Young David who slew Goliath experimented with slings before tackling the giant.

Question

Young David who slew Goliath experimented with slings before tackling the giant. He found that he could revolve a sling of length 0.750 m at the rate of 8.00 rev/s. If he increased the length to 1.050 m, he could revolve the sling only 6.00 times per second. (a) What is the speed of the stone for each rate of rotation? m/s at 8.00 rev/s m/s at 6.00 rev/s (b) What is the centripetal acceleration of the stone at 8.00 rev/s? m/s2 (c) What is the centripetal acceleration at 6.00 rev/s? m/s2 Need Help? Talk to a Tutor

Explanation / Answer

r1= 0.75 m,

w1 = 8 rev/s = (8*2*3.14)rad/s = 50.26 rad/s

r2 = 1.05 m ,

w2 = 6rev/s =(6*2*3.14)rad/s = 37.7 rad/s

(a) v1 = r1*w1

        = (0.75*50.26)

v1= 37.69 m/s

v2 = r2*w2

    = (1.05*37.7)

v2 = 39.58 m/s

(b) ac =v^2/r

a1 = v12/r1

    = (37.69*37.69) / 0.75

a1 = 1894 m/s^2

(c) a2 = v22/r2

         = (39.58*39.58) / 1.05

a2 = 1492 m/s^2

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