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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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