Question

1. (5) A 300 lb block of ice must be lifted 60 feet using a rope that weighs 120 lbs. The rope is retracted at a rate of 6 feet. The ice is melting at a rate of 3 lbs. Find the min work required to lift the block of ice.

Answer 1

the rope: at rope 60 Olution, Work done to pull let ene foot of ene builolong be origin , and the building as y-axis. So, a small parst of the a height y ft above origin of length dy will have mass equals to dm = 120 o dy dm zdy Work required to put this mass a height of (60-4) ft will dw= dmg (60-4) 29 (60-4) dy => W = f 2g (60-4) dy |W, = 3600g Work done to pull are block utols and as 1/min. metting at be ile is being purred at 6th 3 lbs /min ersler 2 B ice meeting at 32 lbsift dm - 1/2 => M(Y) = -5/2 tc dy a m (0) = 300 = M(Y) = 300-9/2 so work done to move mly from a 60ff hear 1 to a height woll be W = 55°300 –92)9 (600-y)dy 0 W₂ = 522000g = (3600+ 522000)9 = 16819200 W Total