- #1

TomK

- 69

- 14

- Homework Statement
- Archimedes' Principle.

- Relevant Equations
- upthrust = weight of water displaced

density = mass/volume

volume of object submerged = volume of water displaced

mass x g = weight

I was asked this question:

Assume you're sitting in a boat (you and the boat, together, are a mass M) which also contains a heavy object (of mass m). The boat (inc. you and the heavy object) is floating in a pond (a fixed body of water, rather than open sea). If you throw the object overboard (it sinks) and remain seated in the boat, will the water level of the pond rise, fall, or stay the same?

Below, I have given my proposed answer, and I wanted to ask if it made sense:

When the object is in the boat: weight of displaced water = (M+m)g = (M+Vd)g

This is because masses M and m are both floating.

volume x density = mass

d = density of object

V = volume of objectWhen the object is thrown overboard: weight of displaced water = (M+1000V)g

This is because the volume of submerged object = volume of water displaced by object.

Assumes density of water = 1000kgm^-3Comparing the two equations: We know d (density of object) is greater than 1000, because the object sinks in water.

When the object is thrown overboard, the weight (and volume) of displaced water decreases.

Therefore, the water level must have fallen.

Is this the correct conclusion to make? Could you prove this scenario in-practice, or would your boat not stay afloat with the object in it?

Assume you're sitting in a boat (you and the boat, together, are a mass M) which also contains a heavy object (of mass m). The boat (inc. you and the heavy object) is floating in a pond (a fixed body of water, rather than open sea). If you throw the object overboard (it sinks) and remain seated in the boat, will the water level of the pond rise, fall, or stay the same?

Below, I have given my proposed answer, and I wanted to ask if it made sense:

When the object is in the boat: weight of displaced water = (M+m)g = (M+Vd)g

This is because masses M and m are both floating.

volume x density = mass

d = density of object

V = volume of objectWhen the object is thrown overboard: weight of displaced water = (M+1000V)g

This is because the volume of submerged object = volume of water displaced by object.

Assumes density of water = 1000kgm^-3Comparing the two equations: We know d (density of object) is greater than 1000, because the object sinks in water.

When the object is thrown overboard, the weight (and volume) of displaced water decreases.

Therefore, the water level must have fallen.

Is this the correct conclusion to make? Could you prove this scenario in-practice, or would your boat not stay afloat with the object in it?