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Lubov Fominskaja [6]
3 years ago
15

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 meas

ure 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.
Physics
1 answer:
Crank3 years ago
5 0

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

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