Question

Motionless chain A frictionless tube lies in the vertical plane ard is in the shape of a func- tion that has its endpoints at the same beight but is otherwise arbitrary end, as shown in Fig. 2.9. Show, by considering the net force of gravity along the curve, that the chain doesn't move Fig. 29

Ive tried this question over and over again... pondered over it last night but in vain. Can someone solve this for me, I’ve given up. Thanks in advance

Answer 1

Break the chain in small segments. To get the net force on chain, at every segment we must look at the force tangent to the tube.

Break the chain in small segments. To get the net force on chain, at every segment we must look at the force tangent to the tube. Take force = dT the dT will add up for enoy segment let length be dl in direction dl gravitation force on the segment is = -lambda g dl y lambda in density Component of force in direction of dl dF = -lambda g dl y. dl dl dl = dl = dn x + dy y dF = -lambda g dy implies F_net = integral dF = -lambda g integral^0_0 dy = 0 It motionless.