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Answer to Question #6275 in Mechanics | Relativity for Bradley

Question #6275
A ferry boat is 6.1 m wide and 7.1 m long. When a truck pulls onto it, the boat sinks 7.59 cm in the water.
What is the weight of the truck? The acceleration of gravity is 9.81 m/s2 .
Answer in units of N
Expert's answer
There are two forces acting on the boat without a truck:
1) Gravitational
force F = g * m,
where m is the mass of a boat
2) Archimedian
force Fa = pho * g * V,
where pho=1000kg/m^3 is the density of the
water, and
V is the volume of boat below the level of
water.

Since the level of boat is fixed these forces are equal
F =
Fa

When the truck pulls on the boat then the forces will change by the
same amount: dF = dFa,
and
dF = Mg, where M is the mass of a
truck,
dFa = pho g V1, where V1 is the displaced volume of water:

V1 = 6.1 * 7.1 * 0.0759 = 3.2872 m^3

Hence the mass of the truck
is
M = pho g V1 / g = pho * V1 = 1000 * 3.2872 = 3287.2 kg

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