Question

< Homework 10 Question 10 The mechanism shown in the figure (Figure 1)is used to raise a crate of supplies from a ship's hold. The crate has total mass 56 kg A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius 0.34 m and a moment of inertia I = 2.5 kg. m2 about the axle. The crate is suspended from the free end of the rope. One end of the axle pivots on frictionless bearings, a crank handle is attached to the other end. When the crank is turned the end of the handle rotates about the axle in a vertical circle of radius 0.12 m, the cylinder turns, and the crate is raised. Figure < 1 of 1 10.12 m

Answer 1

Force required to accelerate the crate, Fc = weight (mg) + accel. force (ma)

Fc = 56kg x (9.81 + 1.40)m/s = 627.76 N

Torque at cylinder due to crate, Tc = Fc x r = 627.76 N x 0.34m = 213.438 Nm

Torque required to accel. cylinder, T' = I.α

T' = 2.50 kg.m² x (1.40 / 0.34) = 10.294 Nm (v = rω→dv/dt = r.dω/dt→ a = r.α→α = a/r)

Total torque required = Tc + T' = (213.438 + 10.294) = 223.732 Nm

Torque at handle, Fh x 0.12m = 223.732 Nm

Fh = 223.732 / 0.12

Fh = 1864.43 N

so Fh = 1.9 x 10³ N (put this value if unit is in NEWTON )

or Fh = 1.9 kN ( put this value if unit is in Kilo - Newton )