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A student is asked to calculate the centripetal acceleration of a hummingbird that makes a complete circle in 0.43 seconds. If the circle has a radius of 0.25 m, what is
the correct setup for determining the centripetal acceleration of the hummingbird?
(3.65m/s)2/0.25m
(3.65m/s)2-0.43
O (0.435)2 / 25m
O (0.432.25m

Respuesta :

onyebuchinnaji

The centripetal acceleration of the hummingbird is [tex]\frac{(3.65)^2}{0.25} = 53.29 \ m/s^2[/tex]

The given parameters;

  • time of motion of the hummingbird, t = 0.43 s
  • radius of the circle, r = 0.25 m
  • number of revolution of the hummingbird = 1 rev per 0.43 s

The angular speed of the hummingbird is calculated as follows;

[tex]\omega = \frac{1 \ rev}{0.43 \ s} \times \frac{2\pi \ rad}{1 \ rev} =14.61 \ rad/s[/tex]

The linear speed of the hummingbird is calculated as follows;

v = ωr

v = 14.61 x 0.25

v = 3.65 m/s

The centripetal acceleration of the hummingbird is calculated as follows;

[tex]a_c = \frac{v^2}{r} \\\\a_c = \frac{(3.65)^2}{0.25} \\\\a_c = 53.29\ m/s^2[/tex]

Thus, the centripetal acceleration of the hummingbird is [tex]\frac{(3.65)^2}{0.25} = 53.29 \ m/s^2[/tex]

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