Name________________________ Block_____________ Date Due__________________
Pre-calculus Physics
Labs – Newton’s Second Law
SMART PULLEY LAB
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:
Part II:
Vary M2 while keeping the total mass of M1 + M2 constant.
Vary M1 while keeping M2 constant.
M1
M2
1
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.cmbl. Re-size your dt graph so that it fills most of your
screen. Select options::graph options::axis options and 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: Varying Force with Constant Total Mass
1. Refer to your data table for Part I, 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 and its contents and write this into the “M1” column in your
table. Write the measured total mass of your 10.0 g + 50.0-g masses into the “M2” column.
Next calculate the value of “Applied Force = M2*g” and write this into the “Applied Force” column
in your table. Finally calculate the “Theoretical a = F/(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 10.0 g + 50.0 g mass (M2)
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 “dt” 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 “dt” parabola (good data only), click the blue f(x) button,
and choose quadratic::try fit::OK. Record the value of 2A (i.e. 2 x A where A = the t2 coefficient)
in the “Experimental a” column in your data 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. Next take the 10.0 g mass off the end of the string and put it into the cart. Put one of the
20.0 g masses onto the string along with the 50.0-g mass. Note that you now have more mass
on the end of the string (70.0g) while the total of the mass on the string and in the cart (M1 + M2)
2
has not changed. Repeat steps 1-4 above. Continue in this manner so that trials 3, 4, and 5
have masses of 80.0 g (50.0+20.0+10.0), 90.0 g (50.0+20.0+20.0), and 100.0 g (50.0+50.0)
respectively on the end of the string, while the total of the mass on the string and cart (M1 + M2)
stays the same.
PART II: Constant Force and Varying Mass
1. Now remove all masses from your cart, keeping the 100.0 g mass on the string from the
last trial (#5) in Part I. Fill in your data table for trial #1 (Part II), proceeding as in Part I.
2. For the rest of Part II, place combinations of the large wood and metal blocks in the cart
as shown in trials 2-6 on the data table. Proceed as in Part I. Note that M2 stays constant at
100.0g throughout Part II. Be sure to tape the blocks to the cart in trials #4 and #6!!!!
PART III. Analyzing your data and printing your graphs
1. When done with Part II, quit the LoggerPro program and select the Graphical Analysis
icon.
2. From the trials in Part I, plot "Experimental a" on the x-axis and "F" on the y-axis. Adjust
Xmin and Ymin so both are 0. Do a linear regression. Make sure axes are labeled appropriately
and your graph has a meaningful title, and then print your graph.
3. From the trials in Part II, plot "Experimental a" on the x-axis and "Total Mass = (M1+M2)"
on the y-axis. Adjust Ymin and Xmin so that both are 0. Then choose the blue f(x) button and
select inverse::try fit::OK. Make sure axes are labeled appropriately and your graph has a
meaningful title, and then print your graph.
3
Trial
#
Set-up
Cart
+
Load
Hanging
Mass
Applied
Force
Theoretical
a
Experimental
a
M1
M2
F = M2*g
F/(M1 + M2)
2A
(kg)
(kg)
(N)
(m/s2)
(m/s2)
% Error
Part
I
1
cart+20+20+50
2
cart+10+20+50
3
cart+20+50
4
cart+10+50
5
Part
II
cart+10+20+20
1
cart
2
cart+wood
3
cart+met1
4
cart+wd+mt1
5
cart+mt1+mt2
6
cart+w+mt1+mt2
Masses
Measured
mass (kg)
cart
wood
metal #1
metal #2
4
Atwood’s Machine Lab
A classic experiment in physics is the Atwood’s machine: Two masses on either side of a
pulley connected by a light string. When released, the heavier mass will accelerate downward
while the lighter one accelerates upward at the same rate. The acceleration depends on the
difference in the two masses as well as the total
mass.
Objectives
 Use a Photogate and Smart Pulley to study
the acceleration of an Atwood’s machine.
 Determine the relationships between the
masses on an Atwood’s machine and the
acceleration.
40 cm
Materials
computer
Vernier computer interface
Logger Pro
Vernier Photogate with Super Pulley
mass set
string
Preliminary SETUP
1. Measure two 10-g masses, two 20-g masses and two 50-g masses. Record your data in
the table below.
10 g
#1
20 g
#1
10 g
#2
50 g
#1
20 g
#2
2. Draw a schematic diagram of the masses hanging over the pulley. Label one M1 and the
other M2.
3. "Straighten out" the pulley and label the forces and masses.
4. Write the equation for acceleration.
5
5. Calculate the acceleration for the masses listed below. The "Experimental a" and
"Percent Error" columns will be filled in later.
M1
M2
10 g
20 g
10 g
30 g (10 g +
20 g)
10 g
50 g
20 g
30 g
20 g
50 g
30 g
50 g
40 g (20 g +
20 g)
50 g
Theoretical a
Experimental a
Percent
Error
Procedure
1. Connect the smart pulley photogate to the “Dig/Sonic#1” port on your LabPro interface.
2. After opening LoggerPro 3.3, choose file::open::Probes and Sensors::Photogates::Pulley.
Re-size your dt graph so that it fills most of your screen. Select options::graph options::axis
options and 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.
3. Hook the appropriate masses to the string on either side of the pulley. One lab partner
should hold the pulley motionless until the next step is complete.
4. The other partner should then click on the “collect” button to activate the timing. At this
point, the pulley should be released and timing will begin. A table and “dt” 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.
5. Now click and drag across the “dt” parabola (good data only), click the blue f(x) button,
and choose quadratic::try fit::OK. Record the value of 2A (i.e. 2 x A where A = the t2 coefficient)
in the “Experimental a” column in your data 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”.
6. Repeat for the other mass combinations.
6
Grading and how to submit your work
Page 1
1. Physics Heading
a. Names of all group members
b. Lab title (Newton’s Second Law Labs)
c. Date Due
d. Your lab block
2. Summary of Smart Pulley Lab
a. Graphs: Experimental a as a function of Net Force and Acceleration as a
function of mass
Page 2
Analysis Questions: Type your complete thought complete sentence answers to
questions 1 -6. Type the answers (letter only) to the multiple choice questions in a nice
table at the bottom of the page
1. Why did the value of your experimental acceleration steadily increase as you progressed
from trial 1-5 in Part I?
2. Why did the value of your experimental acceleration steadily decrease as you
progressed from trial 1-6 in Part II?
3. What are some valid reasons why the theoretical acceleration turns out to be larger than
the actual acceleration in this experiment?
4. a) What is the relationship between force and acceleration according to your F vs a
graph for Part I? Express your answer as a proportion (i.e. a ~ F, a ~ 1/F, a ~ F2,
etc.)
b) What is the relationship between mass and acceleration according to your m vs a
graph for Part II? Express your answer as a proportion. (i.e. a ~ m, a ~ 1/m, a ~ m2,
etc.)
5. The y-intercept on your graph F vs a should have been greater than zero. Why?
6. a) 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 F vs. Exp a graph?
b) 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 F vs. exp a graph?
Questions 7-13 refer to the diagram below in which the system accelerates when M2 is
released. Unless otherwise mentioned, the string does not stretch.
M1
M2
7
________ 7. Which comparison of the two mass’s accelerations is correct?
A. a1 = a2
B. a1 > a2
C. a1 < a2
________ 8. FT1 is the force the string exerts on M1. The force of gravity on the hanging
mass is F2 = M2g. During the time that the system accelerates how does
the size of FT1 compare to the size of F2?
A. F1 = F2
B. F1 > F2
C. F1 < F2
________ 9. a) 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
________
________
b) 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
10.
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
________ 11. 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
________ 12. 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
Page 3
1. Data Table
2. A sample graph of Displacement as a Function of Time clearly illustrating how you
calculated the acceleration in each case.
3. A general formula for acceleration of an Atwood Machine (a as a function of g, m1 and
m2).
8