• In defiance of gravity?

• It may well seem like.

• Yet, push a bit too far and gravity will win.

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Physics Maths
age: 14 – 16

# Card stack

Your physics text book probably claims that an object will tip and fall over if its center of gravity lies outside the object's base. So how is it possible to shift a card well beyond the base of the stack?

Learning objective

Understanding the concept of tipping and the center of gravity.

Finding mathematical patterns.

Playing or index cards

Arrange the stack so that the top card lies outside the stack base.

1. Why can you do this without the stack tipping and falling over?

2. Can you find a mathematical pattern how far out you can push each layer?

Guiding Questions (if needed)

Where is the center of gravity of the whole stack?
› Always above the base of the stack.

Where is the center of gravity of each part of the stack?
› Always above (and therefore supported by) the part of the stack below it.

Findings

While the top card can be pushed out almost half its length, the second card can only overhang a bit less than 1/4. In general, no layer n can be pushed out more than 1/(2n). To push the top card beyond the base of the stack, one therefore needs to shift at least 4 cards.