Question

You have a set of calipers that can measure thicknesses of a few inches with an uncertainty of ± 0.005 inches. You measure the thickness of a deck of 52 cards and get 0.590 in:a. If you now calculate the thickness of 1 card, what is your answer, including its uncertainty?b. You can improve this result by measuring several decks together. If you want to know the thickness of 1 card with an uncertainty of only 0.00002 in., how many decks do you need to measure together?

Answer 1

Answer:

a) x = (0.0114 ± 0.0001) in , b) the number of decks is 5

Explanation:

a) The thickness of the deck of cards (d) is measured and the thickness of a card (x) is calculated

        x = d / 52

        x = 0.590 / 52

        x = 0.011346 in

Let's look for uncertainty

       Δx = dx /dd Δd

       Δx = 1/52 Δd

       Δx = 1/52  0.005

       Δx = 0.0001 in

The result of the calculation is

        x = (0.0114 ± 0.0001) in

b) You want to reduce the error to Δx = 0.00002, the number of cards to be measured is

           #_cards = n 52

The formula for thickness is

           x = d / n 52

Uncertainty

          Δx = 1 / n 52  Δd

         n = 1/52 Δd / Δx

         n = 1/52 0.005 / 0.00002

         n = 4.8

Since the number of decks must be an integer the number of decks is 5