- #1
Stormblessed
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Homework Statement
An experiment was conducted to determine the relationship between metre-stick projection from a table (L) on the vertical depression of the free end (y). Using the collected data, graphs had to be plotted until a linear relation was found, and the equation of the line had to be found. To find the relationship, trial and error method had to be used. Note: all graphs are attached.
Here is the method:
1. Clamp a metre stick horizontally so that the first 20 cm project
beyond the lab table. Measure the vertical height of the free end
above the floor under zero load. Record in the table.
2. Attach a mass ( 500 g to 1 kg ) to the free end. Measure the vertical
height of the free end from the floor and record.
3. Repeat the above procedure for projections (L) in steps of 10 cm,
maintaining the constant load. Measure the vertical height of the
free end above the floor at each projection, each time checking the
zero load height.
4. Determine the vertical depression (y) corresponding to each
projection (L) and record.
After finding the relationship, answer this: Do you think the cross-sectional area of a metre-stick (cross sectional area is referring to the area of the rectangular face at one of the ends of the metre stick) has any effect on the vertical depression at a given extension? Discuss. Describe an experiment you might perform to test your prediction.
Homework Equations
Here is the collected data:
L (projection) - 0 cm; y (vertical depression) - 0 cm
L (projection) - 20 cm; y (vertical depression) - 0.1 cm
L (projection) - 30 cm; y (vertical depression) - 0.5 cm
L (projection) - 40 cm ; y (vertical depression) - 1.2 cm
L (projection) - 50 cm ; y (vertical depression) - 3.6 cm
L (projection) - 60 cm ; y (vertical depression) - 5.1 cm
L (projection) - 70 cm ; y (vertical depression) - 8.0 cm
L (projection) - 80 cm ; y (vertical depression) - 11.7 cm
The Attempt at a Solution
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I first plotted a graph using the collected data, which resulted in an exponential relationship. Then, as per the trial and error method, I squared the L values and replotted the data, but the result was still exponential (curve). I then cubed the L values and plotted the points again, which resulted in a somewhat linear relationship. Using this, I found the relation to be: y = 2 x 10^-5(L^3). However, I am not sure this is correct, as when I plug in the L values into the equation, the result is quite off from the y values in my data set. Also, I am not sure if the graph of y vs L^3 is linear (it looks a bit off).
I am also completely stumped for the cross sectional area question (Do you think the cross-sectional area of a metre-stick (cross sectional area is referring to the area of the rectangular face at one of the ends of the metre stick) has any effect on the vertical depression at a given extension? Discuss. Describe an experiment you might perform to test your prediction.) (I have no idea.)
Thanks
All graphs are attached.