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2 years ago

A fan has four identical, symmetrically placed blades. The blades are rotating clockwise at twenty revolutions per second.

Physics

1 answer:

elena55 [62]2 years ago

5 0

Answer:

A) t = 1.249 10⁻² s, B) f = 80 Hz, C) f = 20 Hz,

D) slowly advancing an angle of approximately Δθ = 0.05 rad each flash

E) In each flash it seems to go backward an angle of Δθ = -0.05 rad

Explanation:

A) To make it appear that the blades are immobile, it implies that every time the light turns on, a blade should be in the same position, therefore, as we have 4 blades, they must rotate an angle of 2π/4,

θ = π / 2

θ = 1.57 rad

taking the angle let's use the endowment kinematics relations

θ = w₀ t + ½ α t²

in general the fans rotate at constant speed α= 0

θ = w₀ t

t = θ / w₀

let's reduce the magnitudes to the SI system

w₀ = 20 rev / s (2π rad / 1rev) = 125.66 rad / s

let's calculate

t = 1.57 / 125.66

t = 1.249 10⁻² s

B) the fastest speed for the blades to rotate is when one blade of a complete turn , we use the relationship between the fecuance and the period

f = 1 / T

f = 1 / 1.25 10⁻²

f = 80 Hz

C) we have two possibilities:

* a yellow dot is placed on each sheet

In this case the angular velocity of the blade is the same at all points, therefore the results obtained should not change

* a yellow dot is placed on a single sheet.

Here for the point to remain fixed the angle of rotation must be

θ= 2π rad

the time is

t = 2π / 125.66

t = 5 10⁻² s

the maximum frequency is

f = 1/5 10⁻²

f = 20 Hz

D) The copy strobe rotates at f = 19 Hz, the time between each flash is

t = 1/19

t = 5.26 10⁻² s

this time is higher, so the angle turned is large

θ = w t

θ = 125.66 5.26 10⁻²

θ = 6.61 rad

the relationship between this angle and the angle of a circle is

θ = 1,052

We can see that it is this time the blade rotates 1 complete turns, for this the position of the blade changes us, for the other 0.052 rad the blade rotates a little more than the circumference therefore it seems that it is slowly advancing an angle of approximately

Δθ = 0.05 rad each flash

E) in this case changes the flash speed

t = 1/21

t = 4.76 10⁻² s

the angle rotated is

θ = 125.66 4.76 10⁻²

θ = 5.984 rad

θ / 2π = 0.95

in that case, the blade did not complete the turn, therefore in each flash it seems to go backward an angle

Δθ = -0.05 rad

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