Challenge Questions

The rock will not displace any more water than it did in the boat.

Nothing, The water is already displaced by the weight in the boat. The boat may ride a little higher in the water due to the loss of 150lbs. of weight....

The level of the lake goes up. This is because the rock displaces more water (by mass) in the boat than it can (by volume) in the lake.

Nick Gustard.

The lake level will remain the same.

The buoyancy applied to a force is independent of the density of the object. Whether something "floats" in a medium depends on the relationship between the density of the medium and the density of the object. If the question was does the rock float, then the size of the rock would be important. The volume of any medium to create any buoyancy equal to the force in the medium will always be the same. The volume against which it acts will determine if the object will float in that medium.

remains the same.

The water level in the lake remains unchanged. The weight of the rock in the boat results in the boat dispalcing more water to stay afloat; therefore' when the rock is thrown overboard the same volume is displaced. Boat rises higher i water but lake stays the same.

The rock is of volume x. your boat sits in the water unloaded (except for you) it displaces volume y. you add the rock to the boat by mysterious means and now you boat sinks a couple of inchs and now displaces an extra volume of z. assumption by your average shape of a rock and the average shape of a boat the boat wins by its z being greater than x. so if the rock is removed then there is less volume taken by the boat so the lake gets to not be force up higher by all those darn volume takers of space, gravity works to fill that space with water and your lake is lower by how ever many micro units of elevation. Of course thats assumeing the lake is big and can travel up and down with out draining, the shape of your rock, the tidal forces and all those other rediculous factors that won't come in to play so you can have a nice tidy question and answer.

This is a simple buoyancy(although a bit tricky) question. When the rock is thrown into the lake it displaces an amount of water equal to the volume of the rock. When the rock is kept afloat by the boat it displaces an amount of water equal in weight to the rock. Since a typical rock has a specific gravity of approximately 2.6, the rock on the boat displaces a volume of water 2.6 times its volume just to keep the rock afloat.

Therefore when the rock is thrown into the lake the water level drops.

Time.

What happens to the level -compared to when?

Unless the rock initially came from the bottom of the lake in the first place,

the level would rise.

Now, is that boat put in/removed from the lake when not used for displacing an amount of water equal in weight to itself (and contents)?

Nothing will happen. The level of the lake will stay at the same level. The boat with the rock in it (assuming the boat is in displacement mode) already displaces the volume of the 150 pound rock (about 0.75 cubic feet). If the boat were a surface effect type then this might not be true, but since you are fishing I assumed otherwise.

A good point about "displacement mode"! Part of fishing is getting to that favorite spot. If the boat was running 90 mph with only the lower unit in the water, when the rock was thrown overboard the lake level would stay the same or rise!

That is only if you account for lift forces from the forward motion of the boat. If you assume little lift, the force from the prop in the water will still cause the same amount of displacement as if the boat were standing still. Actually, it would rise because the motor is providing more force to overcome friction.

Now, the mass of the boat has not gone away, but if it is going fast enough to ride on the prop alone, then there are significant aerodynamic forces supporting the boat and depressing the surface under it, not to mention the surface disruption behind from the water piled up by, and resisting the flow from, the prop. The sum of the upward vector of the angled prop force and the aerodynamic forces certainly equals the weight of the boat, but the effect on the lake is obviously, to even the most casual observer, very complex: ripples, cavities, currents, waves, etc.

And when you throw the rock overboard, the boat may go faster as the vector from the prop does not need to help support it, so the nose can come down reducing the aerodynamic losses, providing force for more acceleration before the speed-induced forces balance out again. Meanwhile, the whole lake is, on average and for the moment, still lower, just like when the boat was relatively motionless except for the rocking from the fool stagering around in it with a rock. Of course, the transient loss of ballast for the bow may make the boat flip over backwards, resulting in even more chaotic motion. :-}

If we are taking all of this into account, then it also depends where the moon is in the sky as well as all of the other planets, and the distance the earth is away from the sun.

have a nice job

Are you expecting the moon's gravity to tilt the surface, or expand the water, or make the rock bigger or smaller in volume for it's weight, or the boat to float higher in the full moon, as ships do? You can run the numbers for that, using some ballpark example values for the elements, just as we did for the metric cylindrical lake calculations above. Let us know how much it contributes. If that is within a couple orders of magnitude, then we can go on to the sun. If that is within a couple orders of magnitude, then we can go on to the planets, but their positions won't line up very well very often.

However, the gravity is changing very slowly, and when the rock moves from the boat to under water, assuming it sinks, it induces a temporary step change in the lake. The question is, on top of all the other forces holding the lake in something like equilibrium, what is the step?

Silly question, obviously the lake will still be level. Unfortunately the lake will not slope with a rock at one end.

The level of the lake would not change. The rock in the boat was already "in" the lake, because the boat displaces the water based on the weight of the contents. By throwing the rock out of the boat, you are simply transferring the displacement from the boat to the rock.

1. When the rock is submerged in water it displace an amount of water equal to its volume.

2. When the rock is in the boat it will displace an amount of water equal in weight to the rock. Since rock has a specific gravity of approx. 2.6, the rock in the boat displaces an amount of water 2.6 times the volume of the rock.

3. Remember in both cases there is a buoyant force acting on the rock.

a) In the case of the submerged rock the buoyant force acting is equal to the weight of an equivalent volume of water. Since this buoyant force is less than the weight of the rock, the rock sinks to the bottom of the lake.

b) When the rock is on the boat the buoyant force just to keep the rock afloat (the weight of the boat is not considered here because in both instances the boat is present) is equal to the weight of the rock or the weight of water having 2.6 times the volume of the rock. Which is only logical since it takes more displaced water to keep the rock afloat than to let it sink.

4. Since the rock at the bottom of the lake displaces less water, the lake's water level will fall when the rock is thrown into the lake.

I was going to try this one again for a "Good Answer", (there are only four in 320 post) but I could not have said it clearer or more concisely than you did, excellent GA!

.... i made an assumption that the rock was granite (density 2.7) and if so... the level of the lake will lower by 42L total volume...without the size of the lake obviously we cant give the actual drop in the water level...

why am i so anal...???

you didnt take into account that the average density of the boat will be greater with the rock in it and will thus ride lower in the water and displace the 150lbs of water the rock would displace when in the water.

take a boat with vertical walls - this will solve the dilemma

the level of water will up