course Phy 201
Again sorry for this being out of order for the assignments!
Alternative to Step-by-Step instructions:This section consists of an alternative to the step-by-step instructions given below. You may choose whether to do the experiment by these alternative instructions, or by the subsequent step-by-step instructions.
If you prefer follow this alternative, which asks you to design and conduct your own investigation, you may insert into the preceding box a text document with your answers to the following questions, and a concise but comprehensive explanation of the basis for your answers. If you have questions, you may submit a partial document.
• At each level of reduction, on the average, by what factor would you multiply or divide a measurement made by one of the ruler copies in order to express the measurement in standard centimeters?
o For each ruler I only measured to 10 centimeters. To measure accurately I used a standard centimeter ruler along with each of the copied rulers to see the difference in each.
o Ruler Copy: Suppose to be: Actual size:
o Full 10 cm 9.85 cm
o Single 10 cm 6.2 cm
o Double 10 cm 1.2 cm
o Triple 10 cm 0.7 cm
Therefore, for each ruler I took the actual size divided by what it was supposed to be.
9.85cm/ 10cm = 0.985
The same strategy applies to each ruler copy.
• To measure the length of an object with one of the rulers you would find the difference in the positions of its two ends, and multiply this by the conversion factor you determined in the first step. This would give you the measurement in standard centimeters.
o Ruler Copy: Suppose to be: Actual size: % Smaller:
o Full 10 cm 9.85 cm 1.5
o Single 10 cm 6.2 cm 38
o Double 10 cm 1.2 cm 88
o Triple 10 cm 0.7 cm 93
Therefore, for each ruler I took the actual size divided by what it was supposed to be and multiplied by 100. For example,
9.85cm/ 10cm = 0.985 * 100 = 98.5%
Next I subtract the number obtained from 100,
100% – 98.5% = 1.5%
This means that the full size ruler is 1.5% smaller than the actual size of a standard ruler measured in centimeters. The same strategy applies to each ruler copy.
The question posed here is
By what factor would you multiply or divide a measurement made by one of the ruler copies in order to express the measurement in standard centimeters?'
This means that for each level of reduction, you need a single number which, when multiplied by a measurement made with that ruler, gives the measurement in standard centimeters.
For example if something measures 8.3 cm on the triply reduced ruler, multiplying by this factor would give the actual measurement in centimeters.
What would be the actual length of an object which spans 8.3 cm on the triply reduced ruler? By what number would you multiply 8.3 to get this result?
If you were to cut out a paper rectangle with dimensions about 1.2 cm by 8 cm, and in this manner measure the length of each of its edges as precisely as possible, using rulers at each level of reduction, which level of reduction would give you the most accurate results and which the least, and why?
The full sized ruler would give the most accurate results because it has an uncertainty of only 1.5% which is obviously the lowest percentage among all of the rulers. The least accurate ruler copy is the triply reduced copy. The copy has a distortion of 93% from what a normal centimeter reads.
Would your answer be the same for all measurements? Why or why not?
Yes the answer would be the same for all measurements because the copies do not change. It doesn’t matter what you are measuring; the full size will always be the most accurate of the copies and the triply reduced copy will always be the least accurate.
What do you think would be the percent error for a length measurement at each level of reduction?
o Ruler Copy: Suppose to be: Actual size: % Smaller:
o Full 10 cm 9.85 cm 1.5
o Single 10 cm 6.2 cm 38
o Double 10 cm 1.2 cm 88
o Triple 10 cm 0.7 cm 93
What do you think would be the percent error for a width measurement at each level of reduction?
Ruler Copy: Percent error:
Full 30 %
Single 56%
Double 72%
Triple 79%
The instructions say that to take a measurement, you multiply the measurement on the paper ruler by the factor you found in the first part. This will convert your measurement into standard centimeters. The question here is of the measurement obtained by this method, which if you have found the factor accurately should give a result very close to the actual measurement in centimeters.
You have answered the question as if the reading on the ruler was not multiplied by the necessary factor; in this case your answer would be correct. But the measurement includes multiplication by the factor.
• If you actually cut out the rectangle, you would be unable to cut a perfect rectangle. Specifically, focus on the difference between your two width measurements.
At which level of reduction would you expect your data to give you the most precise indication of this difference, and why?
According to my data, the full sized copy would give a more precise indication of the difference of my triangle because it has the least amount of percentage of reduction; 30%.
• Due to optical distortions, measurements made in one area of a given copy might differ from measurements made in another area.
For which level of reduction do you observe the most optical distortion between different locations of the page?
I think the triply reduced copy gives the most optical distortion between different locations on the page because it is so much smaller. For someone with bad eyes it almost appears that the tiny centimeters ticks on the page are all running together.
What is the maximum percent error you would expect between the same measurement made at different locations on this page?
I would say about 1% error because that is the average amount of percent error for most distortions. Most people can read the centimeter ticks within at least .1 higher or .1 lower of the reading.
If you have answered these questions satisfactorily you may submit your document. If you prefer to use the step-by-step instructions, you may of course do so.
You need to revise your answers in terms of the measurement process as defined in the questions. You have not correctly addressed the question of precision or optical distortion. Optical distortion is different that reduction factor or magnification factor.