Question #b625e

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Question #b625e

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Answer 1 · 2017-01-01T23:23:44

$56.23$ $56.23$ mph, rounded to two decimal places.

Explanation:

For circular motion we have the following equation connecting linear velocity $v$ $v$ , of a point located at radius $r$ $r$ , and rotating with an angular frequency $ω$ $omega$

$v = r ω$ $v=romega$ ........(1)
and $ω = 2 π f$ $omega=2pif$ .....(2)
where $f$ $f$ is frequency of rotation.

Combining (1) and (2) we get
$v = r (2 π f)$ $v=r(2pif)$
Inserting given values after converting inch to mile and minute to hour

For $14$ $14$ -inch diameter blade: $r = \frac{14}{2} = 7$ $r=14/2=7$ inch
$v_{14} = (\frac{7}{12 \times 3 \times 1760}) (2 π \times \frac{3150}{\frac{1}{60}})$ $v_14=(7/(12xx3xx1760))(2pixx3150/(1/60))$
$\Rightarrow v_{14} = 7 \times \frac{2 π \times 3150 \times 60}{12 \times 3 \times 1760}$ $=>v_14=7xx(2pixx3150xx60)/(12xx3xx1760)$
$= 131.20$ $=131.20$ mph
Similarly for $8$ $8$ -inch diameter blade: $r = \frac{8}{2} = 4$ $r=8/2=4$ inch
$\Rightarrow v_{8} = 4 \times \frac{2 π \times 3150 \times 60}{12 \times 3 \times 1760}$ $=>v_8=4xx(2pixx3150xx60)/(12xx3xx1760)$
$= 74.97$ $=74.97$ mph

Difference in linear velocity of two $= v_{14} - v_{8}$ $=v_14-v_8$
$= 131.20 - 74.97$ $=131.20-74.97$
$= 56.23$ $=56.23$ mph, rounded to two decimal places.

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Question #b625e

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