An aluminum boat made in science class has a mass of 15 g and a volume of
450.00 cm?. If one penny has a mass of 2.50 g, how many pennies can be added to the boat before it sinks in water? Explain how you determined your answer.
To determine how many pennies can be added to the boat before it sinks, we need to calculate the buoyant force exerted on the boat by the water.
First, we need to find the density of the aluminum boat. Density is defined as mass divided by volume:
Density = mass/volume
Given that the mass of the boat is 15 g and the volume is 450.00 cm³, we can calculate:
Density = 15 g / 450.00 cm³ = 0.033 g/cm³
The density of water is approximately 1 g/cm³, so the boat will float as long as its density is less than that of water.
Next, let's determine the mass of the boat in grams. 1 cm³ of water is equivalent to 1 gram. So, the mass of the boat is also 450.00 grams.
Now, let's add pennies to the boat. Each penny has a mass of 2.50 g.
To calculate the total mass of the boat and the pennies, we add the mass of the boat to the mass of the pennies:
Total Mass = Mass of Boat + (Number of Pennies * Mass of Each Penny)
Let's assume that we can add x pennies to the boat before it sinks.
Total Mass = 450.00 g + (x * 2.50 g)
For the boat to float, the density of the boat with the added pennies should be less than the density of water.
Density of Boat + Pennies < Density of Water
(Mass of Boat + Pennies) / Volume of Boat < Density of Water
(450.00 g + (x * 2.50 g)) / 450.00 cm³ < 1 g/cm³
Simplifying the equation:
450.00 g + (x * 2.50 g) < 450.00 cm³
450.00 + (x * 2.50) < 450.00
x * 2.50 < 0
This last inequality shows that we cannot add any number of pennies to the boat without violating the laws of physics. Therefore, the boat cannot support any pennies and will sink.