Question

A plastic boat with a 25 cm² square cross section floats in a liquid. One by one, you place 50-g masses inside the boat and measure how far the boat extends below the surface.
Your data are as follows:
Mass added, m(g) - Depth, d(cm)
50 - 2.9
100 - 5.0
150 - 6.6
200 - 8.6
Graphing either m versus d or d versus m gives a straight line. In the graph shown above, we chose to plot d on the vertical axis and m on the horizontal axis. From the equation for the line of best fit given, determine the density rho of the liquid.
Please Explain.

Answer 1

Answer:

Explanation:

Archimedes principle states that the upward buoyant foce exrted on a body is equal to th wight o the liquid displaced.

Now, the buoyant force on the boat is given by:

$(m+m_b)g=V\rho g$

$V$ is the volum $\rho$ is the density $m_b$ is the mass of the boat and $m$ is the mass added to the boat.

$(m+m_b)g=(Sd)\rho$

$S$ is the surface area and $d$ is the depth.

$m=Sd\rho - m_b...(1)$

The equation for thebest fit linis,

$d=(0.374m/kg)m+0.11m$

Re-arrangethis equati for $m$

$m=\frac{d}{(0.374m/kg)}-\frac{0.11m}{0.374m/kg}...(2)$

From equations(1) and (2),

$Sd\rho=\frac{d}{0.374m/kg}$

the density is,

$\rho=\frac{1}{S(0.0374m/kg)}=\frac{1}{(25cm^2)(\frac{1m^2}{10^4cm^2})(0.374m/kg)}=1.069\times 10^3 kg/m^3$

Therefore, the density of the liquid is

$\rho=1.07\times 10^3 kg/m^3$