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Question

Young David who slew Goliath experimented with slings before tackling the giant. He found that he could revolve a sling of length 0.600 m at the rate of 7.00 rev/s. If he increased the length to 0.900 m, he could revolve the sling only 5.00 times per second.
(a) What is the speed of the stone for each rate of rotation?
m/s at 7.00 rev/s, at m/s at 5.00 rev/s
(b) What is the centripetal acceleration of the stone at 7.00 rev/s?
(c) What is the centripetal acceleration at 5.00 rev/s?

Answer 1

(a) Length of the sling (r)= 0.6 m
Number of revolutions/second= 7
Speed = (Circumference x No. of rev./sec)
.............= 2 π r x 7 = (2 x 22 x .6 x 7) / 7
.............= 26.4 m/s at 7 rev.per sec
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Length of the sling (r) = 0.9 m
Number of revolutions/second = 5
Speed = (Circumference x No. of rev. /sec)
.............= 2 x π x r x 5 = (2 x 22 x .9 x 5) / 7
.............= 28.29 m/s at 5 rev. per sec
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(b) Centripetal acceleration at 7 rps= v² / r
...........................................=(26.4)² / 0.6 = 1161.6 m/s²
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(c) Centripetal acceleration at 5 rps = v² / r
...........................................= (28.29)² / 0.9 = 889.25 m/s²
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Answer 2

The string length is the radius r of the arc. At n revs per sec, the stone travels a distance of 2*π*r. The stone's speed is then 2*π*r*n.

Once you have the speed, the centripetal acceleration is -v^2 / r.

Answer 3

Who Slew Goliath