When an open-faced boat has a mass of 5750 kg , including its cargo and passengers, it floats wi

step 1 Okay, so in this problem we have a boat floating on the water. Let's put here the boat and he's

When an open-faced boat has a mass of 5750 kg , including...

When an open-faced boat has a mass of 5750 $\mathrm{kg}$ , 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?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Archimedes' Principle

This principle states that any object wholly or partially immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid that is displaced. It is fundamental in calculating how much of a floating object is submerged and in determining the displaced volume based on the object’s mass and the fluid’s density.

Buoyancy Equilibrium

For an object floating in equilibrium, the weight of the object exactly equals the weight of the displaced fluid. When a fixed volume of the object is submerged, this balance of forces ensures the object remains afloat. Adjusting the mass of the object will change the submerged fraction required to balance its weight, which is key in solving problems involving weight reduction to achieve different submersion levels.

Fluid Density and Displacement

The density of the fluid, in this case freshwater, relates mass and volume and is used to convert between the weight of the displaced fluid and its volume. Knowing the density allows one to calculate how much volume of water must be displaced to support a given mass, making it essential in determining both the overall volume of a floating structure and the impact of reducing its mass for safety or performance reasons.

Transcript

Please give Ace some feedback