Helicopter Lift Force Calculation

[strugglin-physics]

A 7850 kg helicopter accelerates upward at 0.545 m/s^2 while lifting a 1250 kg car. What is the lift force exerted by the air on the rotors?

What is the tension in the cable ignoring its mass that connects the car to the helicopter?

Net Force = ma, so I did (7850)(0.545) + (1250)(0.545) = 4959.5 N but that answer is incorrect and I know if I don't have the right answer for the first one I will not be able to solve the second one.

Would appreciate someone's assistance, thank you.

 

[Tide]

I think you left out gravity!

 

[strugglin-physics]

Maybe you are correct... hmm... but where would I include it in this formula... Net Force = ma?

 

[Tide]

The total acceleration will be the acceleration due to gravity plus the acceleration produced by the helicopter.

 

[strugglin-physics]

so you're say that my a should equal .545 + -9.8 giving me an answer of -84221?

 

[Tide]

Let me state that a little more clearly. The net force acting on the car is the sum of the gravitational force and the force due to the helicpopter:
$$\vec F = \vec F_g + \vec F_h = m \vec a$$
so the force excerted by the helicopter is
$$\vec F_h = m \vec a - \vec F_g$$
Now gravity pulls downward (i.e. it's negative) so the net force in the vertical direction is F = ma - (-mg) = m(a+g) which is also the tension on the cable.

 

[strugglin-physics]

I'm feeling rather dumb as I still don't know what the lift force exerted by the air on the rotors is, but I do appreciate your attempt to help me understand. Maybe the solution will come to me...

Thanks again.

 

[Tide]

The lift force exerted on the air will be equal to the tension on the cable plus the force required to accelerate the helicopter upward!

 

[strugglin-physics]

Duh... now that seems pretty obvious! Thank you.