Pulley Analysis
By:
Aaron Ake
Team 20
Wonder Factory A
Instructor:
Dr. David Trevas
Submitted towards partial fulfillment of the requirements for
– November 18, 2016
Department of Mechanical Engineering
Northern Arizona University
Flagstaff, AZ 86011
________________________________
*The underline indicates the lead student for the experiment.
INTRODUCTION
Early civilizations dating back to 1500 BC are thought to be some of the first people to use pulleys. These early
civilizations are thought to have used pulleys to lift large buckets of water [1]. Over time pulleys have evolved
from single pulley systems to very large and complex systems used in modern day sailing and construction.
For this analysis four separate yet functional pulley systems will be compared. The first being a single pulley.
The single pulley is what is thought to be used by early civilizations. The second system is a moving pulley.
The moving pulley is a simple configuration that has many uses, one such use is during vehicle recovery when
using a snatch block. Third is a two-pulley system with one of the pulley floating and fourth system is a
multiple pulley system sometimes called a block and tackle. Block and tackle setups are commonly used in
construction and sailing.
METHODS
Analysis for the four different pulley systems will be calculated using free body diagrams, a separate diagram
will be created for each system. These diagrams show how the force of an object pulling on the line effects the
amount of force needed to move an object.
There will be two assumptions made in the calculations for this analysis. One assumption that is being made is
that there is no friction between the line and the pulleys. This assumption is being made because there are many
types of materials used to make lines and pulleys. The second assumption is that the mass is being lifted in the
air and not dragged on the ground.
The following equations will be used to analyze the four systems. Equation 1 below is used to determine the
tension in the lines going around the pulley and the final force needed to hold or lift the object.
𝑻=
𝑭
𝒏
Equation 1
Where:
T = the tension in the line
F = Force due to the mass being lifted by the pulley
n = number of lines attached to the mass. For the block and tackle configuration this value is the
number of wraps on the upper pulley
The second equation used in this analysis is the equation for the mechanical advantage. Mechanical advantage
is defined by how the supplied force is amplified by using a tool, mechanical device or system [2]. Equation 2
shown below is used to calculate the mechanical advantage of the system [3].
𝑭
𝑴𝑨 = 𝑻 = 𝒏
Equation 2
Where:
MA = systems mechanical advantage
T = the tension in the line
F = Force due to the mass being lifted by the pulley
n = number of lines attached to the mass. For the block and tackle configuration this value is the
number of wraps on the upper pulley
The following figures were used as free body diagrams (FBD). These FBD’s are used to aid in calculating the
forces needed to move an object attached to the specific system. Figure 1 - Single Fixed Pulley shows a
single pulley with a single line. In Figure 3 - Double Pulley a double pulley with one of the pulleys moving is
shown, this system also uses one pulley and one line. In Figure 4 – Block and Tackle a typical block and
tackle configuration is shown.
Figure 1 - Single Fixed Pulley [1]
Figure 2 - Single Floating Pulley [1]
Figure 3 - Double Pulley [1]
Figure 4 – Block and Tackle [1]
RESULTS
For the four systems, a standard mass of 100kg was be used. Having this mass fixed will show the differences
between the tensions in the lines, the force required to move the object as well as differences in mechanical
advantage between the three systems.
SINGLE FIXED PULLEY SYSTEM
The single pulley system as shown in Figure 1 - Single Fixed Pulley utilizes a single pulley which is fixed
and the line passes around over the pulley and is then pulled on to move or lift the object. The tension in the
line is equal to the force exhibited by the object in this case is 981 N as shown in Table 1. This system is
used for smaller and lighter objects where a small machine or a person is to lift the object. The mechanical
advantage is 1:1, meaning to hold the object in place one would need to exert 981 N of force on opposite end
of the line. If the object was being moved then a force over 981 N would then need to be applied.
Table 1 - Single Fixed Pulley Tension
mass
(kg)
100
gravity
(m/s^2)
9.81
Number of Lines (n)
Tension (N)
1
981
Mechanical
Advantage
1
SINGLE FLOATING PULLEY SYSTEM
This single pulley system utilized a floating pulley as shown in Figure 2 where the mass is attached to the
pulley, one end of the line is fixes and the other end is where the force is exerted to move the object. In this
system, there are effectively two lines acting on the mass and there for the force of the object is divided
equally between the two lines. To hold the mass still a force of 491 N would need to be applied. As Table 2
shows, the mechanical advantage has doubled when compared to the single fixed pulley to 2:1. This is due to
the force of the mass being split between the two sides of the line.
Table 2 - Single Floating Pulley Tension
mass
(kg)
100
gravity
(m/s^2)
9.81
Number of Lines (n)
Tension (N)
2
490.5
Mechanical
Advantage
2
DOUBLE PULLEY
The double pulley configuration works like a combination of both a single fixed pulley and a single floating
pulley. The calculations for both the tension in the line and the mechanical advantage for the double pulley
shown in Figure 3 are the same as the single float configuration and is shown in Table 3. Also, the amount
of force needed to hold the object in place and to lift the object are the same as the single floating pulley.
Table 3 Double Pulley Tension
mass (kg)
100
gravity
(m/s^2)
9.81
Number of Lines (n)
Tension (N)
Mechanical Advantage
2
490.5
2
BLOCK AND TACKLE
The results for the block and tackle are shown in
Table 4 below. This configuration is similar to the double pulley but has the ability to scale for large objects
or to significantly reduce the amount of force required to move or hold an object. As seen the table, going
from a two line (same as the double pulley) to a ten line block and tackle the forces are reduced
approximately 80%. The mechanical advantage is increase from 2:1 to 10:1.
Table 4 - Block and Tackle Tensions
mass (kg)
100
100
100
100
100
gravity
(m/s^2)
9.81
9.81
9.81
9.81
9.81
Number of Lines (n)
Tension (N)
Mechanical Advantage
2
4
6
8
10
490.5
245.25
163.5
122.625
98.1
2
4
6
8
10
CONCLUSIONS
In conclusion, many different pulley configurations can be used to reduce the amount of force needed
to move or hold an object in place. The amount of reduction is proportional to the number of pulleys
used in the configuration. Block and tackle systems can be configured to the user’s requirements while
keeping the space used by the system to a minimum. The double pulley configuration can also be
configured to reduce the same force. The disadvantage of the different configurations of this system is
the amount of space needed, as pulleys are added the overall length also increases.
References
[1] New World Encyclopedia, "Pulley," MediaWiki, [Online]. Available:
http://www.newworldencyclopedia.org/entry/Pulley. [Accessed 15 November 2016].
[2] Wikipedia, "Mechanical Advantage," Wikimedia Foundation, Inc, 14 11 2016. [Online].
Available: https://en.wikipedia.org/wiki/Mechanical_advantage. [Accessed 16 November 2016].
[3] Wikipedia, "Pulley," Wikimedia Foundation, Inc., 10 November 2016. [Online]. Available:
https://en.wikipedia.org/wiki/Pulley. [Accessed 15 November 2016].