You have a need to determine the density of a material you are working with. To

Question

You have a need to determine the density of a material you are working with. To do this you take a sample of the material and measure both the mass and volume. In order to determine how accurate your measurements are, you take a series of 100 repeated volume measurements and 50 repeated mass measurements (data below) Use this data to determine the standard deviation in your volume and mass measurements. You want to calculate how precisely you are able to determine the density using your technique. Use the standard deviations of the mass and volume, along with the propagation of error formula from Chapter 3, to determine the uncertainty in the density calculations.

34.45061

volume

24.63972

24.00228

25.34866

25.1779

2. According to Newton’s law of cooling, the time t needed for an object at an initial temperature T0 to cool to a temperature T in an environment with ambient temperature Ta is given by

t=ln(T_o-T_a )/k-ln(T-T_a )/k-

where k is a constant. Assume that for a certain type of container, k = 0.025 min1. Let t be the number of minutes needed to cool the container to a temperature of 50F. Assume that T0 = 70.1 ± 0.2F and Ta = 35.7 ± 0.1F. Estimate t, and find the uncertainty in the estimate.

Please help with these questions, thank you

                                                                                 Mass 34.4283 34.56713 34.3955 34.57939 34.4668 34.48056 34.43782 34.37694 34.48398 34.53616 34.62927 34.59796 34.71744 34.48244 34.47263 34.5264 34.49123 34.55914 34.54304 34.53277 34.53675 34.621 34.50053 34.41347 34.43871 34.43128 34.4228 34.53979 34.52034 34.2853 34.64111 34.33284 34.54592 34.64507 34.39555 34.48382 34.63265 34.35405 34.54382 34.41575 34.384 34.42543 34.4889 34.4294 34.46472 34.41785 34.551 34.53253 34.63651

34.45061

volume

24.63972

24.00228

25.34866

25.1779

24.87068 24.57649 24.69034 25.16905 25.8122 24.77193 24.5769 24.79703 24.88891 24.74429 24.85406 25.21055 25.07934 24.99635 24.91741 24.86439 25.34053 25.37188 24.94366 24.96645 24.94746 24.47161 25.57573 24.79863 24.88547 25.38867 25.262 24.78532 25.36784 24.70565 25.2448 24.54456 25.55839 24.84373 24.83697 25.06346 25.06388 24.92448 25.10571 24.67722 25.34724 24.92846 25.10474 24.97372 24.92702 24.89725 25.56002 25.26803 24.3054 25.26875 25.48815 24.67926 25.02156 25.02773 25.32607 25.09754 25.2235 25.2508 25.31917 24.72344 25.0304 25.77227 25.09242 25.22431 24.4643 25.08889 25.23771 25.66841 24.63524 24.6626 24.90152 24.63175 25.51641 24.50875 24.74331 25.28145 25.28325 24.77545 25.43451 24.22003 25.19422 24.67696 25.12151 24.6023 24.77829 24.79113 24.80764 24.48808 24.95988 24.81398 25.33991 25.6629 25.16465 24.88458 24.93551 24.49835

Explanation / Answer

1. Mean & std dev are as follows:

To compute the SD of density (uncertainty in measurement) following formula is used:

VAR(X/Y)=(2Y2X+2X2Y)/4Y

Excel formula:

2. Estimation of time t=

excel formula:

Mass Volume Mean 34.495728 24.99293 SD 0.090667869 0.344335

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