When an open-faced boat has a mass of 5750 kg, including its cargo and passengers, it floats with the water just up to the top of its gunwales (sides) on a freshwater lake.

(a) What is the volume of this boat?

(b) The captain decides that it is too dangerous to float with his boat on the verge of sinking, so he decides to throw some cargo overboard so that 20% of the boat’s volume will be above water. How much mass should he throw out?

Question

22-01-2024
Physics

High School

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When an open-faced boat has a mass of 5750 kg, including its cargo and passengers, it floats with the water just up to the top of its gunwales (sides) on a freshwater lake.

(a) What is the volume of this boat?

(b) The captain decides that it is too dangerous to float with his boat on the verge of sinking, so he decides to throw some cargo overboard so that 20% of the boat’s volume will be above water. How much mass should he throw out?

Answer :

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MattZayn9 MattZayn9 · Answer 1 · 2024-09-13T04:59:15-04:00

The volume of the boat is 5.75 m3. To ensure that 20% of the volume remains above water, the captain should throw out 1150 kg of mass. This is based on the principle of flotation and the density of freshwater.

When an open-faced boat has a mass of 5750 kg and it floats with water just up to the top of its gunwales, the boat is displacing a volume of water with a weight equal to its own weight. This follows from the principle of flotation, which states that a floating object displaces a weight of fluid equal to its own weight.

To find the volume of the boat (a), we use the density of freshwater (approximately 1000 kg/m3) and the mass of the boat to calculate the displaced volume, which is equal to the volume of the boat itself. The formula for this is V = m/ρ, where 'm' is the mass and 'ρ' is the density of freshwater. So, the boat's volume would be 5750 kg / 1000 kg/m3 which equals 5.75 m3.

For part (b), if the captain wants 20% of the boat's volume to be above water after throwing some cargo overboard, he would have to reduce the mass of the boat so that only 80% of its original volume is submerged. Since the submerged volume is directly proportional to the mass, the altered mass (mnew) can be found using 0.8 * original mass, which gives us 0.8 * 5750 kg = 4600 kg. Therefore, the mass to throw out is the difference between the original mass and the new mass: 5750 kg - 4600 kg = 1150 kg.