a) Density of the liquid: \(823.5kg/m^3\)
b) Weight of the liquid: 1372 N
Explanation:
Translation of the text:
"A full tank with liquid weighs 175kg. Which is 5 times the mass of the empty vessel. Knowing that the inside volume of the vessel is 0.17kl, calculate:
a) the density of the liquid;
b) the weight of the liquid."
a)
We know that the full tank with liquid has a total mass of M = 175 kg. We can write the total mass as
\(M=m_L + m_V\) (1)
where
\(m_L\) is the mass of the liquid
\(m_V\) is the mass of the vessel
We also know that the total mass M is 5 times the mass of the empty vessel, so we have:
\(M=5m_V\\m_V=\frac{M}{5}=\frac{175}{5}=35 kg\)
which is the mass of the empty vessel.
Therefore, we can find the mass of the liquid only using (1):
\(m_L=M-m_V=175-35=140 kg\)
The density of the liquid is given by
\(d=\frac{m}{V}\)
where
m = 140 kg (mass of the liquid)
V = 0.170 kL = 170 L = \(0.170 m^3\) (volume of the liquid, which is equal to the volume of the vessel)
So we get
\(d=\frac{140}{0.170}=823.5kg/m^3\)
b)
The weight of a body is given by
\(F=mg\)
where
m is its mass
g is the acceleration due to gravity
For the liquid in this problem, we have
m = 140 kg (mass)
\(g=9.8 m/s^2\) (acceleration due to gravity)
Therefore, its weight is
\(F=(140)(9.8)=1372 N\)
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