Ship in a Tub
A toy ship is floating in a cylindrical container 10 centimeters in diameter that is partially filled with water. How much will the level of the water rise if a silver teddy bear weighing 100 grams is loaded on the ship? By the way, silver has a density of 10.49 g/cc.
A 100 gram weight added to the ship will cause the ship to go lower into the water and displace an equal weight of water to continue floating (Archimedes principle of buoyancy). According to the Merk Index, the density of water is 0.997 grams/cubic centimeter at room temperature and, therefore, the volume of water displaced is 100 g / (0.997 g/cm3) = 100.3 cc. The density of the object loaded on the ship is not relevant.
The diameter of the cylindrical container is 10 cm and its volume is calculated by the formula V = πr2h, where r = 5 cm. Solving for h we can calculate the change in water level caused by a volume change V of 100.3 cc.
h = V/(πr2) = 100.3 cm3 / (3.1416 × 25 cm2) = 1.28 cm
Your Answer
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