A helicopter of mass M and weight ,W,rises with vertical acceleration, a, due to the upward thrust ,u, generated by its rotor.The crew and passengers of total mass ,m, and total weight,w, exert a combined force R on the floor of the helicopter.Write an equation for the motion of: (a)the helicopter and (b)the crew and passengers

To write the equations of motion for the helicopter and the crew/passengers, we will apply Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.

(a) Equation for the motion of the helicopter:

The net force acting on the helicopter is the difference between the upward thrust generated by its rotor (u) and its weight (W):

Net force on the helicopter = u - W

From Newton's second law, we can write:

Net force on the helicopter = mass of the helicopter (M) * acceleration (a)

Therefore, the equation for the motion of the helicopter is:

u - W = M * a

(b) Equation for the motion of the crew/passengers:

The net force acting on the crew/passengers is the force exerted by the floor (R) minus their weight (w):

Net force on the crew/passengers = R - w

From Newton's second law, we can write:

Net force on the crew/passengers = mass of the crew/passengers (m) * acceleration (a)

Therefore, the equation for the motion of the crew/passengers is:

R - w = m * a

These equations describe the motion of the helicopter and the crew/passengers.