**Example 3**:

Figure above shows an empty boat floating at rest on water. Given that the mass of the boat is 150kg. Find

- the upthrust acting on the boat.
- The mass of the water displaced by the boat.
- The maximum mass that the boat can load safely if the volume of the boat at the safety level is 3.0 m³.

**Answer**:

a. According to the principle of flotation, the upthrust is equal to the weight of the boat.

Upthrust,

F = Weight of the boat

= mg = (150)(10) = 1500N

b. According to the Archimedes' Principle, the weight of the water displaced = Upthrust

Weight of the displaced water,

W = mg

(1500) = m(10)

m = 150kg

c.

Maximum weight can be sustained by the boat

$$\begin{array}{l}F=\rho Vg\\ F=(1000)(3)(10)=30,000N\end{array}$$

Maximum weight of the load

= Maximum weight sustained - Weight of the boat

= 30,000 – 1,500 = 28,500N

Maximum mass of the load

= 28500/10 = 2850 kg