```Work Done To Stretch A Spring
You will measure the Work needed to stretch a spring. Unlike the force needed to lift a mass,
the force done in stretching a spring is not a constant. The Work can still be calculated using
the area under the force vs. position graph.

First research Hooke’s Law and write the definition at this point in your lab
notebook.
o Write the generalized formula which represents the Law.
o Why does the formula show the force as a negative value? What force is
shown by the formula?
o What does the spring constant of a spring represent? Explain.
1. Open LoggerPro after connecting force probe and motion detector to LabPro. You only
need one graph- change each axis to represent Force vs position.
2. Attach one end of the spring to a rigid support. Attach the Force Sensor hook to the other
end. Rest the Force Sensor on the table with the spring extended but relaxed, so that the
spring applies no force to the Force Sensor.
3. Place the Motion Detector about one meter from the Force Sensor, along the line of the
spring. Be sure there are no nearby objects to interfere with the position measurement.
Motion Detector
Force Sensor
Dual-Range
Force Sensor
Force Sensor
4. The starting point is when the spring is in a
nearly relaxed state (there should just be a
touch of resistance force, but “nearly” 0). Hold
the end of the Force Sensor that is nearest the
Motion
Motion Detector as shown below. The Motion
Detector
Detector will measure the distance to your
hand, not the Force Sensor. With the rest of
your arm out of the way of the Motion Detector
beam, click
. On the dialog box that appears, make sure that both sensors are
highlighted, and click
. You will also need to “reverse direction” of motion probego to Experiment- Set Up Sensors and right click on the motion detector to get to “reverse
direction”.
5. Click
to begin data collection. Within the limits of the spring, move the Force
Sensor and slowly stretch the spring about 35-40 cm over several seconds. Hold the sensor
still until data collection stops. Do not get any closer than 40 cm to the Motion Detector. If
you have done everything correctly, the motion will start at position x=0m and increase as
you move towards the sensor. Repeat experiment until you get a very clean graph.
6. What function best represents the relationship between the force and the displacement of
the spring?
The graph of force vs. position depends on the particular spring you used, but for most
springs will be a straight line. This corresponds to Hooke’s law, or F = – kx, where F is the
force applied by the spring when it is stretched a distance x. k is the spring constant,
measured in N/m.

What is the spring constant of the spring you are experimenting with?

From your graph, how can you determine if the spring follows Hooke’s law?

Do you think that it would always follow Hooke’s law, no matter how far you
stretched it?

What value does the slope of your graph provide?

Why is the slope of your graph positive, while Hooke’s law has a minus sign?
7. How can the work be determined from the force and displacement graph Find the work
done to stretch the spring from 0-10cm, 0-20cm, and 0-30cm. What is the trend? Is it a
linear trend?
8. Create a formula to calculate the Work done to stretch a spring from rest as a function of
the terms k and Δx.
Extensions:
Combine springs in series and parallel and predict the new spring constants of these
combinations.
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