Answer to Question #88015 in Molecular Physics | Thermodynamics for gc

Question

A boat (with a flat bottom) and its cargo weigh 7,400 N. The area of the boat's bottom is 3 m2. How far below the surface of the water is the boat's bottom when it is floating in water?

Answer 1

Archimedes' principle - weight of displaces fluid equals to weight of object.

Density of water $\rho = 1000\, \text{kg m}^{-3}$

Gravity acceleration $g= 9.8\, \text{ms}^{-2}$

$$F = 7400\, \text{N} = m\cdot g = \rho S h g$$

$$h= \frac{F}{\rho S g} = \frac{7400}{1000\cdot 3 \cdot 9.8}\, \text{m} = 25\, \text{cm}$$

Answer: 25 centimeter