Question

a boy whirls a stone in a horizontal circle 1.8m above ground by means of a spring 1.2m long. the spring breaks and the stone flies off horizontally, striking the ground 9.1m away . find the centripetal acceleration during the circular motion?

ans:- 188m/s2

Answer 1

A boy whirls a stone in a horizontal circle 1.8m above ground by means of a spring 1.2m long. The spring breaks and the stone fly off horizontally, striking the ground 9.1m away. Find the centripetal acceleration during the circular motion?

Equations for projective motion:

$$v t = l$$ $$h = \frac {g t ^ {2}}{2}$$

where $l = 9.1 \, \text{m}, h = 1.8 \, \text{m}$

Therefore, initial speed of stone equals:

$$v = \frac {l}{\sqrt {2 * \frac {h}{g}}}$$

And centripetal acceleration:

$$a = \frac {v ^ {2}}{r} = \frac {l ^ {2} g}{2 r h} = 188 \, \text{m/s}^2$$

Answer: $188 \, \text{m/s}^2$