Atwood,s machine 2
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University of Texas, San Antonio *
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Course
1951
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
8
Uploaded by BarristerHare3850
Atwood’s Machine Lab Online
Background
Newton’s 2
nd
Law (NSL) states that the acceleration a mass
experiences is proportional to the net force applied to it, and
inversely proportional to its inertial mass (). An Atwood’s
Machine is a simple device consisting of a pulley, with two
masses connected by a string that runs over the pulley. For an
‘ideal Atwood’s Machine’ we assume the pulley is massless, and
frictionless, that the string is unstretchable, therefore a constant
length, and also massless.
Consider the following diagram
of an ideal Atwood’s machine.
One of the standard ways to
apply NSL is to draw Free
Body Diagrams for the masses
in the system, then write Force
Summation Equations for each Free Body Diagram. We will use
the standard practice of labeling masses from smallest to largest,
therefore m
2
> m
1
. For an Atwood’s Machine there are only
forces acting on the masses in the vertical direction so we will
only need to write Force Summation Equations for the y-
direction. We obtain the following Free Body Diagrams for the
two masses. Each of the masses have two forces acting on it.
Each has its own weight (
m
1
g, or m
2
g
) pointing downwards, and
each has the tension (
T
) in the string pointing upwards. By the
assumption of an ideal string the tension is the same throughout
the string. Using the standard convention that upwards is the
positive direction, and downwards is the negative direction, we
can now write the Force Summation Equation for each mass.
In the Force Summation Equations, as they are written here, the
letters only represent the
magnitudes
of the forces acting on the
masses, or the accelerations of the masses. The directions of
these vectors are indicated by the +/- signs in front of each term.
In these equations the + signs are not actually written out, but
they should be understood to be there. Understanding this we
can see that m
1
is being accelerated upwards at the exact same
magnitude that m
2
is being accelerated downwards. The reason
m
2
is being accelerated downwards is due to m
2
having a larger
weight than m
1
, and therefore there is a greater downwards
acting force on m
2
than m
1
. To solve for the magnitude of the
acceleration that both masses will experience, we can simply use
the substitution method by solving one equation for the tension
T, then substituting that into the other equation. Let’s use the
question for mass 1 to solve for the tension, then insert that into
the equation for mass 2, then solve for the magnitude of the
acceleration.
Here we see that the magnitude of the acceleration the two
masses experience is given by the ratio of the difference of the
two masses and the sum of the two masses all times
gravitational acceleration. Since that ratio will
always
be less
than 1, the acceleration will
always
be less than gravitational
acceleration. As the ratio gets closer to 1, then the value of the
acceleration of the masses approaches the value of gravitational
acceleration. However, as the value of this ratio gets closer to
zero, then the value of the acceleration approaches zero as well.
Also, comparing the second to last line of the steps to determine
the acceleration to Newton’s Second Law we get.
Here we see that the net force acting on each mass is equal to
gravitational acceleration times the difference of the two masses.
From the above algebra we can clearly see that as well.
Setup
1. Go to the following website:
http://physics.bu.edu/~duffy/HTML5/Atwoods_machine.ht
ml
2. You should now see the following
Procedure: Constant Total Mass
1. Near the bottom center of your screen set Mass of block 1
to 1.1 kg, and record this value in the Constant Total Mass
Table for Run 1 in your work sheet.
2. Near the bottom center of your screen set the Mass of block
2 to 0.9 kg, and record this value in the Constant Total
Mass Table for Run 1 in your work sheet.
3. Click on the play button which is a bit to the left of the
bottom center of the yellow box the Atwood machine is
located in.
a. The value for acceleration is given near the top left of
the yellow box. Record this value in the Constant
Total Mass Table for Run 1 in your work sheet.
b. Click the reset button right below the bottom right of
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the yellow box.
4. Repeat this procedure increasing the of Mass of block 1 by
0.1 kg, and decreasing the Mass of block 2 by 0.1 kg for
each run and record the new values for the next run in the
Constant Total Mass Table in your work sheet till all the
rows in the table are filled out.
a. Note, the total mass (m
1
+ m
2
) for each run should
equal 2.0 kg.
b. For the last run m
1
= 2.0 kg, and m
2
= 0.0 kg.
c. The software is using g = 10.0 m/s
2
.
Procedure: Constant
N
et Force
1. Near the bottom center of your screen set Mass of block 1
to 1.1 kg, and record this value in the Constant Net Force
Table for Run 1 in your work sheet.
2. Near the bottom center of your screen set the Mass of block
2 to 0.4 kg, and record this value in the Constant New
Force Table for Run 1 in your work sheet.
3. Click on the play button which is a bit to the left of the
bottom center of the yellow box the Atwood machine is
located in.
a. The value for acceleration is given near the top left of
the yellow box. Record this value in the Constant
Total Mass Table for Run 1 in your work sheet.
b. Click the reset button right below the bottom right of
the yellow box.
4. Repeat this procedure increasing the of Mass for both
blocks by 0.1 kg, and recording their new values for in the
Constant Net Force Table for the next run until all the rows
in the Constant Net Force Table are filled out.
c. Note, the difference bet the two masses (m
1
- m
2
) for
each run should equal 0.7 kg.
d. For the last run m
1
= 2.0 kg, and m
2
= 1.3 kg.
e. The software is using g = 10.0 m/s
2
.
Analysis of Atwood’s Machine Lab
Online
N
ame____________________________________________
Course/Section_______________________________________
Instructor____________________________________________
Constant Total Mass Table (20 points)
Run m
1
(kg) m
2
(kg) m
1
+m
2
(kg) a(m/s
2
) F
net
(
N
)
1
2
3
4
5
6
7
8
9
10
Complete the above chart. Use the acceleration and total mass to
calculate .
Show some calculations to receive credit.
1.
What is a real-world application of an Atwood's Machine? (4 points)
2.
For the Constant Total Mass data (Table 1), using Excel, or some other graphing software, plot a
graph of F
net
vs. a, with the trendline displayed on the graph. Make sure to turn this graph in with
your lab worksheets. (15 points)
3.
(a)
What are the units of the slope? (4 points)
(b)
What physical quantity does the slope of the best-fit line represent? (4 points)
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Constant
N
et Force Table (20 points)
Run m
1
(kg) m
2
(kg) m
1
+m
2
(kg) a(m/s
2
) F
net
(
N
)
1
2
3
4
5
6
7
8
9
10
Complete the above chart. Use the acceleration and total mass to
calculate .
Show some calculations to receive credit.
5.
For the Constant Net Force data (Table 2), using Excel, or some other graphing software, plot a
graph of, a vs 1/M
tot
, with the trendline displayed on the graph. Make sure to turn the graph in
with your lab worksheets. (15 points)
6.
(a)
What are the units of the slope? (4 points)
(b)
What physical quantity does the slope of the best-fit line represent? (4 points)
7.
In this experiment, we made the assumption that the tension and the acceleration experienced by
the two subsystems, the two different masses, were exactly the same.
Why are these good and/or
valid assumptions? (5 points)
8.
Above, we derived an equation for the acceleration: .
Briefly explain what the numerator and
denominator are in a physical sense. (5 points)
6