#6 Determining density of cylinders/mass of suspended object

Determining density of cylinders/mass of suspended object

introduction:

After we learn how to read vernier caliper, we try to measure the cylinders diameter and height. Then measure the mass to find the density. Knowing that every thing we measure have error, we estimates their error and calculate it to find the error of density.

Next, we use two spring scale to determination of an unknown. 

those are the materials we have in this lab
















Thesis:
(1)We estimate the error of mass are + or - 0.1g and the height and diameter are + or -0.01cm.
collect the date and use the method(I will tell in calculate part) to calculate the density. 
(2)find the vertical and horizontal component to find the mass the error estimate of degree and force are + or - 0.1

Calculate:

(1)

these are the date we measure

to find the density(P) error we all of the estimate error then find it by three different way

1.
∂P ∂P ∂P dP = —— dm + —— dr + —— dh ∂m ∂r ∂h
find every single number and fill in

2.

∂m ∂r ∂h dP/p = —— + —— + —— m r h

this on is what we use. First if all, calculate the density without the estimate error
P=mass/volume = 4m/πhd^2      p=8.8126   ,   2.7406    ,   7.7417 g/cm^3
the 1 dp= (0.1/56+2*0.01/1.28+0.01/5) *8.8126= 0.1711
      2 dp=(0.1/27+2*0.01/2.6+0.01/4.9)*2.7406=0.0368
      3 dp=(0.1/58.7+2*0.01/0.99+0.01/9.85)*7.7417=0.1774
3.
using the logarithm method
p= m/πhd^2  using log and take differentials

(2)

the left hand spring got 4N with 51 degree and right hand spring got 3N with 46 degree.

We can find mass= 4*cos51。+3*cos46。= 4.60N

and then 4.6/9.8=0.47(kg)
F= F1*cos51。+F2*cos46。
dF=(0.1/4+0.1/51+0.1/3+0.1/46)*0.47=0.0625*0.47=0.03












result:
(1)the density are 
8.8126±0.1711   ,   2.7406±0.0368    ,   7.7417±0.1774

(2) mass is 0.47±0.03kg