Question

A bird generates a lift of 3 x 10^1 N at its maximum velocity of 14m/s, the bird has a mass of .020kg what is the tightest radius that it can turn and maintain its altitude?

Answer 1

Answer on Question #48382, Physics, Mechanics | Kinematics | Dynamics

A bird generates a lift of $3 \times 10^1 \, \text{N}$ at its maximum velocity of $14 \, \text{m/s}$, the bird has a mass of $0.020 \, \text{kg}$ what is the tightest radius that it can turn and maintain its altitude?

Solution:

The force equation

$$ma = F - mg$$

where $a$ is the centripetal acceleration, $a = \frac{V^2}{R}$.

$$m(a + g) = m\left(\frac{v^2}{R} + g\right) = T$$

Thus,

$$a = \frac{F - mg}{m} = \frac{F}{m} - g = \frac{30 \, \text{N}}{0.020 \, \text{kg}} - 10 \, \frac{\text{m}}{\text{s}^2} = 1490 \, \text{m/s}^2$$ $$\frac{v^2}{R} = a$$

Thus,

$$R = \frac{a}{v^2} = \frac{1490}{14^2} = 7.6 \, \text{m}$$

Answer: $R = 7.6 \, \text{m}$

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