A 7900- helicopter accelerates upward at 0.90 while lifting a 1100- frame at a construction site.

A) What is the lift force exerted by the 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

m*a = Liftforce - m*g

In this case m is the combined mass of the helicopter and frame,

so

9000*0.9 = Liftforce - 9000*g

Solve for lift force

B) Drawing a free body diagram on the frame:

T - mg = m*a

T - 1100*9.8 = 1100*0.9

Solve for T

C) Drawing a free body diagram on the helicopter:

Liftforce - 7900*g - F(cable) = 7900*a

A) The lift force exerted by the air on the helicopter rotors is approximately equal to the weight of the frame being lifted. So, it's like the air is saying, "Hey helicopter, you can't just leave that frame hanging there, I'll help you out!" and provides a lift force equal to the weight of the frame.

B) The tension in the cable can be determined by the sum of the forces acting on the frame. Since the frame is accelerating upwards, the tension in the cable needs to be strong enough to counteract the weight of the frame and also provide the necessary upward force. So, it's like the tension in the cable is saying, "Don't worry frame, I got you! I'll lift you up and make sure you stay in place!"

C) The cable exerts an equal and opposite force on the helicopter. So, it's like the cable is saying, "Hey helicopter, don't forget about me! While I'm helping you lift the frame, I'm also exerting a force on you in the opposite direction, keeping you balanced and stable!"

A) To find the lift force exerted by the air on the helicopter rotors, we can use Newton's second law of motion which states that force is equal to mass times acceleration (F = m * a).

The mass of the helicopter can be calculated by adding the mass of the frame (1100 kg) to the mass of the helicopter itself (7900 kg), resulting in a total mass of 9000 kg.
The acceleration is given as 0.90 m/s^2.
Thus, the lift force can be calculated as follows: F = m * a = 9000 kg * 0.90 m/s^2 = 8100 N.

B) The tension in the cable can be found by considering the forces acting on the frame. We have the force of gravity pulling it downward (mg) and the tension in the cable pulling it upward. Since the frame is not accelerating in the vertical direction, these two forces should be equal.
The force of gravity can be calculated as the mass of the frame (1100 kg) multiplied by the acceleration due to gravity (9.8 m/s^2), resulting in 10780 N.
Thus, the tension in the cable is also 10780 N.

C) The force exerted by the cable on the helicopter is equal in magnitude but opposite in direction to the tension in the cable. Therefore, the force exerted by the cable on the helicopter is also 10780 N, directed downward.

To find the answers to these questions, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Let's break down each question step by step:

A) What is the lift force exerted by the air on the helicopter rotors?
To determine the lift force, we need to calculate the net force acting on the helicopter. The net force is equal to the sum of the gravitational force pulling the helicopter down and the force required to accelerate the helicopter upward.

1. Calculate the gravitational force:
Gravitational force = mass of the helicopter * acceleration due to gravity
Gravitational force = 7900 kg * 9.8 m/s^2

2. Calculate the net force:
Net force = mass of the helicopter * acceleration of the helicopter
Net force = 7900 kg * 0.90 m/s^2

3. Subtract the gravitational force from the net force to find the lift force:
Lift force = Net force - Gravitational force

B) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?
The tension in the cable is equal to the force required to accelerate the frame upward. We can calculate this by using the mass of the frame and the acceleration of the helicopter.

Tension = mass of the frame * acceleration of the helicopter

Note: In this case, the acceleration of the frame is the same as the acceleration of the helicopter because they are connected.

C) What force does the cable exert on the helicopter?
The force exerted by the cable on the helicopter is equal in magnitude but opposite in direction to the tension in the cable. Therefore, the force exerted by the cable on the helicopter is simply the negative of the tension in the cable.

Force exerted by the cable on the helicopter = - Tension

By plugging in the given values and performing the calculations, you can find the answers to each of these questions.