Question

So I have a question regarding my first advanced physics Lab. I missed the first day so I need quite a bit of guidance. We had to measure the density of materials, in this case a cylindrical rod, and we were given a cylindrical rod, string, balance and meter stick. Note that one side of our rod was cut and one side was round (shown in the pic below). Below is the calculations we did and the results we got for the first trial. (we had 3 trials)For my part in the Lab report, I need to do UNCERTAINTY ANALYSIS and DISCUSSION. I was wondering if anyone could help me and guide me a little bit with this.

,0131 /n ,979m L -97. 2 474 49 48, L2 1 th 5 co 383 kg P383 16. | |引3110 フ[c dス9

Answer 1

here the uncertainty in the measurement can be determined right from the volume analysis.

That is The length and diameter of the cylinder. The simplest way to determine the uncertainty of certain measurement is the graduation in the instrument used.

For example, if a scale measures the value l = 0.1 cm then the uncertainty is
Here the uncertainty in the measurement can be determined right from the volume analysis. That is The length and diameter of the cylinder. The simplest way to determine the uncertainty of certain measurement is the graduation in the instrument used. For example, if a scale measures the value l = 0.1 cm then the uncertainty is plusminus 0.05cm. Likewise, the uncertainty in diameter analysis is plusminus 0.005cm thus the uncertainty in volume is pi (plusminus 0.005^2/2)(0.05) = plusminus 0.98125 times 10^-6cm^3 or plusminus 0.98m^3 Likewise in trail 1: the formula is, = m_0 = m_1 L_1/L_o uncertainty in mass is plusminus 0.25Kg (assuming the mass scale is graduated as 1Kg to 5Kg with the smallest reading as 0.5 Kg) thus error in center of mass = 0.25Kg Hence the uncertainty in density calculation is = 0.25Kg/plusminus 0.98m^3 = 0.255Kg/m^3 this is the uncertainty in the density of the rod for Trail 1. Likewise for the remaining trails the uncertainty can be calculated. the percentage error is (0.255/2916.93)
. Likewise, the uncertainty in diameter analysis is

thus the uncertainty in volume is

Likewise in trail 1:

the formula is,

uncertainty in mass is (assuming the mass scale is graduated as 1Kg to 5Kg with the smallest reading as 0.5 Kg)

thus error in center of mass =

Hence the uncertainty in density calculation is

this is the uncertainty in the density of the rod for Trail 1.

Likewise for the remaining trails the uncertainty can be calculated. the percentage error is (0.255/2916.93) x 100 = 0.008% error.

Since the error percentage in experiments should be less than 0.5%, thus the calculation for trail 1 is correct.

VOLUME CORRECTION:

volume =

therefore volume of rounded part = 0.0229 x 10^-4

total volume = 1.31 + 0.0229 x 10^-4 = 1.332 x 10^-4 m³

now coming to the uncertainty part

uncertainty in volume changes to 0.98 + 0.032 m³

= 1.012 m³

density (uncertainty) = 0.255 Kg/ 1.012 m³

= 0.251 Kg/m³

Answer 2

here the uncertainty in the measurement can be determined right from the volume analysis.

That is The length and diameter of the cylinder. The simplest way to determine the uncertainty of certain measurement is the graduation in the instrument used.

For example, if a scale measures the value l = 0.1 cm then the uncertainty is
Here the uncertainty in the measurement can be determined right from the volume analysis. That is The length and diameter of the cylinder. The simplest way to determine the uncertainty of certain measurement is the graduation in the instrument used. For example, if a scale measures the value l = 0.1 cm then the uncertainty is plusminus 0.05cm. Likewise, the uncertainty in diameter analysis is plusminus 0.005cm thus the uncertainty in volume is pi (plusminus 0.005^2/2)(0.05) = plusminus 0.98125 times 10^-6cm^3 or plusminus 0.98m^3 Likewise in trail 1: the formula is, = m_0 = m_1 L_1/L_o uncertainty in mass is plusminus 0.25Kg (assuming the mass scale is graduated as 1Kg to 5Kg with the smallest reading as 0.5 Kg) thus error in center of mass = 0.25Kg Hence the uncertainty in density calculation is = 0.25Kg/plusminus 0.98m^3 = 0.255Kg/m^3 this is the uncertainty in the density of the rod for Trail 1. Likewise for the remaining trails the uncertainty can be calculated. the percentage error is (0.255/2916.93)
. Likewise, the uncertainty in diameter analysis is

thus the uncertainty in volume is

Likewise in trail 1:

the formula is,

uncertainty in mass is (assuming the mass scale is graduated as 1Kg to 5Kg with the smallest reading as 0.5 Kg)

thus error in center of mass =

Hence the uncertainty in density calculation is

this is the uncertainty in the density of the rod for Trail 1.

Likewise for the remaining trails the uncertainty can be calculated. the percentage error is (0.255/2916.93) x 100 = 0.008% error.

Since the error percentage in experiments should be less than 0.5%, thus the calculation for trail 1 is correct.

VOLUME CORRECTION:

volume =

therefore volume of rounded part = 0.0229 x 10^-4

total volume = 1.31 + 0.0229 x 10^-4 = 1.332 x 10^-4 m³

now coming to the uncertainty part

uncertainty in volume changes to 0.98 + 0.032 m³

= 1.012 m³

density (uncertainty) = 0.255 Kg/ 1.012 m³

= 0.251 Kg/m³