Respuesta :
Answer:
[tex]\rho=995.50\ kg.m^{-3}[/tex]
[tex]\bar w=9765.887\ N.m^{-3}[/tex]
[tex]s=0.9955[/tex]
Explanation:
Given:
- volume of liquid content in the can, [tex]v_l=0.355\ L=3.55\times 10^{-4}\ L[/tex]
- mass of filled can, [tex]m_f=0.369\ kg[/tex]
- weight of empty can, [tex]w_c=0.153\ N[/tex]
So, mass of the empty can:
[tex]m_c=\frac{w_c}{g}[/tex]
[tex]m_c=\frac{0.153}{9.81}[/tex]
[tex]m_c=0.015596\ kg[/tex]
Hence the mass of liquid(soda):
[tex]m_l=m_f-m_c[/tex]
[tex]m_l=0.369-0.015596[/tex]
[tex]m_l=0.3534\ kg[/tex]
Therefore the density of liquid soda:
[tex]\rho=\frac{m_l}{v_l}[/tex] (as density is given as mass per unit volume of the substance)
[tex]\rho=\frac{0.3534}{3.55\times 10^{-4}}[/tex]
[tex]\rho=995.50\ kg.m^{-3}[/tex]
Specific weight of the liquid soda:
[tex]\bar w=\frac{m_l.g}{v_l}=\rho.g[/tex]
[tex]\bar w=995.5\times 9.81[/tex]
[tex]\bar w=9765.887\ N.m^{-3}[/tex]
Specific gravity is the density of the substance to the density of water:
[tex]s=\frac{\rho}{\rho_w}[/tex]
where:
[tex]\rho_w=[/tex] density of water
[tex]s=\frac{995.5}{1000}[/tex]
[tex]s=0.9955[/tex]
Explanation:
The given data is as follows.
Volume of pop in can, V = [tex]355 \times 10^{-6} m^{3}[/tex]
- Mass of a full can of pop is as follows.
W = mg
= [tex]0.369 \times 9.81[/tex]
= 3.6198 N
Weight of empty can, [tex]w_{1}[/tex] = 0.153 N
- Now, weight of pop in the can is calculated as follows.
[tex]w_{2} = W - w_{1}[/tex]
= 3.6198 - 0.153
= 3.467 N
- Calculate the specific weight of the liquid as follows.
[tex]\gamma = \frac{\text{weight of liquid}}{\text{volume of liquid}}[/tex]
= [tex]\frac{3.467}{355 \times 10^{-6}}[/tex]
= 9766.197 [tex]N/m^{3}[/tex]
- Density of the fluid is calculated as follows.
[tex]\rho = \frac{\gamma}{g}[/tex]
= [tex]\frac{9766.197}{9.81}[/tex]
= 995.535 [tex]kg/m^{3}[/tex]
- Now, specific gravity of the fluid is calculated as follows.
S.G = [tex]\frac{\text{density of liquid}}{\text{density of water}}[/tex]
= [tex]\frac{\rho}{\rho_{w}}[/tex]
= [tex]\frac{995.535}{1000}[/tex]
= 0.995
