Newton's second law to find mass

[songoku]

Homework Statement

the rotor blades of a helicopter propel 2500 kg of air vertically downwards every second. The air, initially at rest, is accelerated to a speed of 15 ms^-1. If the helicopter starts to rise with an acceleration of 12.5 ms^-2, the mass of the helicopter is...

a. 1680 kg
b. 2500 kg
c. 2000 kg
d. 3000 kg
e. 3750 kg

Homework Equations

F = dp/dt

The Attempt at a Solution

let m₁ = mass of helicopter and m₂ = mass of air
When the helicopter reaches 15 ms^-1 :

F = dp / dt

m₁g = d(m₂v) / dt

m₁g = v dm₂/dt

m₁ = 15 * 2500 / 10 = 3750 kg

But in the manual, the answer is (a). Where is my mistake? Thanks

 

[Andrew Mason]

Homework Statement

the rotor blades of a helicopter propel 2500 kg of air vertically downwards every second. The air, initially at rest, is accelerated to a speed of 15 ms^-1. If the helicopter starts to rise with an acceleration of 12.5 ms^-2, the mass of the helicopter is...

a. 1680 kg
b. 2500 kg
c. 2000 kg
d. 3000 kg
e. 3750 kg

Homework Equations

F = dp/dt

The Attempt at a Solution

let m₁ = mass of helicopter and m₂ = mass of air
When the helicopter reaches 15 ms^-1 :

F = dp / dt

m₁g = d(m₂v) / dt

m₁g = v dm₂/dt

m₁ = 15 * 2500 / 10 = 3750 kg

But in the manual, the answer is (a). Where is my mistake? Thanks

What if the helicopter simply hovered? What downward force would that require? Now add to that the upward acceleration. How much force does that require? Add them together.

AM

 

[songoku]

Hi AM

I don't really get what you mean...If the helicopter simply hovers, then the force required will the same as its weight, which like what I've done above. And there will be no acceleration if the helicopter hovers.

Thanks

 

[Andrew Mason]

Hi AM

I don't really get what you mean...If the helicopter simply hovers, then the force required will the same as its weight, which like what I've done above. And there will be no acceleration if the helicopter hovers.

Thanks

Do a free body diagram. The net force = mass x acceleration. What are the forces that act on the helicopter? Add them vectorally and set that net force to equal the mass x acceleration.

AM

 

[songoku]

Hi AM

Oh now I understand where my mistake was. Thanks a lot for your help !