Question

A boat is designed to be able to float in a fluid. The boat is constructed so that its mass is 29.6 g and its volume is 147.7 cm³. The boat will be placed in a fluid with a density of 2.4 g/mL. How much mass (in grams) can be added to the boat before it would sink?

a) 35.8 g
b) 41.2 g
c) 53.6 g
d) 62.1 g

Answer 1

The maximum amount of mass that can be added to the boat before it sinks is 353.3 grams.

Step-by-step explanation:

The first step to determining how much mass can be added to the boat before it sinks is to calculate its buoyant force. The buoyant force is equal to the weight of the fluid displaced by the boat. To find the weight of the fluid, we can use the formula: weight = density x volume. In this case, the density of the fluid is given as 2.4 g/mL and the volume of the boat is 147.7 cm³. Multiplying these values together gives us the weight of the fluid displaced, which is 353.3 grams.

To prevent the boat from sinking, the weight of the additional mass added to the boat should not exceed the buoyant force. Therefore, the maximum amount of mass that can be added is 353.3 grams.