A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take $$g = 10$$ m/s$$^2$$)

Solution :

Speed of car :

$$54\text{ km h}^{-1}$$

$$= \frac{54 \times 1000}{3600}$$

$$= 15\text{ m s}^{-1}$$

Radius of turn :

$$r = 20\text{ m}$$

Centripetal acceleration :

$$a_c = \frac{v^2}{r}$$

$$= \frac{15^2}{20}$$

$$= \frac{225}{20}$$

$$= 11.25\text{ m s}^{-2}$$

For pendulum in turning car :

$$\tan\theta = \frac{a_c}{g}$$

$$= \frac{11.25}{10}$$

$$= 1.125$$

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