- #1

dinospamoni

- 92

- 0

## Homework Statement

A set of 59 playing cards of length L = 15 cm are stacked on the edge of a table so that the length of the overhang of the top card with respect to the table is maximized. A stack of only 6 such cards is illustrated. This problem requires you to draw an accurate Free Body Diagram of each card (or, at least of about 4 of the cards). To do these correctly, you will need to understand normal forces and torque.

a) What is the overhang distance of the tip of the top card?

b) How many cards are needed to extend the total overhang of the top card to at least 28 cm?

c) What is the offset distance between cards 30 and 31, assuming that the top card is number 1?

## Homework Equations

We are supposed to be using series and the ones I was given are:

(the sum should be read from left to right = bottom to top)

i=0 Ʃ n-1 (ar^i) = a(1-r^n)/1-r

i=0 Ʃ n (ar^i) = a(1-r^n+1)/1-r

if abs(r) <1

i=0 Ʃ ∞ (ar^i) = a/1-r

i=1 Ʃ ∞ (ar^i) =ar/1-r

## The Attempt at a Solution

I've been trying to find a series to work this out for hours. A few I've come up with but are unsuccessful I think:

1) L/2 + L/4 + L/8 + L/16 + ... + L/2^n

2) i=0 Ʃ n-1 (L/2)(1/2)^i

3) (L/2)(1+ 1/2 + 1/4 + 1/8 +... +1/2^n-1

I got this one from the first one, but thought it might make a difference with the L/2 out of the picture

These are all for part a. I don't want to start the other parts until I get a grasp on what I'm doing.

But really anything that could help with any of them is appreciated. Thanks!