A Windmill Blade Centripetal Acceleration Calculation

A windmill turbine generates electricity by converting wind energy into mechanical energy

On a good windy day, the windmill blades can spin up to 18.0 revolutions per minute. If a windmill blade has a length of 140 feet and spins at the maximum rate, what is the centripetal acceleration at the end of the blade expressed in units of gravitational acceleration g?

Therefore, the centripetal acceleration at the end of the blade expressed in units of gravitational acceleration g is 0.0023 g.

The centripetal acceleration at the end of the blade expressed in units of gravitational acceleration g can be calculated using the formula given below;

where v is the linear velocity and r is the radius of the blade.

Let's find the value of v. One revolution of the windmill blade covers a distance equal to the circumference of a circle.

The circumference of a circle can be calculated by multiplying the diameter of the circle by pi.

Therefore, the circumference of the windmill blade can be calculated as follows:

Length of the windmill blade = 140 feet

Diameter of the windmill blade = 140 feet

Therefore, the radius of the windmill blade can be calculated by dividing the diameter by 2: r = 140 / 2 r = 70 feet

The circumference of the windmill blade can be calculated as follows:

C = πd C = π(140) C = 440 feet

Therefore, the distance covered by the end of the blade in one revolution can be calculated as:

Circumference of the blade / No. of revolutions = (440 feet/rev) / (18 rev/min) = 24.44 feet/min = 4.56 x 10-4 mile/min

The distance covered by the end of the blade in one minute can be converted to meters per second (m/s) as follows:

1 mile = 1609.34 meters 1 minute = 60 seconds

Therefore, the distance covered by the end of the blade in one minute is 0.695 meters per second (m/s). The value of r is 70 feet, which is equivalent to 21.34 meters.

The formula for centripetal acceleration can be expressed as follows:

a = v2/r

Where a is the centripetal acceleration, v is the linear velocity, and r is the radius of the blade.

Substituting the values for v and r gives us:

a = (0.695 m/s)2 / (21.34 m) = 0.0226 m/s2

The acceleration due to gravity (g) is 9.81 m/s2, so the centripetal acceleration at the end of the blade expressed in units of gravitational acceleration g is:

a/g = 0.0226 m/s2 ÷ 9.81 m/s2 = 0.0023 g

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