ENG H191 Hands-on Lab
Lab 3: Springs and Levers
Introduction
Background
Potential energy is a resource that is often overlooked. Powering devices
with electro-mechanical devices is often the first thought, but not always the
most efficient. Springs, gravity, and other forms of stored energy, used with
leverage, can provide a simple and effective means for actuating devices. For
example, cranking the handle of a music box compresses a spring, which
drives the device.
Purpose
The purpose of this lab is to familiarize you with the properties of some basic
types of springs, and to use the concept of leverage in building a scale.
Basic Principles
In this lab write-up, we will cover some basic principles behind:
1) Properties of three types of springs, and
2) Leverage.
Lab Experience
The lab experience will encompass:
1) Standard measurements of spring constants,
2) Independent measurements of spring constants, and
3) Building a scale.
Properties of Springs
Introduction
A spring is any material that is designed to resist a change in shape. In
contrast, a solid object tries to keep its form. The degree to which a material
resists a change in form is called the spring constant. The spring constant
defines the amount of force that must be generated in order to stretch,
compress, bend or deflect a spring by a certain amount.
There are several types of springs; each is best suited to oppose a change in
shape in a particular direction. Compression springs are the most commonly
used type.
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Compression
Springs
Compression springs are found in a wide range of sizes and strengths. From
tiny, light duty springs found in a lock barrel, to large, heavy-duty shock
absorber springs in an automobile. The spring constant of compression
springs defines the amount of the decrease in the length that the spring
undergoes under a certain load.
Spring
Constant of
compression
springs
The spring constant (K) demonstrates a linear relationship between Force and
Displacement. The linear nature of springs is acceptable for most springs
over their typical range. However, the actual relationship between Force and
Displacement is more complicated. For practical purposes, assuming a linear
relationship is a standard practice.
When assuming a linear relationship, it is reasonable to treat any known
position of a spring as its zero position and use ‘F = K x’ from that reference
point.
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Interplay of
Force and
Distance
Consider a 2400-pound automobile with 4 identical shock absorbers. If the
car is equally balanced over each tire, then each shock absorber will support
600 lbs. (ignoring angles and lever arms in the suspension system). If the
shock absorbers have a spring constant of 100 lbs/inch, how much are the
springs compressed from their no-load position?
F=Kx
F = Force on each spring (600 lbs)
K = spring constant (100 lbs/inch)
x = Compression of spring (inches)
x = 600 lbs / (100 lbs/inch) = 6 inches
Following the same problem, if a 200-lb. man sat in the car, equally
distributed over all 4 tires, how much lower would the car sit?
It is NOT necessary to add the 200 lbs. to the 2400lb weight of the car and
redo the problem. One can simply treat this as a new problem, calling the
current position of the car zero.
F=Kx
F = 200/4 = 50 lbs. on each tire
K = 100 lbs./inch
x = 50 lbs. / (100 lbs./inch) = 1/2 inch
The car sunk an additional 0.5” when the man sat in the car. If the weight of
the car and the man were taken into account and the problem was referenced
from the no-load position of the shock absorbers then the answer would be
identical, but changing the reference position of the car simplified the
problem.
Tension
Springs
Tension springs are another style of spring that resists change in stretching.
The formula is identical (F = K x) for relating forces to change in length.
However, x = the increase in length for tension springs.
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Torsion
Springs
Torsion springs are designed to resist twisting. Torque is rotational force, and
degrees or radians are rotational distance. Instead of using the formula F = K
x for linear displacement, we use . Where is the torque and is the
angular displacement. Torque is measured as a Force x Distance (moment
arm). Consider a wrench, if a mechanic is tightening a bolt and he/she holds
their hand 6 inches away from the axis of the bolt and pulls with 20 lbs. of
force this produces 1/2 x 20 = 10 ft lbs. of torque on the bolt.
Torsional springs are used to move or support rotating objects such as hinges
or levers. A mousetrap uses a cocked torsion spring as its stored energy. A
tape measure is a torsion spring, when the tape is pulled out of its case the
coil inside becomes very tight, the tape is pulled back in to increase the size
of the coil (trying to achieve a no-load position).
Leaf
Springs
Leaf springs are yet another type of springs They are used to provide rigid
support (high spring constant) where there is limited space along the axis of
support. Leaf springs are often used as a rear shock absorber in trucks.
Other Forms
Of Springs
A simple version of a spring is a thin piece of metal that flexes, typically a
piece of spring steel (a type of steel with good elastic properties).
This hinge will attempt to open because the spring force of the flexed metal.
The spring steel is mounted on one end and free to slide on the other.
Some other forms of "springs" are rubber bands, bungee cords and other
elastic cords. Any object that flexes under load has some spring properties.
For structures and beams the formulas for computing the deflection can be
more complicated, but the behavior is the same: the object produces a
restoring force attempting to return to its no-load position.
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LEVERAGE
Introduction
Leverage is the basis for the simplest 'machines' such as wheelbarrows, pry
bars, and car jacks. A lever is simply a method of transferring work from one
location to another.
Work and
Force Relation
Work is calculated as Force x Distance:
W (Ft-lbs) = F (lbs) x D (feet)
Incidentally Work and Torque have the same units; the D in each of the
formulas refers to a different distance. For torque, the D is the moment arm,
or distance away from a rotating axis (a distance perpendicular to the line of
force). For work, the distance is calculated in the direction of the force. If a
10-lb. object is lifted 5 inches then 50 in-lbs. of work have been
accomplished, but no torque is present.
Example of
Leverage
For example, if a pry bar is used to lift the base of a heavy object:
The lifting force is greater than the force applied to the pry bar because the
operator has a mechanical advantage: He/she is farther away from the fulcrum
than the load. If the operator supplies 100 lbs. of force, it would generate 800
in-lbs. about the fulcrum, which translates into 800/2 = 400 lbs. of force to lift
the object. However, if no motion of the object occurs, then no work is done.
Work is done when the object is moved and the operator supplies the force of
100 lbs. over a certain distance. If the object was lifted 1 inch then the work
done on the object is:
W=FxD
F = Force applied to object = 400 lbs.
D = Distance the object is moved = 1 inch
W = 400 x 1 = 400 in-lbs.
If 400 in-lbs. of work were done on the object then the operator must have
done 400 in-lbs. of work.
W (operator) = 400 in-lbs. = F x D
F (operator) = 100 lbs
D (operator) = 400 in-lbs. / 100 lbs = 4 inches
Notice the trade off between force and distance. The operator uses a low
force to lift the object but he/she must move a greater distance to accomplish
the work. This principal applies throughout all forms of mechanical
advantage: "you can't get something for nothing,” force gained means
displacement wasted.
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LAB EXPERIENCE
Make sketches of equipment used in class; include them in your lab write-up.
Determination
of Spring
Constants
Standard Measurements
Determine the spring constant of all compression, tension and torsional
springs provided. Be sure to take adequate data in order to get accurate
results.
Independent measurements
Compute the spring constants of two tension springs hanging in a V
formation. DO NOT separate them and compute them separately. Hint: the
sum of forces acting on an object at rest or moving at a constant speed is zero.
(Some guy called Newton said that once.) Be sure to record your set up so
that it could be duplicated.
Questions
1)
Produce a graph for each of the three types of springs tested (at least
3 graphs total). Are the springs perfectly linear? If your graphs are
curved slightly is this due to the springs or the experimental
method? Plot at least three data point per graph.
2)
What are the two values of K for the "V" hanging springs? Explain
(with calculations) the method used to find the values.
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Build a Scale
Using the items provided and some creativity, build a scale capable of
weighing up to 250 lbs. Calibrate it and demonstrate its effectiveness. Think
about safety issues, and check your apparatus with your lab instructor before
testing it.
Questions
3)
How accurate is your scale? Calculate this using ± values for each
of your parameters. Is this accuracy acceptable for a simple scale?
Explain.
4)
Comment on the safety of the scale. Describe any possible hazards
either from failure of the device, or through use or miss-use of the
scale.
LAB REPORT
Format
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General
Guidelines
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Lab report format (INDIVIDUAL or TEAM) will be announced in lab.
Follow the sample lab report format provided.
Nominally 4-5 pages in length (including figures and tables).
Cover page
Description of Experimental Apparatus
Introduction/Background
Description of tests. Obtain graphs and sketch test setups. Graphics:
Tension, Compression, and Torsion.
For Each Spring Type
 Plot weight vs. Distance.
 Provide sketch of test setup
 Derive equations. Compute spring constants.
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Description of "V" test. Computation of spring constants.
Description of scale design. Development of scale. Include equations
and sketches. Comment on accuracy.
Analysis of results/Summary.
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