Question

How many US pennies (mass 2.5 grams) can you stack on an ice cube having a mass of 4.20 kg floating in water, before it starts to sink? (let the density of the water be 1000 kg/m3 and the ice cube be 917 kg/m3)

Answer 1

Ice can not sink if its density is less than or equal to that of water. To solve the problem we need to know the mass that the ice must have to match the density of the water, then subtract the ice mass. That difference in mass is divided by the mass of an American cent and finally you get the number of coins that can be stacked before the block of ice sinks.

First step: The volume of the ice block will be determined

where is the density of the ice, is the mass of the ice and is the volume of the ice.  Solving for , you get

Second step: We will determine the mass that the block of ice must have so that it is the same density of the water. For this, the ice volume calculated above will be used.

Third step: Now we determine the difference between the mass of the block of ice and the mass that the ice block must have so that its density is the same as the water.

Step Four: To determine the amount of American cents that can be stacked before the ice block sinks, we divide the into the mass of a coin.