Let\'s say you are holding a bag of potatoes that you want to buy. The seller te

Question

Let's say you are holding a bag of potatoes that you want to buy.
The seller tells you that it will cost $0.37 per lb.
He then tells you that it weighs 10.0 pounds.
You really want these potatoes; there are no potato sellers within miles and you are tired.
You have a problem; you don't trust this guy selling the potatoes.
It so happens that you have a bag of tomatoes that weighs 2.25[lb].
You know this weight is accurate because you just bought them at a store where you work.
(Your job is to calibrate the scales; and you are very good at your work.)
You see that the man (the one you don't trust) has a walking staff next to his chair.
It appears uniform in density.
You ask to borrow it.
He raises his eye brow and hands it to you.
You carefully balance it horizontally on top of the guy's cash register.
You hang the tomatoes on one side of the walking stick at an arbitrary distance from the cash register.
You then carefully hang the potatoes on the opposite side of the cash register such that the whole system balances.
The man at this point is sweating while watching you.
You methodically take a bobby-pin out of your hair.
You measure the distance from the register to the tomatoes to be 12 bobby-pins.
You then measure the distance to the potatoes to be 3.25 bobby-pins.
How much do the potatoes actually weigh?
Potato Weight =  [lb]
Use Three Significant Figures or N/A if there is not enough information to answer.

4. How much money are you going to save if you convince the vendor that your potatoes don't weigh the 10[lb] he says they weigh?
$  
Answer within a cent (round if necessary). ie. 0.93 OR 8.24

5. What is the best way to verify (in part three of the experiment) that you properly measured the weight values at each of the three eye-hooks from the board? (That is, before trying to balance the board.)

Explanation / Answer

Since the stick is balanced, the sum of torques about the pivot point is zero. Let M = mass of potatoes and m = mass of tomatoes, b = length of a bobby pin. Then the torques are:

0 = M*p*b*g - m * t*b*g where p = number of bobby pin lengths from potatos to pivot, t = no. of bobby pin lengths from tomatoes to pivot.

=> M = m.t/p = 2.25*12/3.25 = 8.307 lb

Excess weight charged = 10 - 8.307 = 1.693 lb

Money saved is 1.693* 37 cents = 62.64 = 63 cents

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