A little aluminum boat (mass of 14.50g) has a volume of 450.00cm3. The boat is placed in a small pool of water and carefully filled with pennies. If each penny has a mass of 2.50g, how many pennies can be added to the boat before it sinks?
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To find out how many pennies can be added to the boat before it sinks, we need to determine the buoyant force and the weight of the boat with the added pennies.
1. Begin by calculating the weight of the boat:
Weight of the boat = mass of the boat × acceleration due to gravity
The mass of the boat is given as 14.50g, which we need to convert to kg for consistency.
1 kg = 1000 g
Mass of the boat = 14.50g ÷ 1000 = 0.0145 kg
The acceleration due to gravity is approximately 9.8 m/s².
Weight of the boat = 0.0145 kg × 9.8 m/s² = 0.1421 N
2. Next, calculate the buoyant force acting on the boat:
Buoyant force = density of water × volume of the boat × acceleration due to gravity
The density of water is approximately 1 g/cm³ or 1000 kg/m³.
Density of water = 1000 kg/m³
Volume of the boat is given as 450.00 cm³, which we need to convert to m³ for consistency.
1 m³ = 1,000,000 cm³
Volume of the boat = 450.00 cm³ ÷ 1,000,000 = 0.000450 m³
Buoyant force = 1000 kg/m³ × 0.000450 m³ × 9.8 m/s² = 4.41 N
3. Now, we can determine the maximum weight the boat can hold without sinking.
Maximum weight = Weight of the boat + Buoyant force
Maximum weight = 0.1421 N + 4.41 N = 4.5521 N
4. Finally, find the number of pennies that can be added to the boat by dividing the maximum weight by the weight of a single penny.
Number of pennies = Maximum weight ÷ weight of a penny
The weight of a penny is given as 2.50g, which we need to convert to kg for consistency.
Weight of a penny = 2.50g ÷ 1000 = 0.0025 kg
Number of pennies = 4.5521 N ÷ 0.0025 kg = 1820.84
Since we cannot have a fraction of a penny, the maximum number of pennies that can be added to the boat before it sinks is 1820.
Archimedes Principle states that a body is buoyed up by a force equal to the weight of the water displaces. The volume of the boat is 450 cc so it can displace that much. How much will 450 cc water weigh? How many pennies to overcome that?
175pennies
180
A little aluminum boat (mass of 14.50g) has a volume of 450.00cm3. The boat is placed in a small pool of water and carefully filled with pennies. If each penny has a mass of 2.50g, how many pennies can be added to the boat before it sinks?
Answer : 175pennies