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?

How Can You Eliminate the Effects of Air Resistance?

Last Problem:

A large stone is 100 times heavier than a small stone, but when dropped at the same time, they fall with the same acceleration (ignoring air resistance). This is a lesson we all learned in 5th grade.

Why doesn’t the large stone accelerate faster? Is it because of its weight, its energy, its surface area or its inertia perhaps?

Answer:

It does seem odd that the heavier object does not fall faster than the lighter object, but experiments prove this to be false. (You may have done your own experiments when you were younger!).

Newton’s second law of motion shows that acceleration is directly proportional to force (weight in this case) and inversely proportional to mass. The equation is:

a = f/m

where:

a = acceleration

f=force

m=mass

Resistance to motion due to mass is called inertia. Therefore, even though a large stone may weigh 100 times more than a small stone, it has 100 times more mass (and inertia). Thus, the two factors cancel each other out.

Ignoring air resistance (which can be a factor for lighter objects), acceleration of every falling body near sea level is 32 feet per second.

Today’s 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!

The Pull of Gravity

Last Problem:

Do astronauts on the moon weigh the same as they do on the earth?

Answer:

No.

The surface of the moon’s gravitational pull is approximately one-sixth (1/6) that of the earth’s gravitational pull. This means astronauts on the moon will weigh 1/6th of what they will weigh when they are earth bound.

Today’s Problem:

A large stone is 100 times heavier than a small stone, but when dropped at the same time, they fall with the same acceleration (ignoring air resistance). This is a lesson we all learned in 5th grade.

Why doesn’t the large stone accelerate faster? Is it because of its weight, its energy, its surface area or its inertia perhaps?

How Much Do Astronauts Weigh?

Last Problem:

Can you measure your weight anywhere in the universe using a spring scale?

Answer:

Yes. Weight is a relative magnitude and your weight may change from planet to planet or star to star, but a spring scale will always be capable of measuring weight – even if your weight happens to be zero (0) in that particular location.

Today’s Problem:

Do astronauts on the moon weigh the same as they do on the earth?

How Versatile is a Spring Scale?

Yesterday’s Problem:

The earth is not a perfect sphere. It is a bit flat at the top and it bulges at the equator. It is a bit fat in the middle (like some of us beings).

Given this information (which really is true – no joke here) can you work out where you weigh more – at the North Pole, at the South Pole or at the equator?

Answer:

Your weight is a measure of the gravitational pull of the earth’s mass upon your body. The closer you are to the earth’s center of mass, the more strongly you will feel its pull.

Because of the earth’s bulge then, you weight about .5% less at the equator than you do at either of the poles.

Today’s Problem:

Can you measure your weight anywhere in the universe using a spring scale?

How Much Do You Weigh?

Last Problem:

A blacksmith has been asked to make one long chain from five three-link bits of chain. Can you find a way to do it so that she has to make just three welds?

By “Three Link Bits of Chain” we mean a a short chain with three circular links that are connected. A middle link is joined together with two outer links. There are five of these short three link chains and the blacksmith needs to make one long chain from these five short three link chains.

Answer:

One of the small chains has to be separated into its three separate links. This is then used to link together the other four short chains, making the one long chain.

Today’s Problem:

The earth is not a perfect sphere. It is a bit flat at the top and it bulges at the equator. It is a bit fat in the middle (like some of us beings).

Given this information (which really is true – no joke here) can you work out where you weigh more – at the North Pole, at the South Pole or at the equator?