Author: manabunnow4zph

Odd Ball Out

Last Problem:

I tied some thin thread around a heavy book. As I held both ends of the string. I asked a friend which end would snap when I pulled on the string from the bottom.

If my friend said the upper part, I pulled on the string and the lower part broke. If my friend said the lower part, I pulled on the string and the upper part broke. My friend could never guess the correct answer no matter what choice they made.

How am I able to achieve this remarkable and quite magical feat?

Answer:

When I pull on the string from the bottom slowly and steadily, the top part of the string must bear both the weight of the book and the strength of the pull. The tension on it is greater than the tension on the lower half, so the top thread will break first.

If I pull with a sharp jerk, inertia comes into play. The book is little affected by the jerk at first, so the force of the jerk is not transmitted to the top string. The tension is therefore greater on the bottom thread and it breaks first.

Today’s Problem:

A pool hall owner has just purchased five bushels of colored pool balls, one each of red, blue, green and orange. All the balls weigh 100 grams, he discovers, except for the balls of one color which all weigh 110 grams.

The owner wants to use a spring scale that is accurate to within 10 grams to find out which color ball is too heavy (i.e., 10 grams over weight). Professional games are played here and he will be in big trouble if the players learn that the balls are not weighed evenly at 100 grams each.

His 10 year old daughter tells him he can figure out which color is the overweight ball with with one weighing on the spring scale. How does he do this (with help from his daughter)?

How Did I Do It?

Yesterday’s Problem:

Which will weigh more – a cubic meter of large steel balls or a cubic meter of small steel balls? Does it make a difference that more small steel balls can be packed into the same space or container than the large steel balls?

Answer:

Whether the steel balls are large or small, packed spheres will occupy about .5235 cubic meters for every cubic meter of space they are packed in. This is independent of the size of the ball, as long as the radius is small in relation to the size of the box.

Even though each void is smaller for tightly packed small spheres, there are more voids altogether. Each box will weigh the same.

Today’s Problem:

I tied some thin thread around a heavy book. As I held both ends of the string. I asked a friend which end would snap when I pulled on the string from the bottom.

If my friend said the upper part, I pulled on the string and the lower part broke. If my friend said the lower part, I pulled on the string and the upper part broke. My friend could never guess the correct answer no matter what choice they offered.

How am I able to achieve this remarkable and quite magical feat?

Weight of Small Versus Large Steel Balls

Last Problem:

If you drop a coin and a small slip of paper at the time, the coin will inevitably reach the ground at the same time. The coin lands on the ground first because of air resistance which slows the descent of the paper.

Figure out a way to demonstrate that the coin and the paper ought to fall at the same rate as the paper in the absence of air resistance, even in a normal room on the earth. The room is on the earth, not the moon!

Answer:

To eliminate the difference in air resistance, place the slip of paper on top of the coin. Then, drop the coin, giving it a slight spin to keep it horizontal as it falls. The coin and the paper should fall together.

Today’s Problem:

Which will weigh more – a cubic meter of large steel balls or a cubic meter of small steel balls? Does it make a difference that more small steel balls can be packed into the same space or container than the large steel balls?