1. The helicopter can produce a maximum downward air speed v = 24m/s in a slipstream of diameter D = 9 m. Knowing that the weight of the helicopter and crew is 15 kN and assuming air density ρ= 1.21 kg/m3 , determine the maximum load that helicopter can lift while hovering in midair. (29.3 kN)
2. In the helicopter a vertical tail rotor is used to prevent rotation of the cab as the speed of main blades is changed. Assuming that the angular velocity of the cab remains zero. determine the force exerted by the tail rotor when the speed of the main blades is changed uniformly from 180 to 240 rpm in 12 s. Also determine the final horizontal velocity of the cab which has a mass of 567 kg and is initially at rest. (64.9 N ; 1.17 "z/s)
3. A uniform cylinder A has a mass m = 3 kg , radius r = 150 mm , and can roll without sliding on a cart C of mass M = 5 kg. Cylinder A is attached to a spring AB of stiffness (constant) k = 100 N/m in as shown. The system is released from rest when the spring is stretched Δx = 20 mm. Neglecting wheel friction, determine the velocity of the cart and the angular velocity of the cylinder when the spring first reaches its undeformed state. (40.8 mm, ; 0.726 f1)
4. A thin homogeneous rod of mass m= 0.8 kg is used to form the shaft shown. Knowing that the m 100 mm shaft rotates with a constant angular velocity ω = 20 s-1, determine the dynamic reactions at supports A and B. [A = (2.58 N)k : B = (-2.58 N)kl.
