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Anastaziya [24]
3 years ago
5

An electric fan is turned off, and its angular velocity decreases uniformly from 500 rev/min to 200 rev/min in 4.00 s.

Physics
1 answer:
Veseljchak [2.6K]3 years ago
3 0

Answer:

a) -1.25 rev/s² and 23.3 rev

b)  2.67s

Explanation:

a) ωФ_o_z = (500 rev/min)(1min/ 60s) => 8.333 rev/s

ωФ_Z= (200 rev/min)(1min/ 60s) => 3.333rev/s

time 't'= 4 s

angular acceleration 'αФ_Z'=?

constant angular acceleration equation is given by,

ωФ_Z= ωФ_o_z + αФ_Zt

αФ_Z= (ωФ_Z - ωФ_o_z )/t => (3.333-8.333)/4

αФ_Z= -1.25 rev/s²

θ-θФ_o = ωФ_o_z t + 1/2αФ_Zt²

      =(8.333)(4) + 1/2 (-1.25)(4)²

      =23.3 rev

b) ωФ_Z=0   (comes to rest)

ωФ_o_z = 3.333 rev/s

αФ_Z= -1.25 rev/s²

ωФ_Z= ωФ_o_z + αФ_Zt

t= (ωФ_Z - ωФ_o_z)/αФ_Z => (0- 3.333)/-1.25

t= 2.67s

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y=0 m is the ball final height (when it hits the ground)

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0 m=1.1 m+(2.2 m/s)(cos 30\°)t-\frac{9.8 m/s^{2}}{2}t^{2} (3)

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Substituting the known values and choosing the positive result of the equation, we have:  

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Now, substituting (6) in (2):

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x=1.12 m (8) This is the horizontal distance at which the ball hits the ground.

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