A capstan is a rotating drum (cylinder) over which a rope or cord slides in order to increase the tension due to friction. If the difference in tension between the two ends of the rope is 500 N and the capstan has a diameter of 10 cm and rotates with angular velocity 10 rad / s . Capstan is made of iron and has mass 5 kg , specific heat 1000 ~J / kg K . At what rate does temperature rise ? Assume that the temperature

Step-by-step solution

(a) The net torque that the rope exerts on the capstan, and hence the net torque that the capstan exerts on the rope, is the difference between the forces of the ends of the rope times the radius of the capstan. The capstan is doing work on the rope at a rate P= =F_ net r 2 rad T =(520 ~N ) (5.0 10⁻² ~m ) 2 rad (0.90 ~s ) =182 ~W , or 180 W to two figures. A larger number of turns might increase the force, but for given forces, the torque is independent of the number of turns. (b) T t = Q / t mc = P mc = (182 ~W )