# Does Throwing an Object Overboard Affect Pond Water Level?

• TomK
In summary, when an object is in a boat (with itself and the water it displaces), the water level changes when the object is thrown overboard. However, if an object is heavier than water, it will sink when thrown overboard.
TomK
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?

berkeman and Delta2
TomK said:
Is this the correct conclusion to make?
The reasoning is correct.
TomK said:
would your boat not stay afloat with the object in it?
Do you think that having an object denser than water in a boat would necessarily make it sink?
TomK said:
M+1000V
Better to write M+ρwV, or, if you must substitute numbers, quote units: M+(1000V kg/m3).

Delta2
Thank you for the response. This answers my question.

I think my misconception came from thinking that the object (more dense than water) would have to be sufficiently heavy to displace more water when thrown overboard.

However, my working shows that, under the assumed circumstances, m could really be any value and the water level would still change (though it would have to be heavy to make a measurable difference in real-life).

## 1. How does throwing an object overboard affect pond water level?

Throwing an object overboard can cause a temporary disturbance in the water level of a pond. This is because the displacement of water by the object creates a small wave or ripple that can cause the water level to rise or fall slightly. However, this effect is usually very small and does not have a significant impact on the overall water level of the pond.

## 2. Does the size of the object thrown affect the water level?

Yes, the size of the object can have a small impact on the water level. Larger objects will displace more water and create a bigger wave or ripple, potentially causing a slightly bigger change in the water level. However, this effect is still minimal and will not significantly alter the water level of the pond.

## 3. Can throwing multiple objects overboard affect the water level?

Throwing multiple objects overboard at the same time can cause a larger disturbance in the water level of the pond. This is because the combined displacement of the objects will create a bigger wave or ripple. However, this effect is still temporary and the water level will eventually return to its original state.

## 4. How does the depth of the pond affect the water level when an object is thrown overboard?

The depth of the pond can affect the water level when an object is thrown overboard. In shallower ponds, the disturbance caused by the object will have a greater impact on the water level compared to deeper ponds. This is because the wave or ripple created by the object will have less distance to travel before reaching the edges of the pond.

## 5. Is there a difference in the water level when an object is thrown overboard in still water versus moving water?

Yes, there can be a difference in the water level when an object is thrown overboard in still water versus moving water. In still water, the disturbance caused by the object will be contained within the pond, resulting in a small change in the water level. However, in moving water, the disturbance can be carried away by the current, resulting in a smaller impact on the water level of the pond.

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