Tangible: What Springs to Mind?

Background: Developing mathematical models

Scientists and engineers often perform experiments to determine how one variable affects another. Using graphs and fitting tools, scientists and engineers can produce simple mathematical models which predict how a physical system works. In this lab, you will produce a mathematical model for springs. The data you will be working with will answer two basic questions:

• What is a simple mathematical formula tha relates the amount of a spring stretches to the weight hung from it?
• How do the numbers in an experimentally determined formula relate to physical properties of the spring?

Equipment

• Spring
• Stand for spring
• Weights
• Ruler

Precautions

Do not stretch the spring beyond its elastic limit! Pulling too hard may ruin it.

Preliminary observations

Observe the spring oscillating with a small and then a big amplitude. How do the periods compare? Contrast this with a bouncing ball.

Roughly measure the spring stiffness for half the spring length (by holding the spring at its center). Roughly how does it compare to the whole length?

Bend the sping at the center to connect both ends to the same mass. Predict what the stretch should be.

Taking and recording data

1. Starting with just the 50 g weight support, measure the length of the spring. Enter your results into Excel.
2. Add a 50 g weight, and measure the new length, recording the result in Excel.
3. Keep adding weights and measuring the length.
4. Determine the simplest equation that relates the amount the spring stretches to the force (not mass) applied to the spring. Check out the tips on how to use curve fitting to produce meaningful results. Note that some of the data may not be useful for figuring out the formula. (For low masses, the spring is not completely stretched.)
5. Interpret the numbers in the fit equation you get. How are the numbers in the equation related to physical properties of the spring? [Hint: If you're not sure what the numbers mean, figure out what units the numbers have.]