A suspicious suitcase and a boat (July 2021 Challenge Question)

Good answer.

One way of looking at it is that the water provides a lifting force to counteract the weight of the suitcase when the suitcase is in the boat, suspended from the boat with a fishing line, or floating on the water. The water does this by being raised to a higher elevation, like a hydraulic see-saw. If the suitcase sinks, the bottom of the lake is supporting part of the weight of the suitcase, and hence, the water level would be lower.

'Zackly my line of thinking too. But, I could have missed something along the way and maybe someone else can set me straight.

In short, a floating object displaces its weight in water. A sinking object (denser than water) displaces less than its weight in water. Its weight is reduced by the weight of water displaced.

In the boat, the suitcase adds its weight to the boat, and since the boat is floating, the suitcase plus boat displaces their total weight in water.

If the suitcase is thrown in the water, if it floats, it is displacing its own weight in water. If it sinks, it is displacing less than its own weight in water, lowering the water level.

If the (heavier than water) suitcase is suspended from the boat with a fishing line, the weight on the line is reduced by the weight of water displaced. The force on the line causes the boat to displace the remaining weight in water. The water level will be the same as if the suitcase were in the boat.

I think your logic is valid.

Thanks !!

GA. What can be added is:

1) The suitcase might sink for two reasons: it’s heavier than the equivalent volume of water or it’s not watertight – in this case water will enter the suitcase and replace the air inside it so, eventually the suitcase will sink. Note that in the second case the water level change will be smaller than in the first case (because the suitcase will be filled with water instead of air). So, in any case, if the suitcase sinks the water level change will be smaller than the equivalent volume of 2.5lb of water (some 1.13dm³ in metric units).

2) The level change will depend on the size of the lake. I don’t know what is the meaning of a “medium sized lake” but I suppose it should have at least a surface of 1km² to host fishing boats. If we consider this size, a change smaller than 1.13dm³ corresponds to a change in level smaller than 1.13x10^-6mm, which is practically unmeasurable.

So, a probably more accurate answer might be: “If the suitcase floats, there is no change in the water level. If the suitcase sinks to the bottom, then the water level theoretically falls but with an unmeasurable amount”.

As the boat is floating, the density of the boat and its contents is less than that of the water. This means that the weight of the water displaced by the boat and the contents is equal to their combined weight. If the density of the suitcase is less than that of the water, then there will be no change in water level because it is same whether suitcase floats within the boat or independently. If the density is equal to or more that that of water, then suitcase will sink or float such that its no portion is above water level, replacing less water compared to what it was replacing while in the boat. So the water level will fall.

Yes. Points!

The amount of water that the suitcase displaces is equivalent to adding that much water to the lake and as a result the water level will rise...A 5 lb suitcase would displace a very small amount of water 5 lbs of water would be just over a half gallon at nearly .6 gal....

Sea level rise could attributed to things being added to the ocean, like containers that fall off ships at sea...

...of course the suitcase being on the boat has already contributed to the displacement of the vessel, so no change to water level would occur regardless of position movement in the immediate timeframe...

For a 5 lb suitcase to sink in water it would need to be smaller than 4" by 6" by 6": there is no such thing. Therefore the suitcase (which is almost certainly empty) must float; the water level must remain the same, and, the fishing line is irrelevant.

Depends if the suitcase contains a high impedanse water activated C4 bomb, then the water will definitely rise quite alarming as will the stunned fish so have you landing net at the ready for a bonus.

Does one factor the evaporation of the perspiration produced as a result of heaving the <...suspicious 5lb suitcase...overboard...> into the calculation?

Of course, were the suitcase to sink, then the spin of the earth will increase...

Does anyone have any Aspirin, please...

To begin with it will rise.

Mind you this is only for a fraction of a second, as the force you exert to elevate the suitcase in the process of throwing it overboard causes the boat to sink deeper into the water, increasing its displacement for a moment and causing a corresponding increase in water level.

Following that it will rapidly revert to a static or lower state as other posters have explained well.

The wording in riddles and challenges like this always has importance. All words are significant. I'm triggered by the words 'fishing boat', 'suspicious' and 'fishing line'.

I am not interested in fishing yet I find myself on a fishing boat. I have a suspicious suit case. Am I trying to traffick drugs across this lake, possibly on the exact border between two countries? Triggered by the appearance of a patrol vessel, which shows interest in my cruise from one side to the other side of the lake, I throw the suit case overboard - on a fishing line. Perhaps the coast guards can now determine that I threw something overboard by monitoring any change in the level of the lake? Perhaps it would be easier to monitor the depth of my vessel in the water?

With the size of a medium-sized lake, it certainly would not be easy to measure the water level from any perspective. Any waves or even ripples on the surface of the water would make measurement difficult.

It will also matter from where one measures the lake level. The boat and land reference points will have opposite rise or fall views with different magnitudes. The magnitude from the boat's perspective will be greater than from the land. Therefore the boat perspective will be easier to measure. However, it appears the land perspective is intended and what others are discussing. So I will use that reference, too.

Tossing the suitcase will briefly cause the lake to rise for greater than 5 pounds of upward force will be needed at the suitcase to toss it up. Once the suitcase is airborne the lake no longer provides the 5-pound normal force for the suitcase, the lake will fall and produce a wave with the boat as the origin. When the suitcase impacts the surface of the lake if it initially floats from the surface tension of water and the suitcase has yet to fill with water then a greater than 5-pound normal force will still be needed to decelerate the suitcase. The lake will rise for the deceleration but come back to its original level until the suitcase submerges. A new wave originating at the splashdown point will appear, too. As the suitcase sinks to the bottom buoyancy and viscous drag effects occur but only buoyancy affects the lake level. The lake falls a little. When the suitcase reaches the bottom the lake bottom provides the added normal force that viscous drag once did. If the fishing line is shorter than the depth of the lake then buoyancy from suitcase and boat volume displacement will return the lake to the original point.

Good luck to anyone trying to measure this.

In my view if the suitcase sinked completely, the lake water would slightly rise equivalent to the volume of water displaced by the suitcase.

If it did not sink, like when the suitcase is being held by a fishing line then the lake water may also not change, since the removal of the 5 lb weight will make the boat rise a little bit, which will make the lake water fall a bit but that fall may be offset by the partially submerge suitcase.. In which case, any change in water level may just depend on how buoyant the suitcase is..

<...rise or fall...> relative to what, exactly?