Part I - DENSITY

 

1. Consider a solid metal ball of mass M and diameter D. You are given the problem of determining the density of the metal by measuring M and D.

   

   The ball's mass is measured with a simple laboratory balance, and the following results are obtained for M:

   927 gm       929 gm       925 gm       927 gm       928 gm
   929 gm       930 gm       928 gm       929 gm       927 gm
   

   The ball's diameter is measured with a vernier caliper, and the following results are obtained for D:

   5.88 cm       5.83 cm       5.83 cm       5.85 cm       5.83 cm
   5.81 cm       5.82 cm       5.84 cm       5.83 cm       5.82 cm
   

   1. Plot a histogram of the distribution of the ten values for M and find the mean value and the standard deviation of the distribution.
   2. Do the same for the distribution of D values.
   3. Determine the density of the metal and indicate the uncertainty in your result.

2. Estimate the density of your own body. Do this by first estimating the volume of your body, thinking of it as an assemblage of cylinders, spheres, truncated cones, etc., and make the measurements necessary to estimate the volume of each part. Note that the volume of a truncated cone,

   is given by .

   Your estimate of the uncertainty of the volume will not be determined by calculating a standard deviation, since you need to make each measurement only once, but rather by estimating the accuracy of each measurement and of the model. Divide your total volume into your mass (an object that weighs 2.2 lbs. on earth has a mass of 1 kg.) to obtain an estimate of your density. Compare this with the density of water. Do you float or sink in fresh water?