selected in step 3 above.
11. Click on the Statistics tool (graph toolbar) to turn it on and then on the black triangle
and select Mean. The mean value for the selected region should show on the screen.
We want a precision of three decimal places here. To change the precision, click
open Data Summary (left of screen), click on Force, click on the Gear icon that
appears, and choose 3 Fixed Decimals from the pop-up that appears. Although the
data looks rather noisy, the average is well defined. Record the Mean value in the
table on line 1 of the “f1” column.
12. Repeat the above steps 7 and 8 for the “20 g Run 1”, entering the force in line 2, and
so on for all five runs.

PROCEDURE B
1. Add a 250-gram mass bar to the cart.

2. Repeat Procedure (Part A) except label the runs “10 g Run 2”, etc.

3. Repeat the Analysis except enter the acceleration values in column “a2” and the
force values in column “f2”.
4. Find the mass in kilograms of the Smart Cart and the mass of the Smart Cart plus
the mass bar.

5. Uncertainty:
1. It is valuable to estimate the uncertainties in this experiment. An easy way to do
this is to repeat the “50 g Run 2” two more times and see how much the
acceleration varies. Enter your extra two values under in lines 6 and 7 of the
“a2” column of the first table.
2. What is your estimate of the uncertainty in the acceleration?
6. On a new page in Capstone, create a graph of f 1 vs. a 1 and another graph of f 2 vs.
a2.

CONCLUSIONS
1. Examine the force vs. acceleration graphs. Graph 1 is the force (f1) versus
acceleration (a1) plot for the cart and sensor. Graph 2 is the force (f2) versus
acceleration (a2) for the cart with the compact mass added.
2. Do these graphs support Newton’s second law? Explain your answer fully! Don’t
forget that there is some uncertainty here ( a from Procedure B). Does it explain
any deviations from what Newton would predict?
3. Would you expect the vertical intercept to equal zero? Is it? Explain.
4. What physical property does the slope of a Force vs. Acceleration graph represent?
Hint: what are the units of the slope? Why are the slopes different? Explain.
5. How well do your slopes match what you should expect?