Dimensional Analysis Problem?

Ms. McDonald likes to cut her grass with her fast lawn mower that travels at 122 rpm when she’s moving at 3.2 mph. Find the radius of the mower’s wheel in inches?

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  • Anonymous
    8 months ago
    Favourite answer

    (1) Circumference of a circle:

    C = 2 π r | |

    r | radius

    C | circumference

    therefore,

    r = C / (2 π)

    (2) Linear speed vs revolutions:

    v = C * f | |

    v | speed

    C | circumference

    f | revolution frequency

    Therefore,

    C = v / f

    Therefore from the two equations for circumference, we get:

    v / f = 2 π r

    Rearrange to find radius:

    r = v / ( 2 π f)

    = 3.2 mph / (2 π (122/min))

    = 3.2 mph / (2 π {7320/hour))

    = 6.96×10^-5 miles

    = 4.41 inches

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  • 8 months ago

    Did you copy the problem incorrectly?

    Assuming the wheels spin at 122 rpm

    Assuming you can convert miles to inches

    (x mi) * (5280 ft/mi) * (12 in/ft) = 12*5280x in

    And that you can convert h to min

    (x h) * (60 min/h) = 60x min

    Then converting mi/h to in/min is not a problem

    (3.2 mi/h) * (5280 ft/mi) * (12 in/ft) * (1/60 h/min) = 3380 in/min

    Then dividing with 122/min gives you the single circumference of a wheel in inches, and dividing with 2pi gives you its radius.

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  • Amy
    Lv 7
    8 months ago

    Dimensional analysis is seeing that to get a final answer in inches, you'll have to divide mph by rpm.

    Dimensional analysis is converting the 3.2 mph to inches per minute.

    Dimensional analysis does NOT tell you how to get from revolutions to radius. That's geometry.

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  • 8 months ago

    Can’t be bothered

    • ...Show all comments
    • Lv 7
      8 months agoReport

      Then why bother answering anything at all? Is it to get the automatic 2 points?

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