Calculating Lift Force for a Helicopter and Car System

[MorganJ]

Homework Statement

A 13,000-kg helicopter accelerates upward at 0.37 m/s^2 while lifting a 2000 pound car. To the nearest Newton, what is the lift force exerted by the air on the rotors?

Homework Equations

I thought since the problem is dealing with forces, I would use F=ma but that wouldn't be the only equation I would use. I know I am dealing with two masses so I don't know how to arrive at the answer.

 

[kuruman]

You can still use F = ma. In fact you should. The masses move as one, so you can pretend they are a single mass. Don't forget to convert the weight of the car from pounds to mass in kilograms.

 

[MorganJ]

Okay so do I group the helicopter and the car as one by adding the two masses together? And if so, how do I get the lift force? I know it cannot just be by doing F=ma.

 

[kuruman]

Okay so do I group the helicopter and the car as one by adding the two masses together? And if so, how do I get the lift force? I know it cannot just be by doing F=ma.

Yes, you group the helicopter and the car as one. How do you know "it cannot just be by doing F = ma?" Draw a free body diagram and put in all the forces. The force exerted on the system by the air is only one of them.

 

[MorganJ]

it would just be (15000)(0.37), that would be only 5550 N. Wouldn't the number be a bit bigger than that? Wouldn't tension be involved?

 

[kuruman]

First off what does 15000 represent? Let me repeat what I said in post#2. "Don't forget to convert the weight of the car from pounds to mass in kilograms."

Secondly, did you draw a free body diagram? What does multiplying the mass of the (helicopter plus car) system by the acceleration give you? Hint: It is not the force exerted by the air. What force is it?

 

[MorganJ]

Oh, I see! So 2000 lbs. roughly is about 909.1 kg. So 13,000+909.1= 13909.1 kg. (13909.1)(0.37)=5146.367 N. Wouldn't the force be the force of gravity?

 

[MorganJ]

Ok I found the answer. Thank you for your help.

 

[kuruman]

No. The force of gravity is mg. Read up on Newton's Second Law. What does F on the left side of the equaiton stand for?

 

[kuruman]

I am glad you found the answer.