Lab Set-Up
ENG H191 Hands-on Lab
Lab 3: Springs and Levers
Introduction
Purpose
The purpose of this document is to provide assistance in duplicating the
laboratory set-up for the springs and levers exercises. The content of this
document is for the consumption of the teaching staff of the Freshman
Engineering Honors Program at the Ohio State University. It is assumed that
the reader is familiar with the content of the Springs and Levers laboratory
write-up accessible at http://feh.eng.ohio-state.edu/.
Content
This document will include:
1. A list of parts that are needed per team with illustration,
2. A description of the set-up for standard measurements with
illustrations which will include:
 Finding the spring constant for compression springs,
 Finding the spring constant for tension springs,
 Finding the spring constant for torsion springs,
3. A description of the set-up for independent measurements with
illustration, the V-test,
4. A description of a set-up for a possible scale design with illustration,
5. Results and sample data and calculations, and
6. Discussion of main areas of the laboratory experience
Parts List Per Team
Part
-
Small test stand
Large test stand
Rope
 Tension spring
 Torsion spring
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Quantity
1
1
1
2
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



-
-
Compression spring
Washer
Large hooks
String
1
1
2
Length from bench to floor
1
1
1
Weight plate
Hanging scale
Scale hooks
Masking tape
Steel angle bar for making a scale 48” long
Set of weights
A stool that is already at the bench
Small piece of wood
Standard Measurements: Lab Set-up
Compression:
Spring
Constant
The first spring, a compression spring, was placed around a small metal pole
attached to a metal plate. A hollow rod with a circular disk on one end was
then placed over the small pole pushing the spring down. A distance X0 was
then measured from the disk to the metal plate. Various masses were then
added to the top of the disk, compressing the spring between the hollow rod
and the plate. The new distance X was recorded for each mass. Diagram 1
shows the setup.
Set-Up
Illustration
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Compression Spring testing
Tension: Spring To find the spring constant of the tension spring, stand the small test stand on
Constant
its side at the edge of the table with the rolling bar down. Hang the spring
from the center pole and attach string to the spring. Begin to add the hanging
weights to the string. By measuring the increasing distance the spring
constant can be computed. About four data points should give appropriate
results
Set-Up
Illustration
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Tension spring testing
Torsion: Spring
Constant
To find the spring constant of the torsion spring, stand the small test plate on
the table with the rolling bar down. Place the torsion spring on the center pole
and put masking tape over the extension of spring that is touching the plate.
Then connect a length of string to the other extension. The string will then
hang down. By adding weights to the string and measuring the increasing
angle of the spring, the spring constant can be computed. About four data
points should give appropriate results.
Set-Up
Illustration
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Torsion Spring testing
Independent Measurement: Lab Set-Up
V-Test
To find the unknown spring constant of a tension spring, stand the small test
stand at the edge of the table with the rolling bar down. Place the two
compression springs in a triangular form on two poles. Note that the students
must know the constant of the other spring. Add a length of string to the
vertex where the springs meet. Begin to add weights to the string. By
measuring the dimensions of the triangles and comparing the difference, the
constant of the unknown can be found. About four data points should give
appropriate results
Set-Up
Illustration
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V-test
Making a Scale: Lab Set-Up
Making a Scale
The students must decide which is the best lever type to use in order to build
and effective scale. There are many ways to do this correctly; we will provide
the following description of a possible scale design just as an example. The
weighing scale consisted of a long metal bar placed over the crossbar of a lab
stool, which acted as a fulcrum. A string was tied on one end so that an object
or person could balance on the bar. At the other end a different string
connected a spring scale to the bar and the ground. One person stood holding
down the string so that the spring scale could measure the force. The other
two people held down the stool in order to keep the fulcrum in place.
Diagram 4 details the setup.
Set-Up
Illustration
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Possible Scale
Results: Sample Data and Calculations
Charts
The charts that follow show the calculations and data taken for the springs.
X0 = .158 m
Compression
Spring
Mass
0 kg
.05 kg
.10 kg
.15 kg
.20 kg
.25 kg
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Force
0N
.49 N
.98 N
1.47 N
1.96 N
2.45 N
7
Dist. X
0m
.154 m
.151 m
.149 m
.144 m
.141 m
| X - Xo |
0m
.004 m
.007 m
.009 m
.014 m
.017 m
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X0 = 0 m
Tension
Springs
Mass
0 kg
.05 kg
.10 kg
.15 kg
.20 kg
.25 kg
Dist. X
0m
.001 m
.0025 m
.008 m
.010 m
.016 m
D = .02 m
Torsional
Spring
Force
0N
.49 N
.98 N
1.96 N
4.90 N
Weighing Scale
Accuracy
Graphs
Force
0N
.49 N
.98 N
1.47 N
1.96 N
2.45 N
Torque
0 Nm
.0098 Nm
.0196 Nm
.0392 Nm
.0980 Nm
Weighed
130 lbs
120 lbs
150 lbs
Y Dist.
0m
.004 m
.006 m
.012 m
.030 m
Actual
150 lbs
123 lbs
154 lbs
Angle
0°
11.31°
16.70°
30.96°
56.31°
% Error
13.30%
2.44%
2.60%
The following graphs will be used to calculate the spring constants for each of
the different types of springs. The slope of the graph is k, the spring constant.
This comes from Hooke’s Law F = kx. A graph of force vs. distance will
yield the spring constant because F/x = k. In the case of the torsional spring,
which is based on rotational motion rather than linear motion, the equation
which must be used is  = K. Torque was measured by using Fd, where F
was the gravitational force acting down, and d was the length of the hook.
Theta was calculated by measuring the downward displacement of the hook.
Knowing the length of the hook, tangent could be used to find the angle.
Since / = K, the slope of the line shows the spring constant, K. Using
linear least square fit, the line of best fit can be found. The slope of this line
yields the spring constant for each situation.
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Discussion
Discussion
The spring constant for the compression spring comes out to be 145 N/m, 143
N/m for the system of tension springs (71.5 per spring), and .00177 N/m for
the torsional spring. The tension springs can be calculated individually since
the force acting down in equal and opposite the sum of the forces acting up.
Thus, the force is split between the two springs. These results have a fair
amount of accuracy associated with them. Possible errors include friction,
human error in measurement, and random errors. The spring graphs should,
ideally, be linear. However, the slight deviations represent errors in
measurement and/or random occurrences.
The weighing scale was very accurate considering the crude construction of
the device. However, the device was by no means the safest. It was difficult
to get an accurate reading since it was tough for a person to balance on one
end. Usually, only a momentary balance could be maintained. The scale
required at least three people to operate it, and it could potentially be
hazardous if someone fell off one end of the bar.
Concluding
Remarks
The following conclusions could be made from this lab:
 The spring constant is directly related to how much tension is built up
in a spring.
 Spring constants can be easily calculated from graphs of force vs.
distance in accordance with Hooke’s law.
 A safe weighing scale requires a proper platform for a person to
balance on.
 A weighing scale also needs a securely attached fulcrum or supported
area to stand on.
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