What Is the Correct Calculation of Lift Force for an Ascending Helicopter?

[jrbillbrian]

Homework Statement

A helicopter with a mass of 2090 kilograms accelerates up at 3.13 meters per second per second. What lift force is exerted by the air on the propellers?

m = 2090 kg
a = 3.13 m/s/s

Homework Equations

F = ma ?

The Attempt at a Solution

Force = 2090 kg * 3.13 m/s/s = 6541.7 N

Which is apparently incorrect, then I thought I might have read it wrong and I tried -6541.7, which is also wrong. Can anyone tell me what I am doing wrong? Did I forget to factor something in?

 

[Jasso]

What would be the lift force if the helicopter were just hovering?

 

[jrbillbrian]

2090 kg * 9.8 ( 9.8 N in 1 kg)
= 20482 N?

 

[jrbillbrian]

Or would it just be 0? I'm very confused.

 

[Jasso]

20482 N is correct.

F_total = F_lift + mg

The lifting force pushing up on the propellers must be of equal to the weight of the helicopter in the opposite direction as gravity when it hovers (when F_total = 0).

So what would the lifting force be if it accelerated upwards as your original question stated?

 

[jrbillbrian]

F_total = F_lift + mg
F_total = 6541.7 N + 2090 * 9.8?
F_total = 27023.7 ?

I'm just so confused.

 

[Jasso]

F_total = F_lift + mg
F_total = 6541.7 N + 2090 * 9.8?
F_total = 27023.7 ?

I'm just so confused.

Two points here:

1.) Acceleration due to gravity (g) is -9.8 m/s², you forgot that it's negative since it acts downwards.

2.) The acceleration of the helicopter is cause by the total force acting on it, not just the lifting force.

So what force would the lift have to be so that the total force accelerates the helicopter upward at 3.13 m/s²?

 

[jrbillbrian]

so 6541.7 N + (2090 kg * -9.8)
= -13940.3 N

So you would need 13940.3 N?