Welcome to
Ward's Web Pages
Brainteasers
Home Songs Brain Teasers Games & Puzzles Funny Stories Other Stuff Contact Me




Heavier Cans

You have two identical cans of peas, which you weigh on a perfectly accurate scale, and find that each one weighs exactly 1 pound. (All weighings are done in the same location, at sea level, on the surface of the earth.) You have another can which is exactly the same size as either of the cans of peas, but is filled with a denser material. You weigh this can on the same scale and it gives you a weight of exactly 2 pounds. Is the combined mass of the two cans of peas less than, equal to, or greater than the mass of the single can of unknown substance?

Answer:

Answer: The mass of the two cans of peas is slightly greater than the mass of the single can.

If you do not believe this, consider performing the same experiment underwater (with a waterproof scale, of course). Would the scale still give readings showing that the two lighter cans are equal to the weight of the heavier one? No, it would not. This is because any object in a fluid is buoyed upward by a force equal to the amount of the fluid that it displaces. Since the two cans of peas will displace twice as much water as the single can of the other substance, they will be buoyed upward by twice as much force as the other can, and hence, will appear to weigh less (have less mass).

Now let us bring our experiment back onto land again. Are these cans immersed in a fluid that would have a similar effect on our weighings? Yes. We have a several mile deep layer of fluid covering the entire surface of the earth. We call it air! Each can is immersed in this fluid, displacing its own volume of air, and is therefore buoyed upward by the weight of the air that it displaces. Since the two cans are being born upward by twice as much force as the single can, and yet have a resulting downward force (weight) equal to the single can, they must have more mass.

Of course, the difference is very slight, so for practical purposes the difference does not really make a difference. But at this site I don't care about being practical, when I can trip you up by being impractical!