Answers to the suitcase problem

If you are on a boat and toss a suitcase overboard, will the water level rise or fall?

Normally, we wouldn't be interested in the rise or fall of the water level in a body of water large enough to permit boating. In fact, tossing a suitcase out of a boat is not going to change the water level perceptibly. The question is whether it changes the level in principle.

We can try and imagine the problem. Anytime you throw weight out of a floating boat, the boat gets lighter and rises. However, that's not what this question asks. It asks whether the water level rises or falls.

If the suitcase were to be magically removed or evaporated into thin air, the answer becomes more straightforward because the boat would simply be lighter and float higher. This makes the water level decrease.

However in this question, the suitcase is tossed out of the boat, and into the water. This begs us to question further. What if the suitcase sinks? What if the suitcase floats? Will the answer be the same for both cases?

In the case of the suitcase sinking, pretend you throw a heavy suitcase overboard, having first secured it to the boat with fishing line. The boat briefly rises, then the line draws taut as the suitcase sinks as far as the line permits. This makes the boat dragged down by the weight of the suitcase. The displacement of the boat plus suitcase is identical to what it was originally. If you snip the fishing line, the suitcase will sink to the bottom while the boat's hull rises upward. This decreases the volume displaced and hence lowers the water level.

In the case of the suitcase floating, we would be more interested in the weight displaced. In school, we learnt about Archimedes principle, which states that the upthrust acting on an object is equal to the weight of the fluid displaced. If I have a 5kg beach ball floating in a bathtub, the beach ball displaces 5kg of water. Similarly, if I have five 1kg beach balls floating in the same body of water, the total weight of water displaced is still 5kg. This means that the volume displaced is also the same. Hence, if the suitcase floats the water level will remain the same.

Conclusion: tossing a suitcase off a boat makes no difference in water level if the suitcase floats. If the suitcase sinks, the water level falls.

Trivia: Rise or fall?

Here's our trivia for the month of October.

If you are on a boat and toss a suitcase overboard, will the water level rise or fall?

Getting started is always the hardest

The hardest part of studying for exams is getting started itself. Once you get started and develope a rythm, studying becomes less painful.

It is one of the laws of the universe. Newton's first law tells us that things in motion tend to stay in motion, and things at rest tend to remain at rest.

The more we procrastinate and avoid doing the unpleasant stuff, we are actually setting ourselves up for failure. But once we get through the starting phase and make studying habitual, it doesn't become so hard to study.

Just like riding a bike, starting a business, swimming, or training for a marathon, the hardest part is actually getting started itself.

Children's Day

I miss my primary school days when life was simple and plain fun. I miss all the recess times when we would run to the school field to play football during that short 30 min break. Who cares if our white school shoes got caked in mud. Mum would wash it for us anyway. I miss the happiness that erupted whenever the fire-drill bell rang. It means 20 mins of official goofing off! I miss the chit-chat with friends on the school-bus ride home. The school bus was also a place where students waged their pocket money on the buying and trading of dragon ball cards. I miss the days when school ended at 1. This would be followed by an afternoon nap in the comfort of home. I miss all the excursions during after-exam periods. The post-examination period when teachers were busy marking scripts was the best time to go to school.

Here's wishing all children a happy children's day! Enjoy your childhood years and don't be in such a hurry to grow up so fast. Study hard and play hard.

For the P6 students, all the best in the upcoming PSLE exams!