Measuring the Density of Metal Cylinders--Introduction to propagated error calculations
Introduction: In this lab, we learned to use vernier calipers and micrometers to measure objects' dimensions. We used the measurement we obtained with vernier calipers and micrometers to calculate the density of the object, and determine the propagated error.
Apparatus:
This device can measure length of object very precisely. We used this apparatus to obtain the dimensions of object in this lab.
Procedure and data:
First of all, we need to find out the mass of our three objects: copper cylinder, aluminum cylinder, and iron cylinder.
Copper cylinder's mass, 56.7 g
Aluminum cylinder's mass, 20.8 g
Iron cylinder's mass, 61.4 g
Then we used the caliper to measure dimensions of three metal cylinders. and we get the following measurement with uncertainty.
With dimensions of each metal cylinder, we can use the following equations to find volume and density of each of them.
Volume = π(d^2)*h
Density = mass/ volume
And use the following formula to find propagated error:
Result:
Thus, we conclude that the density included propagated error of our 3 metal cylinder to be:
(8.76±0.019)*10^3 kg/m^3
(2.68±0.020)*10^3 kg/m^3
(7.55±0.018)*10^3 kg/m^3
This result should be acceptable since our propagated error is very small.
Introduction:
In this activity, we will try to solve for an unknown mass in a system that was built at equilibrium state. The one we tried to solve was unknown mass #8, and it was the following system:
Protractor: We need the angle of the tension force exert on the unknown mass, in order to calculate the weight of unknown mass.
Data and Calculation:
Following picture is the measured data that we needed to find out the weight of the unknown mass:
Calculation to obtain mass:
With all the calculation we did above, the unknown mass with uncertainty is (1.39+-0.07)kg.
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