Question

NG PART 2 - Density & Mass of Air in Classroom mballoonw/string = 9.359 0.039 (+0.3 %) Mhangingstuff = 25.03y 0.039 (+ 0.1 %) Describe the method used to determine the balloon's volume. Show your calculations, and give your result with an uncertainty appropriate to your method/measurements. Zitb=126.10cm Pa = 119.00ch 26.03 ZITA= 119.00 Po = 128-40 (2003 as a- 18.94 cm b= 20.39 km P: 178.ID on = 2xy a 128.10 2018 balloon

Answer 1

Let's define the volume of the ballon as an ellipsoid. Then:

V = na?b= (18.94)? (20.39) = 30638.38cm

Using the concept of differential of a multivariate function, total uncertainty in volume can be defined as:

av - v da + % 16 = (grab) Aa + (**a")

As measured, the "radius" a and b are function of the perimeter. Then:

P=27"→"= P5 AP = f AP

Taken the perimeter of a circle as the perimeter of the ellipse (in the direction of b) is a good approximation when it is almost circular.

Both perimeters are measured with the same uncertainty, then:

Aa = Ab=P 27

Then:

1 + 3) «د، (د) (*) + (۵۴) (س) = اد

av = f (18.91) (0.03) (20.30 + 18,94) – 22.622cm

V = 30638,38 = 22.622cm

As percentage:

%AV = 22.622 100% = 0.0738% 30638,38

V = 30638.38cm +0.0738%