# Need help with homework problem - Archimede's principle

#### PHYclueless

Hello all. I am new to this site and was hoping someone could help me with a homework problem I'm trying to do.

Here's the problem:
A small ferryboat is 4.0m wide, 6.0m long. When a loaded truck pulls onto it, the boat sinks an additional 4.0cm into the river. What is the weight of the truck?

I found the area by taking 4m(6m)=24m^2. I understand I need to use the bouyancy formula B=PVG. In order to get the pressure would I take P=P+PGH?

The instructor said to take the volume and plug that into the result from Archimede's preinciple which says that the weight of the displaced fluid will equal the weight of the truck.

I don't understand what she means . Can anyone help?

Thank you so much!

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#### Galileo

Homework Helper
The weight of the displaced water resulting from the truck should equal the weight of the truck, by Archimedes' principle.

#### andrevdh

Homework Helper
The ferryboat experiences an additional upwards boyancy force, $B$, equal to the weight of the water it displaced as it sank deeper into the water when the truck pulled up onto it. This force is given by
$$B=mg$$
where $m$ is the mass of the displaced water (by the ferryboat). We can use the density of water to calculate the mass of the displaced water:
$$\rho = \frac{m}{V}$$
where $V$ is the volume of the displaced water - the volume of the ferry that sank into the water as the truck drove onto it. The mass is therefore given by
$$m=\rho V$$
changing the original formula to
$$B=\rho Vg$$

#### PHYclueless

Thank you so much!

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