Question

Young David who slew Goliath experimented with slings before tackling the giant. He found that he could revolve a sling of length 0.700 m at the rate of 6.00 rev/s. If he increased the length to 1.000 m, he could revolve the sling only 4.00 times per second.

(a) What is the speed of the stone for each rate of rotation?
m/s at 6.00 rev/s?______
m/s at 4.00 rev/s?______

(b) What is the centripetal acceleration of the stone at 6.00 rev/s?
m/s^2?______

(c) What is the centripetal acceleration at 4.00 rev/s?
m/s^2?______

Answer 1

(a) Speed of the stone for each rate of rotation which is given as :

At 6 rev/sec,     v = r                                                                 { eq.1 }

where, r = length of the sling = 0.7 m

number of revolutions = 6 rev/sec

= angular speed = 2 / rev

inserting the values in above eq.

v (at 6 rev/s) = (0.7 m) (6 rev/sec) (2 / rev)

v (at 6 rev/s) = 26.3 m/s

At 4 rev/sec,    v = r

where, r = length of the sling = 1 m

v (at 4 rev/s) = (1 m) (4 rev/sec) (2 / rev)

v (at 4 rev/s) = 25.1 m/s

(b) The centripetal acceleration of the stone at 6 rev/s which will be given as :

using an equation, a_c = v² / r                                                                  { eq.2 }

inserting the values in eq.2,

a_c = (26.3 m/s)² / (0.7 m)

a_c = 988.1 m/s²

(c) The centripetal acceleration at 4 rev/s which will be given as :

a_c = v² / r          

a_c = (25.1 m/s)² / (1 m)

a_c = 630 m/s²