A boy whirls a stone with mass 250g in a horizontal circle of radius 1.5m and at height 3.0 m above level ground. The string breaks, and the stone flies off horizontally and strikes the ground after travelling a horizontal distance of 8m. What is the magnitude of the centripetal acceleration and the centripetal force of the stone during circular motion?

Question

anonymous · Answer

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We can calculate the stone's tangential velocity (vo) by determining the amount of time it takes for the stone to fall 3m, then by dividing the x displacement (8) over this amount of time.
$$h=-(1/2)*g*t^2$$
$$t=(-2h/g)^.5$$
$$vo=xf/(-2h/g)^.5$$
Using this, it is a simple matter of plugging this vo value into the centripital acceleration formula to get the acceleration:
$$ac=vo^2/r$$
And plugging into the basic force eqation to get the centripital force:
$$F=mac$$