## Physics: Principles with Applications (7th Edition)

Published by Pearson

# Chapter 5 - Circular Motion; Gravitation - Questions: 12

#### Answer

Airplanes bank when they turn so that the lift force generated by the wings has a horizontal component, which the plane requires to move in a horizontal circle. The required angle can be calculated by $\theta = tan^{-1}(\frac{gr}{v^{2}})$.

#### Work Step by Step

The way to calculate the banking angle is as follows. See the diagram. The lift force’s vertical component balances the plane’s weight. $$F_{L}sin \theta = mg$$ The horizontal component provides the necessary centripetal force. $$F_{L}cos \theta = m \frac{v^{2}}{r}$$ By dividing the two equations and solving, we can find the required bank angle. $$\theta = tan^{-1}(\frac{gr}{v^{2}})$$

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