Equipment Overboard

Classical Mechanics Level 3

A transport boat, carrying extremely heavy equipment like guns and tanks, is sailing in a lake. The boat springs a leak and as a result the boat and all of the equipment sinks.

Compared to when the boat was sailing, what will happen to the water level of the lake after the boat sinks to the bottom?

Remain the same Rise then come to the original level Go down Rise

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Siddharth Gopujkar by Siddharth Gopujkar , 30, India

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3 solutions

Discussions for this problem are now closed

The answer is the level will go down. The reason for that is when the equipment is on the ship, water displaced by it is equal to the weight of the equipment. But when it sinks, the water it displaces is equal to its volume. As density > 1, mass > volume. This makes the level go down.

22 Helpful 0 Interesting 0 Brilliant 0 Confused

Too many variable not considered in this solutions. 1. Size of the Lake 2. Effect of Tornado on the shoreline. was anything washed away. The question would be more realistic if it simply said what if the toy ship has sunk in the bowl of water. Will the water rise or fall.

francis Anthony - 6 years, 11 months ago

The tornado was just a means of capsizing the ship to make it sound interesting. Obviously its not a part of the problem.

Siddharth Gopujkar - 6 years, 11 months ago

it doesn't specify whether the boat is submerged, in which case the air onboard would escape and the water level would go down, if only the equipment went in, the water level should stay the same...

Harry Tippetts - 6 years, 11 months ago

@Harry Tippetts – Generally boats are submerged in water unless you can make them fly

Siddharth Gopujkar - 6 years, 11 months ago

@Siddharth Gopujkar – yes, but air contained within the boat provides buoyancy

Harry Tippetts - 6 years, 11 months ago

@Harry Tippetts – Buoyancy is provided by the displaced water. And if you mean that the boat will also sink with the equipment if the air inside gets displaced, even then the answer remains the same. The level will go down.

Siddharth Gopujkar - 6 years, 11 months ago

I think, water level increases first when ship comes into the lake. When it sinks, water level decreases than the increased level but won't be decreased than the original water level when there was no ship in the lake. Please correct me if I'm wrong and explain in some detail.

Kulin Choksi - 6 years, 11 months ago

Wate level will fall because in order to for the boat to sink water will need to get inside and fill the part of the boat that was below water level when the boat was floating (replacing air).

Which means now, sunken, the boat will occupy less volume. (Air volume was removed and only the volume of its solid parts remain.

The volume of air must constitute a larger percentage of the total volume of the boat than the volume of its solid parts. Otherwise it wouldn't float because it's density will be higher than that of water.

Ebraheem Alsaeed - 6 years, 11 months ago

So the water will be displaced outside from the lake with the amount of volume with respect to the volume of the sinking object inside the lake itself correct? Because volume of object displaced equal amount of water outside from the lake thus decreasing the volume of water inside the lake right?

wazif muhammad - 6 years, 11 months ago

I clicked no change without even thinking twice. I like this problem, it's things like this that help me see new ways to apply my knowledge outside the box. Thanks for the post.

Kaden Bea - 6 years, 11 months ago

Inconclusive. The volume of an equipment is too small to change the water level of a lake.

Topeg Dorosan - 6 years, 10 months ago

ok But when the same equipment will fall down into the river... that will also displace the water however the wait of the objects whether on the ship or apart from it will have the same wait so the water displaced must be equal to the wait of the objects collectively..!

Munish Sharma - 6 years, 10 months ago

Wait i can't understand enough how it is will go down and how it is relative of mass. So when many ships sink there at the lake the water will go down to the height close to zero? that's non sense.

Hafizh Ahsan Permana - 6 years, 11 months ago

No mate. If you put many ships in a lake , the water level initially go up. This increased level will be the one that falls when the ship sinks. Its basic Archimedes Principle. Check it up.

Siddharth Gopujkar - 6 years, 11 months ago
Parth Mehta
Jun 23, 2014

Because tornado will carry some water along with it and also it will throw some water out of the lake while its in motion... thats what i feel so the water level will go down

3 Helpful 0 Interesting 0 Brilliant 0 Confused

what about the rain man ! Love your answer btw

Tanguy Breteche - 6 years, 11 months ago

Guys the water won't spill out of the lake. This is a lake, not a container.

Hak han koh, where would you find guns and tanks made of a material with density 1? If it was hypothetically having the same density of water, the would remain the same.

Kulin, ship was already in the water. The level changes only after the equipment sinks.

Siddharth Gopujkar - 6 years, 11 months ago

Water runs into and from most lakes. Water level decreases then return to normal. So water does spill out of the lake if it is like most lakes.

Bent. O. Jensen - 6 years, 5 months ago
Sukrat Gupta
Jun 28, 2014

Total weight of water displaced = weight of equipments,ship etc,As the density of equipment>> than water therefore more volume of water has to be replaced. As ship shinks the water level decreases.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

confusing! what i think is simply its like when we put stone in glass of water water ll rise in a same way when ship sinks more water ll displace and water level ll rise.. is it?

nikhil surange - 6 years, 11 months ago

Here thing is that suppose there is some water level W1,Now if put ship on it definitely water will increase W2 (W2l>W1). In the problem our reference is W2 , therefore as ship capsized level decreases from W2. This problem is same as ICE cube in full glass of water as ICE melts the level decreases. Hope this might have clear some of your doubts.

Sukrat Gupta - 6 years, 11 months ago

It says no where in the question that the ship starts sinking. Capsizing does not necessarily refer to sinking. The only thing which is clear is that instruments fell in water. if that was so, it would have been impossible to predict the level of water without actual data. One must mention in the question that ship actually SINKS.

मोहन अग्रवाल - 6 years, 11 months ago

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