The Department also wants to know how well lengths (sizes of objects) and distan

Question

The Department also wants to know how well lengths (sizes of objects) and distances (between points) can be measured by a typical person using a meter stick. Of particular interest are distances on the order of 10 cm or so, a small fraction of a meter. You have a meter stick and a block of wood. One way to assess measurement variability would be for each group member independently to make the most careful measurement possible of the length, width and depth of the wooden block. Use this method to get the density of the wooden block and an estimate of the measurement errors involved. 1. Prediction question: Do you think that the uncertainty in measuring lengths, widths, etc. of a wooden block will turn out to be limited mostly by the smallest division on the meter stick, that is to say a millimeter? If not, why not? 2. Method question: How can you study the variability in measurement values for measurements of the same block dimension by the same person multiple times? How about measurements of the same dimension but by different people? Plan: Make up a simple plan for measuring length, width and depth of your wooden block by the members of your group. At the same time, you should figure out the statistics of measurement error. Each member should compute the volume of the block, including an error estimate, measure the mass and finally compute the density. Each member should thus arrive at a value for the density of wood, together with an error estimate. Record your plan here.

Explanation / Answer

1. The mimimum distance that can be measured would be the smallest division on the metre scale. So uncertianity in measuring any length will be 1mm if that is the smallest division on metre scale.

2. When different people measure the same block, or the same person measures the value again and again, the variations in measurements arise from human errors like parallax error , random errors etc. Taking a lot of measurements and then taking an average reduces this type of erorr whiose magnitude can only be guessed by measuring the average anf finding standard deviation of the individiually measuyred values

3. So the plan goes like this

length (l), width(w) and height (h) of the wooden block have to be measured by diffferent people, their average has to be found

then the volume of block is given by l*w*h

assuming the least count of the metre scale to be the uncertianity

error in volume measurement will be dV/V = sqroot((dl/l)^2 + (dw/w)^2 + (dh/h)^2)

where dh = dl = dw = least count of the scale

now for a given mass

density, rho = mass/V

so error in rho measurement d(rho)/rho = dV/V [ for accurate measurement of mass]

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