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Physics 20: eLab Activity

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Spring Constant Determination

Background:

Springs come in many different shapes, sizes and strengths. Making a fair and accurate comparison of springs can be difficult if force and displacement values are not taken into account. One way to obtain the force being applied to a spring is with a force sensor:

By recording what force is applied to a spring and it's displacement, a constant that describes the amount of force per unit of displacement can be determined. This constant is often referred to as the spring constant. The higher the value of the constant, the more force it takes to stretch a spring.

In this activity, you will use a force sensor and ruler to obtain force readings and displacement values from a stretched spring.

The Question:

What is the relationship between the force applied to a spring and its displacement?

Variables:

This experiment involves these variables: force and displacement. Identify and state the manipulated, responding, and controlled variables in this investigation.

Materials:

  • force sensor with hook
  • USB link
  • base and tall support rod
  • lab clamp and rod
  • selection of different short springs with looped ends
  • hanging mass set, preferably in 10 g and 50 g increments

Materials note:

Pasco Scientific has hanging mass sets (item ME-9348) and a Hooke's Law apparatus with springs (ME-9827) that may be useful for this activity.

Procedure:

Step 1:

Plug the sensor into the USB link (that is connected to the computer).

Alternatively, the force sensor could be plugged into a hand-held data collection unit instead of a computer. Any way of collecting digital force readings is acceptable.

Step 2:

Use a lab clamp to attach the force sensor to a support rod so that the hook is oriented downward. When a spring and hanging mass are attached to the force sensor, your set up should look like this:

Step 3:

Raise the force sensor on the support rod so that the spring will have room to stretch as you add mass to the bottom. If you are using the computer to record force data, configure the software to report digital readings of force:

Note that digital force readings recorded by the force sensor may be negative values. This is due to how the force sensor is made; it records pull as negative and push as positive. In the case of this experiment, the indication of "negative" can be ignored if desired.

Step 4:

Hang the first mass from the spring, upon which other masses will be stacked. Take note of the force reading that is indicated by the force sensor. Place a ruler next to the spring (orient it so that increasing values are downward) - it must be held in the same position throughout the experiment, so either clamp it or rest if against the countertop so that it cannot move vertically:

Step 5:

Create a data table that will allow you to record displacement and force data:

Displacement

(metres)

Force

(Newtons)

Record your the force and displacement values from the first mass you attached to the spring. When you measure displacement, be consistent - make sure you are measuring to the same part of the hanging mass everytime.

Add another stackable mass to the spring. Choose masses that are appropriate to the spring - if it is a very "weak" spring, add masses in 10 g increments. If the spring is stronger, you may have to add 50 g increment masses to get noticeable displacement of the spring. Everytime you add a mass, record the force and displacement readings in your table. Repeat the process of adding masses and taking measurements at least 3 times. If enough masses are available, record more measurements - the more, the better.

Step 6:

Repeat steps 4 and 5 with the different springs that you have available.

Step 7:

Use DataStudio software to enter the data you have collected for each of the springs. In DataStudio, you can get a new empty data table by choosing "New Empty Data Table" from the "Experiment" menu. When you have entered the data, label the data "Force vs. Displacement", and enter the appropriate units for each of the variables (the following data is provided as an example, depending on the placement of your ruler, height of your lab stand, and choice of spring, your data will be different):

Step 8:

Use DataStudio software to create a graph of all your spring data. Use the linear fit graphing tool to apply a linear fit to all your sets of data:

Analyzing and Interpreting:

1. What is the pattern formed in the data by applying greater amounts of force to the springs?
2. Write an equation that describes the relationship between force and displacement; be sure to include units in your equation.
3. What does the slope produced by the force vs displacement graph represent?

Forming Conclusions:

4. What is the relationship between the force applied to a spring and its displacement?

Applying and Connecting:

5. Use the data you have collected on the springs you tested to make the following predictions:
  • What would be the displacement of each spring if you applied 14.5 N of force?
  • What force would be necessary for each spring to cause a displacement 0.55 m?

Extending:

6. Would it be possible to complete the experiment analyzing the relationship between force and displacement without the benefit of a force sensor? Describe how you would carry out such an experiment.
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