## Friday, April 04, 2008

When my housemates and I were having dinner yesterday night, someone brought out some interesting questions:

1. There is a boat on a lake, and inside the boat there is a guy and a stone. The guy throws the stone out of the boat. Will the water level of the lake rise, fall, or remain the same? Here the water level is in reference to the land, not the water level of the boat. Also, assume that the total water volume of the lake is constant.

2. What if instead of a stone, the person breaks a wooden plank from the boat and throw it into the lake? Assume that the plank is less dense than the water.

3. You are swimming on the lake. You peed. What will happen to the water level of the lake? What if you are diving instead of swimming?

4. You are sitting on a bath tub with the plug on and some water in the tub. You peed. What will happen to the water level?

5. Same with 4, but instead of peeing, you poo-ed. What will happen to the water level? What about fart? (Thanks to Thow Kong for the brilliant question. :P)
Question 1 is supposedly one of the questions asked during the Oxford university interview. If you are able to solve number 1, you should be able to do the rest since they are kind of similar. Contact Thow Kong for the answer to the last question.

ShouFarn said...

I'm assuming its your average stone that is much denser than wood.

the water level will fall. Density is mass over volume. A rock will have higher mass per same volume as a wooden boat.

So the amount of water displaced by the wood of the ship due to the weight of that rock will be greater since for the same amount of weight the wood has more volume.

Chuck the rock overboard and the water will now displace that weight in terms of the rocks volume, which is smaller than wood. water level drops.

is that right? or am i just farting out of my mouth?

SilverIsle said...

No... Physics... I want to know the answer. Too lazy to think. Haha.

Alvin Ooi said...

ewww so nerdy.

i tried to recall the Archimedes principles, but I got dizzy.

Capablanca said...

For me, the water level remained the same. Assuming the volume of the lake remained constant but that its volume is significantly larger than that of any stone, plank, pee, or poop, the water level will remained the same since a small increase in volume will not affect the population in general.

changyang1230 said...

Hi Capablanca! :) In reality you definitely can't detect the small change of water level. But what if we are assuming here that we have measurement accurate enough to measure the change of water level, however minute it is? Or that the stone / pee / plan have a volume that is not entirely negligible compared to that of the lake's?

WP said...

haha! Interesting questions... let's see.

Let's talk about no. 2 first: I'd say that the water level remains unchanged, because the weight doesn't change (since mass can't be created, and the gravity's not changing) and the volume of the boat/plank submerged in water simply depends on their weight.

1: Don't know whether having the stone sink to the bottom will change anything, but I'm too lazy to think much about it, so I'll go with my gut feeling and say that the water level remains the same :P

3, 4, and 5: don't know, 'cos I don't know what happens to a person's volume when he pees! lol

changyang1230 said...

Archimedes principle is the key to all the problems here. If you remember, he supposedly discovered it when he was bathing, and then he ran out naked shouting Eureka.

So Archimedes principle says that "the buoyancy force acting on an object is the same as the weight of the displaced water".

1. If you sit on a bath tub and you feel 10kg lighter, that really just means that your bum has just displaced 10 litre of water as you sat down.

2. If you are floating, basically you are displacing as many litre of water as your weight, since being afloat implies that the buoyancy is the same as your weight (or else you would be flying to the sky or sinking to the bottom.

In this question, we can use "weight of water" and "volume of water" interchangeably as the density of water is 1 kg/l.

Using those two corollaries of the Archimedes principle:

1. When the stone was on the boat, the total water displaced was the same as (your weight + the boat's weight + the stone's weight), since the boat is floating. But when you throw the stone out of the boat, the total water displaced is (your weight + the boat's weight + the water displaced by the stone). As the stone is sunken, the buoyancy force is less than the weight of the stone - which means the water displaced by the stone is less than the weight of the stone. So if we compare the before and after, we will see that the volume of displaced water will decrease, resulting in lowered water level.

2. No change.

3. If we assume that the density of urine is the same as water in the lake (we can't really tell without actual measurement), then there should be no change of water level if you are floating. Before you pee, the displaced water is "your weight including the urine in bladder". After you pee, the displaced water is "your weight minus the urine"; but then you make up for the minus urine part by adding the urine into the lake (you peed into the lake), so the end result is the same water level.

4. I realised that it's a pretty bad question, because the water level in the bath tub depends a lot on your breathing, movement etc. But in most cases, it will increase. Basically the displaced water in the beginning was the same as however much space your bum and your body occupied under the water level. When you pee, assuming that you don't breath in and all, and that your body shape doesn't change when you pee, you will still displace at least that many space, but you have extra water - tada, higher water level!

5. This is the official answer by Thow Kong - "Have to see whether your poo floats or sinks". GOLDEN.