The crane shown in the figure is lifting a 130-kg crate upward with an acceleration of 4.02 m/s2The cable from the crate passes over a solid cylindrical pulley at the top of the boomThe pulley has a mass of 202 kgThe cable is then wound onto a hollow cylindrical drum that is mounted on the deck of the craneThe mass of the drum is 211 kg, and its radius (the same as that of the pulley) is 0.830 mThe engine applies a counterclockwise torque to the drum in order to wind up the cableWhat is the magnitude of this torque? Ignore the mass of the cable.
Tension in the cable lifting the crate is T 130kg (9.81 + 4.02)m/s? 1798 N and so the torque required to do that lifting is τ1 Td 1798N d where d is the horizontal distance from the drum to the crateWithout the diagram I can't be more specificThe torque required to rotate the pulley is τ2 Iα ?mr? a/r ?mra τ2 ? 202kg 0.830m 4.02m/s? 337 N·m The torque required to rotate the drum is τ3 Iα mr? a/r mra τ3 211kg 0.830m 4.02m/s? 704 N so τ τ1 + τ2 + τ3 1798Nd + 337N + 704N 1798Nd + 1041N·m Hope this helps!
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