Question

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

Let us determine the forces that are applied to the helicopter, namely the forces of gravity, lift force, tension. We use the projection on the vertical axis and get

$m_ha = F_{lift} - m_hg-T, \;\; T = m_f(g+a) \Longrightarrow m_ha = F_{lift} - m_hg-m_f(g+a).$

a) Therefore, $F_{lift} = (m_h+m_f)(g+a) = (7650\,\mathrm{kg}+1250\,\mathrm{kg})(9.8\,\mathrm{m/s^2}+0.8\,\mathrm{m/s^2}) = 94340\,\mathrm{N}.$

b) The tension in the cable is $T = m_f(g+a) = 1250\,\mathrm{kg}\cdot(9.8\,\mathrm{m/s^2}+0.8\,\mathrm{m/s^2}) = 13250\,\mathrm{N}.$

c) The tension is equal to the tension, so it is also $13250\,\mathrm{N}.$