Lab 9: There’s no such thing as a Massless Spring! In lecture we developed the

Question

Lab 9: There’s no such thing as a Massless Spring!

In lecture we developed the theory for a mass oscillating on a spring, assuming that the spring was ‘massless’, or weighed much less than the oscillating mass. Unfortunately, we often have to make do with springs that have some mass. Does the theory need to be revised to agree with experimental data taken using massive springs (which they all are!)?

Question:

How can one revise the theory to include the idea that springs have mass?

I. Introduction:

Discuss the prelab question.

II. Brainstorming and Planning Meeting:

Brainstorm ideas for answering this question. Discuss them, choose a method.

Plan your experiment.

Call the instructor over when you feel you are ready to start taking data, and give him/her a description of what you physically will be doing to gather data.

III. Carry out the Experiment

IV. Class Discussion Whole Class

Each group will present their method and results.

V. Evaluate and Reconsider:

How can you improve your ability to revise the theory?

Do you need a new experimental design? New data?

New ways to analyze and present the data you took?

New arguments in support of your conclusions?

Explanation / Answer

Since the question is not clear, use the datas for relevant help

We have to assume that "at its rest length" means "at its UNLOADED rest length"; otherwise, it would not need to be held. Then twice the amplitude = 11cm, and A = 5.5cm
F = kx
m ·9.8m/s ² = 0.055m ·k
k/m = 9.8/0.055s ² = 178.2 /s ²
sqrt(k/m) = 13.35/s
f = 13.35/2πs = 2.12/s ↠(a)

b) max Ep = ½k ·(0.055m) ² = 1.5e-3m ² ·k
at y = 7cm, Ep = ½k(0.015m) ² = 1.1e-4m ² ·k
∆E = 1.4e-3m ² ·k
This must have become kinetic energy, Ek = ½mv ²
Set them equal, and solve for v ²:
v ² = 1.4e-3m ² ·2 ·k/m
From above, we have k/m = 178.2 /s ²
v = sqrt(1.4e-3m ² · 2 · 178.2/s ²) = 0.71 m/s

c) sqrt(k/(m + 0.1kg) )= ½sqrt(k/m)
square both sides
k/(m+0.1kg) = k/(4m)
m + 0.1kg = 4m
3m = 0.1kg
m = 0.033kg = 33g

d) we've quadrupled the force on the spring; therefore we've quadrupled the displacement.
4 · 5.5cm = 22cm

Here 11 cm is the distance of the object from the spring that is the lowest position.

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