Answer to Question #116386 in Mechanics | Relativity for Michael Mateus

Question

5. A 7650 kg helicopter accelerates upward at 0.80m/s2, while lifting a 1250 kg frame at
a construction site.

a) What is the lift force exerted by air on the helicopter rotors?
b) What is the tension in the cable (ignore its mass) that connects the frame to the
helicopter?
c) What force does the cable exert on the helicopter?

Answer 1

a) What is the lift force exerted by air on the helicopter rotors?

According to Newton's second law:

$$F_L-(m+M)g=(m+M)a,\\ F_L=(m+M)(g+a)=\\ =(1250+7650)(9.8+0.8)=94340\text{ N}.$$

b) What is the tension in the cable (ignore its mass) that connects the frame to the

helicopter?

From the equilibrium of forces we have:

$$T-mg=ma,\\ T=m(g+a)=13250\text{ N}.$$

c) What force does the cable exert on the helicopter?

This force is the tension, 13250 N.