Question

A ship is dragged through a lock by means of a capstan and rope. The capstan, which has a diameter of 500 mm, turns at 30 rpm. The rope makes 3 complete turns around the capstan. ? = 0.25, and at the free end of the rope a pull of 100 N is applied. Find (a) The pull on the ship (b) The power required to drive the capstan.

Answer 1

a) To find pull using eqation

T2/T1=e^(u*theta) where u= 0.25 and since it makes 3 turns therefore theta= 3*360 deg= 1080 deg = 1080*(π/180) rad = 18.852 rad

Therefore e^(u*thets)

= e*(0.25*18.852)

= 111.386 therefore

T2/T1= 111.386 and given T1= 100 N

T2= 111.386*100

T2= 11138.6 N = 11.138 KN

Therefore pull on ship is 11.138 KN

b) Now power P= T2*V where V is velocity

V=r*w and w= 2*π*N/60 where N= 30 rpm and r is radius= 0.25 m

w= 2*π*30/60 = 3.142 rad/s

V=0.25*3.142 = 0.7855 m/s

Power P = T2*V

P = 11.138*0.7855

P= 8.74 kilowtt

Therefore Power required is 8.74 KW