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

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

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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