Physics
18.01.2022 18:30
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Awind turbine has 12,000 kg blades that are 36 m long. the blades spin at 24 rpm

Awind turbine has 12,000 kg blades that are 36 m long. the blades spin at 24 rpm .if we model a blade as a point mass at the midpoint of the blade, what is the inward force necessary to provide each blade's centripetal acceleration?
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austinwst3
austinwst3
4,9(43 marks)

As we know that centripetal force is given as

F = m\omega^2 R

here we know that

m = 12000 kg

R = 18 m

here we assumed that radius is half of the length of blade as here the center of mass is concentrated at mid point of blade

\omega = 2\pi f

\omega = 2\pi \frac{24}{60} = 0.8\pi

now the force is given as

F = 12000\times (0.8\pi)^2 \times 18

F = 1.36 \times 10^6 N

so above is the centripetal force on the blade

natalie2sheffield
natalie2sheffield
5,0(1 marks)

10 s

Explanation:

Given

Engine generates 100,000\ W power

Force exerts F=10,000\ N

Distance traveled d=100\ m

work done is given by

W=F\cdot d\\W=10,000\times 100\\W=10^5\ J

Also, Energy is given as

\Rightarrow E=P\cdot t

Insert the values

\Rightarrow 10^6=100,000\times t\\\\\Rightarrow t=\dfrac{10^6}{10^5}\\\\\Rightarrow t=10\ s

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