The Thrilling Lift: Helicopter and Frame Acceleration
What forces are at play when a helicopter accelerates upward while lifting a construction frame?
(a) How much lift force is exerted by the air on the helicopter rotors?
(b) What is the tension in the cable connecting the frame to the helicopter?
(c) What force does the cable exert on the helicopter?
Answer:
(a) The lift force exerted by the air on the helicopter rotors is 94340 N.
(b) The tension in the cable, disregarding its mass, is 13250 N.
(c) The cable exerts a force of 13250 N on the helicopter.
When a 7180-kg helicopter accelerates upward at 0.80 m/s2 while lifting a 1080-kg frame at a construction site, several forces come into play. The lift force exerted by the air on the helicopter rotors is crucial for the vertical movement. At the same time, the tension in the cable connecting the frame to the helicopter ensures stability and balance during the lift.
Calculating Lift Force:
Using Newton's second law, the lift force can be calculated as FL = (m1 + m2)(g + a) = (7180 + 1080)(9.8 + 0.8) = 94340 N.
Calculating Cable Tension:
The tension in the cable can be found by balancing the forces acting on the frame. T = m2(g + a) = 1080(9.8 + 0.8) = 13250 N.
Therefore, the lift forces and cable tensions are essential components in ensuring the safe and efficient movement of the helicopter and frame during acceleration.