4 ms·
I have no idea and want the answers: Boat + bowling ball = level stays the same? Ball roll = the constant gradient is quickest?
by lostlogin 2mo ago
I have no idea and want the answers:
Boat + bowling ball = level stays the same?
Ball roll = the constant gradient is quickest?
- AlecBG 2mo agoFirst one water is lower. Ball is more dense than water, in boat displaces its weight in water, in water displaces it's volume Dip for hill roll is faster
- CodesInChaos 2mo agoA dip increases the speed (decreasing travel time), but also the distance to travel (increasing travel time). Which of those effects dominates depends on the shape of the dip. The hill decreases speed and increases distance, so it's always slower than the straight line.
- modeless 2mo agoMost things that can fairly be described as a "small dip" should decrease travel time. When I was presented with the problem it came with illustrations to clarify. Surprisingly hard to make it watertight with text alone.
- robocat 2mo agoNext bail 10 litres of water from the lake into the open-topped boat. What are the effects of the 10 litres of air displaced from within the boat?
- RealityVoid 2mo agoLake level stays the same.
- b3lvedere 2mo agoUnless there was a butterfly in that part of the air .. not much.
- ninkendo 2mo agoFirst one depends on the bowling ball. Most alleys have balls ranging from 7lb to 16lb, all the same volume, and the crossover point where they’d sink is 11.6lb. If it was a floating bowling ball, the lake water level would stay the same when you toss it from a boat. If it were a sinking one, it would decrease.
- quietbritishjim 2mo agoI think you're counting the overall sphere as the volume, but water would leak in through the finger holes so only their actual material counts. I suspect different weight bowling balls generally have different volumes.
- kontain 2mo agoAlso if the lake is a mile deep it would pressure the ball more than the air do.
- fenomas 2mo agoBowling balls aren't hollow, they're solid spheres with finger holes drilled in. The varying weights comes from having weighted cores inside.
- quietbritishjim 2mo agoOh OK thanks, I didn't realise. I just had some fun looking at bowling ball cross sections.
- modeless 2mo agoThat's why the problem statement specifies that the bowling ball sinks.
- ninkendo 2mo agoGood point! I skimmed over that part, you’re right.
- IsTom 2mo agoBut won't your boat displace more water by lowering a bit if you've got additional mass on board?
- CodesInChaos 2mo agoThat's what they meant by "in boat displaces its weight in water". While it's in the boat, the amount of water it displaces weighs as much as the bowling ball. While it's in the water, it displaces the volume of the bowling ball, and its weight doesn't matter. The ball is denser than water (since it sinks), so the amount of water it displaces based on its weight is bigger than the amount of water it based on its volume.
- IsTom 2mo agoAh, that makes sense, thanks.
- vdfs 2mo ago> Ball is more dense than water Wouldn't that mean the water level will raise a bit because: displaced weight > displaced volume?
- deleted 2mo ago[deleted]
- a-french-anon 2mo agoI find it very easy to solve some of these physics questions by thinking about a degenerate version of it instead, with exaggerated parameters (since these physics phenomenons are described by continuous/monotonic functions). So for the bowling ball, I replace it with an imaginary marble weighing 1 ton and the answer is now self-evident.
- inigyou 2mo agoYou drop a microscopic black hole off a boat into the lake. Does the water level increase or decrease?
- RealityVoid 2mo agoThe water level decreases, along with the shore and anything with it falling within the event horizon. Any other apocalyptic brain teasers?
- anonym29 2mo agoYou drop a bowling ball off a space boat into a black hole. Has the amount of mass inside the universe increased, decreased, or stayed the same, ignoring the effects of all other changes?
- RealityVoid 2mo agoThe amount of mass inside the universe has stayed the same, it just moved from the boat into the black hole. You're really bored at work one day so to entertain yourself you create 1kg of antimatter along with 1kg of matter. Has the mass in the universe increased or stayed the same?
- kontain 2mo agoThe mass of the observable universe has probably changed a lot by the time the bowling ball hits the bottom.
- cucumber3732842 2mo ago>Ball roll = the constant gradient is quickest? Steep then flat one because it gets up to speed fastest. It's a classic "annoy people who've forgotten that newtonian physics is all integrals" problem. Graph the velocity. Look at area under graph.
- FabHK 2mo agoBoat + bowling ball => level drops. 1) Imagine pushing the boat down into the lake, displacing water. The level would go up. 2) Imagine the ball instead of being in the boat, is attached under the boat by a rope. Same thing. (Imagine it magically moving through the bottom of the boat - it has no impact on the boat or water level). 3) Imagine you cut the rope. The ball will fall, and the boat will bob up. Water level goes down.
- jasmcole 2mo agoThe fastest path involves a small dip, though deriving that fact is non-trivial! Here's one of my old blog posts where I do the derivation: https://jasmcole.com/2020/04/13/briechistochrone https://jasmcole.com/2020/04/13/briechistochrone