SMART PULLEY LAB
NEWTON'S SECOND LAW (ACCELERATION)
PURPOSE: To investigate Newton's 2nd Law of Motion (F = ma) using two masses & pulley.
EQUIPMENT:
Smart pulley and threaded rod
Photogate
Universal table clamp
Cart (with string) and track
Electronic balance
Hooked masses (one 10.0 g, two 20.0 g, and one 50.0 g)
Slotted mass (one 50.0 g)
Large mass blocks (one wood, two metal)
INTRODUCTION: In a pulley setup (as shown below), the gravitational force on the
hanging mass (M2) generates a constant acceleration of both M1 and M2. This investigation
will consist of two parts:
Part I:
Vary m2 while keeping the total mass of m1 + m2 constant.
Part II:
Vary m1 while keeping m2 constant.
m1
m2
PROCEDURE:
1. Set up the equipment as shown in class.
a) Adjust the track so the track is level and taped to the table at both ends.
b) Adjust the pulley height so the string is level.
c) Adjust the string length so that the masses do not hit the floor before the cart gets to
the end of the track.
d) Connect the smart pulley photogate to the “Dig/Sonic#1” port on your LabPro interface.
e) After opening LoggerPro 3.3,

Choose File  Open  Probes and Sensors  Photogates  Pulley

Re-size your Distance-Time graph so that it fills most of your screen.

Double click inside the graph. Click on the Axes Options tab. Adjust the “scaling”
for both the x-axis and y-axis to “manual”.

Then adjust the axes so that dmax = 1.5 m and tmax = 3.0 sec.
2. Use the electronic scale to measure the mass of the cart, the two metal blocks and the wood
block. Record the data in the data table. Assume the hooked and slotted masses are accurate
as marked to 3 significant figures. Be sure to record the masses in kilograms, not grams, to 4
decimal places.
PART I: Constant Total Mass with Varying Force
1. Trial #1: Place two 20.0 g masses and one 50.0 g mass in your cart, and then hang the 10.0 g
mass and the other 50.0 g mass on the end of the string. Add up the total mass of the cart
plus its load and write this into the “m1” column in your table. Write the measured total
hanging mass of your 10.0 g + 50.0-g masses into the “m2” column. Next calculate the value of
“Applied Force F= m2g” and write this into the “Applied Force” column in your table. Finally
calculate the “Theoretical a = m2g/(m1+m2)” as shown in the next column and write in its value.
2. One lab partner should now pull the cart back until the hanging mass almost touches the smart
pulley screw. It is now critical to hold the cart motionless until the next step is complete.
3. The other partner should then click on the “collect” button to activate the timing. At this
point, the cart should be released and timing will begin. A table and Distance-Time graph of
the timing measurements will then appear. There is a lag time before the points start to
appear on the graph. Be sure not to hit the “stop” button until the parabola changes shape,
indicating that the cart has struck the end of the track.
4. Now click and drag across the parabolic section of the curve, click the f(x) button, and do a
quadratic fit. Double the A coefficient and record the value on the table. Then use the
equation % error = (Experimental a – Theoretical a)/(Theoretical a)x100% to find the % error
in the last column. Remember to report the % error as positive if the Experimental “a” is
larger than the Theoretical “a”, and negative if the Experimental “a” is less than the
Theoretical “a”.
5. Trial #2: Next take the 10.0 g mass off the end of the string and put it into the cart. Then
take one of the 20.0 g masses on the cart and hang it on the string (along with the 50.0-g mass
already there). [Note that the total mass in the system has not changed.] Repeat steps 2-4
above.
6. Trials #3-5: Continue in this manner exchanging masses to complete trials 3, 4, and 5, keeping
the total mass (m1 + m2) the same.
PART II: Varying Mass with a Constant Force
1. Trial #1: Remove all masses from your cart. Place 100.0 g on the string. Proceed as in steps
2-4 from Part I. Fill in your data table.
2. Trial #2-5: Place the various combinations of the large wood and metal blocks in the cart as
shown, but keep m2 constant on the string at 100.0 g. Be sure to tape the blocks to the cart in
trial #4!
PART III. Analyzing your data and printing your graphs
1. Click on File  New to open a new graph.
2. Part I Analysis: Plot "Experimental a" on the y-axis and "F = m2g" on the x-axis for each trial.
Adjust Xmin and Ymin so both are 0. Do a linear regression. Determine the slope of your graph
and display it on the graph with the appropriate units. Make sure axes are labeled
appropriately and your graph has a meaningful title, and then print your graph.
3. Part II Analysis: Plot "Experimental a" on the y-axis and "Total Mass = (m1+m2)" on the x-axis.
Adjust Ymin and Xmin so that both are 0. Now click and drag across the data points, click the
f(x) button, and do an inverse fit. Determine the coefficient of your function and display it on
the graph with the appropriate units. Make sure axes are labeled appropriately and your graph
has a meaningful title, and then print your graph.
4. Analysis Questions: Answer the analysis questions. Then staple the two printed graphs, your
data table and the analysis questions in that order.
Name: __________________________
ANALYSIS QUESTIONS
Note: It will be very helpful in answering these questions to know the equation for the
acceleration of the two blocks.
Part I
1. Why did the value of your experimental acceleration steadily increase as you progressed
through the trials in Part I?
2. What is the relationship between force and acceleration according to your “a versus F”
graph for Part I? Express your answer as a proportion (i.e. a ~ F, a ~ 1/F, a ~ F2, etc.)
3. What are some valid reasons why the theoretical acceleration turns out to be larger than
the actual acceleration in this experiment?
4. The y-intercept on your graph “a versus F” graph should have been less than zero. Why?
5. If your track was positioned so it was not level and the cart had to roll uphill, what effect
would this have on the y-intercept of your “a versus F” graph?
6. If your track was positioned so it was not level and the cart had to roll downhill, what
effect would this have on the y-intercept of your “a versus F” graph?
Part II
7. Why did the value of your experimental acceleration steadily decrease as you progressed
through the trials in Part II?
8. What is the relationship between mass and acceleration according to your “a versus mTot”
graph for Part II? Express your answer as a proportion. (i.e. a ~ m, a ~ 1/m, a ~ m 2, etc.)
General
Questions 9-14 refer to the diagram below in which the system accelerates when m2 is
released. Assume the pulley is massless and frictionless. Also assume the string is massless.
m1
m2
________ 9. Which comparison of the two mass’s accelerations is correct?
A. a1 = a2
B. a1 > a2
C. a1 < a2
________ 10. If m2 increases while m1 stays the same size, the value of the acceleration of
the system will:
A. increase
B. decrease
C. stay the same
________ 11. If m1 increases while m2 stays the same size, the value of the acceleration of
the system will:
A. increase
B. decrease
C. stay the same
________ 12. Suppose the two masses are connected by a string whose mass is significantly
large enough to affect the results. In other words, as the mass passes over
the pulley it has the effect of adding more and more mass to m2. As the carts
accelerate, their value of their acceleration will:
A. be constant
B. gradually increase
C. gradually decrease
________ 13. In a perfectly frictionless set-up, the slope of the graph for Part I would be
equal to:
A. m1
B. m2
C. m1 + m2
D. 1/m1
E. 1/m2
F. 1/(m1 + m2)
________ 14. In a perfectly frictionless set-up, the value of A in the graph for Part II would
be equal to:
A. m1
B. m2
C. m1 + m2
D. m1g
E. m2g
F. (m1 + m2)g