‘Twas in the spring,
one sunny day…
Introduction
Springs are simple devices commonly found in all sorts of mechanical devices.
They come in many different forms, but for the most part all behave in a
similar way – the more you pull or push on a spring, the more it changes
length. This change in length is called displacement, and occurs whenever a
force is applied to the spring. Today we are going to investigate the
relationship between the force applied to a spring and its displacement.
To do this, we are going to use a spring balance to measure the force applied
to a spring when it is stretched to specific displacement values and plot the
results on a graph. You are probably familiar with the use of balances to
measure weight. Why do you think that we can also use a balance to measure
force?
Problem Statement
Is the relationship between the force applied to a spring and its
displacement linear or nonlinear?
Preparation
Before you begin, think about how you can use measurement and graphing to
answer the problem statement? How will you record and keep track of your
data? Take a minute or two and formulate a hypothesis about the
relationship between the force applied to a spring and its displacement.
What is the independent variable in this problem? What is the dependent
variable?
Procedure
You will be collecting 10 data points, so choose an appropriate scale that will
allow you to measure ten force vs. displacement pairs. It may help to stretch
the spring somewhat to get an estimate of its range of movement. DO NOT
OVERSTRETCH THE SPRING! Stretching the spring past a certain point
will permanently damage it! We will be measuring a few different springs
today, so your displacement scale may not match that of other groups. Once
you have decided on a scale to use, you may begin collecting data.
Data Collection
1. Place a ruler or meter stick on your table or desk.
2. Place the spring on your table or desk. Hold one end of the spring in
place with your left hand, and position it so that the other end of the
spring is lined up with the “zero” mark on your ruler. If your ruler
measures both English (inches/feet) and Metric (meters) units, use
the side which measures Metric units.
3. Attach your scale to the right hand side of the spring.
4. Without moving your left hand, pull on the scale with your right hand,
stretching the spring until the right hand side of the spring aligns
with your first displacement value.
5. Read the force value on your scale associated with this distance, and
write down its value.
6. Repeat steps 2-5 for the next distance value, and repeat until you
have 10 force vs. displacement pairs.
Analysis
Plot your 10 data points on a graph, putting each variable on the appropriate
axis. Label your graph accordingly.
Discussion Questions
1. Is your data linear or nonlinear?
2. What is maximum displacement value you measured? What was the
force required to maintain this displacement?
3. Use your data to estimate the force required to stretch the spring
twice as far as your highest measured value.
© 2010 John Bush, Colorado School of Mines GK-12 Learning Partnership, http://inside.mines.edu/~jobush/gk12
Support for this work is provided by the National Science Foundation’s Graduate Education, NSF, DGE-0638719
Image By Roger McLassus (Picture taken and uploaded by Roger McLassus.), via Wikimedia Commons
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