Question

9 fig. 1.1 shows a plastic water barrel. the barrel is full of water.

(a) the water barrel contains 0.050 m³ of pure water. the density of pure water is 1000 kg/m³.

calculate the mass of pure water in the barrel.

mass of water = ………………………………………………… kg 3

(b) the density of sea water is 1030 kg/m³. the density of the plastic is 1000 kg/m³. use this
information and the information in (a) to state and explain whether the full barrel will float in
sea water.

statement …………………………………………………………………………………………………………

explanation …………………………………………………………………………………………………………

Explanation:

(a) Step - by - Step Format:

Step1: Recall the density formula

The formula for density is \(
ho=\frac{m}{V}\), where \(
ho\) is density, \(m\) is mass, and \(V\) is volume. We can rearrange it to find mass: \(m =
ho\times V\).

Step2: Substitute the given values

Given \(
ho = 1000\space kg/m^{3}\) and \(V=0.050\space m^{3}\). Then \(m=
ho\times V=1000\times0.050\).

Step3: Calculate the mass

\(m = 50\space kg\)

The density of the barrel - water system (assuming the plastic has a small volume compared to water, and using the density formula for mixtures. If we consider the total mass \(m_{total}=m_{plastic}+m_{water}\) and total volume \(V_{total}\approx V_{water}\) (since the barrel is full of water). If the plastic has a volume \(V_p\) and density \(
ho_p = 1000\space kg/m^{3}\), and water has \(m_w=50\space kg\) (\(V_w = 0.050\space m^{3}\)). Let's assume the mass of plastic is \(m_p=
ho_pV_p\). The total density \(
ho_{total}=\frac{m_p + m_w}{V_p+V_w}\). Since \(
ho_p = 1000\space kg/m^{3}\) and \(
ho_{sea - water}=1030\space kg/m^{3}\), and the water in the barrel has \(
ho = 1000\space kg/m^{3}\) (and plastic density is \(1000\space kg/m^{3}\)), the total density of the barrel - water system \(
ho_{total}<1030\space kg/m^{3}\) (because adding plastic of density \(1000\space kg/m^{3}\) to water of density \(1000\space kg/m^{3}\) will keep the density at most \(1000\space kg/m^{3}\) (if plastic volume is non - zero but small)). According to Archimedes' principle, an object floats if its density is less than the density of the fluid it is placed in.

The density of the barrel - water system (approximate density of water in the barrel \(1000\space kg/m^{3}\) plus plastic of density \(1000\space kg/m^{3}\)) is less than the density of sea water (\(1030\space kg/m^{3}\)). An object floats when its density is less than the density of the surrounding fluid (Archimedes' principle).

Answer:

\(50\)

(b) Answer - Explanation Format