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A thin, flexible metal plate attached at one end to a platform which can be used to measure mass
A thin, flexible metal plate attached at one end to a platform which can be used to measure mass. When the free end of the plate is pulled down and released, it vibrates in simple harmonic motion with a period that depends on the mass attached to the plate. To calibrate the force constant, objects of known mass are attached to the plate and the plate is vibrated, obtaining the data shown above.
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Create a graph of period squared vs mass (T2 vs. m).
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Your graph should look approximately linear. Draw on the graph the line that is your estimate of the best
straight-line fit to the data points. Determine the slope of this line. What information does this slope give?
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An object whose mass is not known is vibrated on the plate, and the average time for five vibrations is measured to be 8.1 s. From your graph, determine the mass of the object.
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Can this device be used to measure mass aboard the International Space Station as it orbits the Earth? Explain.
| mass(kg) | average time for ten vibrations(s) |
| .10 | 8.86 |
| .20 | 10.6 |
| .30 | 13.5 |
| .40 | 14.7 |
| .50 | 17.7 |
Expert Solution
Answer:
2. T = 2 pi sqrt(m/k)
T^2 = 4 pi^2 m/k
so slope = 4 pi^2/k
k = 4*pi^2/5.733=6.89 N/m
3. T = 8.1/5
so
8.1^2 = 5.733*m+0.085
m=11.43 kg
4. Yes it can since it doesnt depend on gravity
PFA
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