Measurements and Error. Density, Absolute Error (precision) of Volume, Relate Error of Average Volume, Absolute error if only trial 2 was performed

Question

A professor determined the mass of 3 pennies using a balance. He suspected that some of the pennies were made of pure copper. He decided to determine the density of a penny by measuring the mass and then obtaining the volume by water displacement.



Trial 1: mass (g) 3.05, Volume of Water (mL) 7.11, Volume of Water + Penny (mL) 7.40

Trail 2: mass (g) 3.11, Volume of Water (mL) 12.23, Volume of Water + Penny (mL) 35.01

Trail 3: mass (g) 3.12, Volume of Water (mL) 35.01, Volume of Water + Penny (mL) 35.37

Absolute Error Balance (g) +0.01

Absolute Error of Graduated Cylinder (mL) +0.02

1. calcuate density for each trail

2. Absolute Error (precision) of Volume (Hint: multiple trials were performed)

3. Relative Error of Average Volume

4. What would the absolute error (precision) of the density be if only trial 2 was performed (Hint: only ONE trial not multiple and density is calculated from two different types of quantities)

Answer 1

1) density is mass/volume

2) Absolute error of volume is +/- .02 ml/sqrt(3) The correction in the error for taking the average of a number of the same measurement is to divide the error by sqrt(n) where n is the number of measurements

3) Relative error in volume is the error in (3) divided by the average volume (x 100 to make is a percent)

4) The propagation of error when multiplying or dividing is the pythagorean sum of the relative errors, so

So δρ/ρ = sqrt((δV/V)² + (δm/m)²) These are from one measurement, so δV = .02 ml, and δm = .01 g. You can calculate the density, ρ and solve for δρ

Please consider a tutor. Take care.