Archimedes Principle - Example 3

Example 3:

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

1. the upthrust acting on the boat.
2. The mass of the water displaced by the boat.
3. 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