A 4000kg helicopter is lifting 700 kg load by generating 56000N thrust. What is the magnitude of the net force on the system? What is the magnitude of the systems acceleration

Answer 1

There are a total of 3 forces that we need to take into account (We will ignore air resistance):

(1) The force of gravity on the helicopter (F_gh)

(2) The force of gravtiy on the load (F_gl)

(3) The thrust produced by the helicopter (F_T)

To solve the first question, we need to add up all the forces: "F_gh + F_gl + F_T = F_net" The force of gravity on the helicopter and the load are in the same direction and pointing towards the earth which we will call downwards (negative sign). So the summation now reads: "-F_gh + -F_gl + F_T = F_net." The force of gravity is just the mass of the object times the acceleration due to gravity (we will approximate using 10 m/s²). Therefore, "F_gh = (4000 * 10) = 40000 N" and "F_fl = (700 * 10) = 7000 N." Plug in the value of thrust into "F_T" and we have our equation, which reads "-40000 + -7000 + 56000 = F_net." So, the net force on the system is F_net = 9000 N (It is asking for magnitude, so if it were negative, we would get rid of the negative sign by taking the absolute value of it. However, it need not worry us here)

To answer the next question, we have to equate our net force to mass * acceleration according to Newton's Second Law: "F_net = ma." We will plug in the net force calculated from the last question and then plug in the total mass of the system (because the net force acts on both the load and the helicopter), which is 4000 kg plus 700 kg, so "m = 4700 kg." Now we solve for acceleration: "9000 = 4700 * a" --> a = 1.9 m/s²