A student investigates the properties of thin rectangular slabs of paraffin wax that…

PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

A student investigates the properties of thin rectangular slabs of paraffin wax that all have the same thickness

t = 1.00\,\text{cm}

but different top-surface areas

A

. The student measures the mass

m

of each slab. The data are shown below.

Top-Surface Area $A$ (cm $^{2}$ )	Mass $m$ (g)
4.0	3.4
16.0	13.6
36.0	30.6
64.0	54.4

Assume the thickness and the density of the wax remain constant for all samples. (a) Show that the volume

V

of each slab can be written as

V = A t

, and then calculate

V

for each of the four samples. (b) Using the calculated volumes and the given masses, construct a graph of mass versus volume on appropriately scaled axes. Draw a best-fit straight line and write its equation in the form

m = m_{0} + \left(\text{slope}\right) V

. (c) From your best-fit line, determine the density of the paraffin wax in both g/cm

^{3}

and kg/m

^{3}

. (d) The accepted density of paraffin wax is

0.90\,\text{g/cm}^{3}

. Calculate the percent error of your experimental value and comment on one possible experimental source of error that could account for the discrepancy.

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