Tension in a rope holding a mass under a helicopter rising at constant speed

[John Mcrain]

Homework Statement

Tension in rope,constant speed

Relevant Equations

F=ma

Helicopter lift weight of 500kg ,weight is connect with load cell to meassure tension.
Neglect aerodynamic drag..

If helicopter accelarate up ,tension is rope is greater than 500kg.
If helicpter accelarate down ,tension is rope is less than 500kg.

If helicopter fly up with constant speed ,tension is rope is 500kg.
If helicopter fly down with constat speed tesnion in rope is 500kg

Am I correct?

 

[PeroK]

Yes. Although, tension is measured in Newtons, not kilograms.

 

[John Mcrain]

Yes.

What will be max velocity of helicopter when fly up if there is no aero drag force(vacuum)?

 

[italicus]

First of all, m=500 kg is a mass, not a weight. If you suppose g = about 10 m/s^2 , the weight is 5 kN .
If the helicopter accelerates up, the tension in the rope iincreases , because T -mg =ma —> T =m(g+a) .
The opposite happens when it accelerates down, write yourself the second equation of dynamics. But be careful, T is always directed from the mass toward the helicopter.
So, if a=0 the speed is costant , and the tension doesn’t change.

 

[John Mcrain]

First of all, m=500 kg is a mass, not a weight. If you suppose g = about 10 m/s^2 , the weight is 5 kN .
If the helicopter accelerates up, the tension in the rope iincreases , because T -mg =ma —> T =m(g+a) .
The opposite happens when it accelerates down, write yourself the second equation of dynamics.
So, if a=0 the speed is costant , and the tension doesn’t change.

Yes I must write mass instead weight..

(if neglect air drag)
So if helicopter fly up with 5km/h or 5000km/h tension in rope in both case is 5kN?

What will determine max speed when helicopter fly up if there is no aero drag(vacuum)?

 

[Steve4Physics]

What will determine max speed when helicopter fly up if there is no aero drag(vacuum)?

Trick question. A helicopter can't work in a vacuum

 

[John Mcrain]

Trick question. A helicopter can't work in a vacuum

Ok let's say it has rocket propulsion..

 

[hutchphd]

A rocket can go as fast as you want (ask the Apollo folks) until Einstein intervenes. The ordinary Helicopter will have some speed of sound issues

 

[John Mcrain]

So if helicoter weight is 5kN and helicoter max lift is 6kN(rocket propulsion),helicopter will accelarate to speed of light if there is no aero drag,only gravity force?

 

[hutchphd]

It will go fast. Einstein says it will not get to speed of light. In practice it will not get even close because of fuel required.

 

[John Mcrain]

It will go fast. Einstein says it will not get to speed of light. In practice it will not get even close because of fuel required.

Yes but it doesn't metter how much thrust it has, 5.1kN or 5 000 000 kN,in both case will try to reach the speed of light.?

 

[hutchphd]

Yes. More thrust just speeds up the process. But rockets provide constant force. This is actually different from a propeller because the air is involved. The rocket doesn't care...it does not "push on the air".

 

[italicus]

So if helicopter fly up with 5km/h or 5000km/h tension in rope in both case is 5kN?

Answer the question by @PeroK, first. He asked you: " What will be max velocity of helicopter when fly up if there is no aero drag force(vacuum)?” Maybe the rope has a breaking load that can’t be overcome? What this breaking load limits, in this problem?
Please, do not speak of relativity and speed of light every now and then, this is a very simple exercise of non relativistic mechanics!

Trick question. A helicopter can't work in a vacuum

@Steve, it is less tricky than what you imagine. It is logical that a helicopter works in air, the blades move down air with their rotation, and for reaction the helicopter stays up. Don’t introduce complications where they are not. The friction that is supposed to be possibly neglected is that on the suspended mass and the rope, we don’t care of the helicopter.

@John

without doubt, starting from rest the helicopter has to reach the speed you suggest, i.e. 5000 km/h , so it must accelerate for a while...But the problem is : is the rope able to sustain the over-tension caused by that acceleration ? Will it not break before? Answer the question by Perok.

 

[John Mcrain]

Answer the question by Perok.

PeroK didnt ask me any question,where are you looking at?

 

[hutchphd]

Please, do not speak of relativity and speed of light every now and then, this is a very simple exercise of non relativistic mechanics!

Please stop telling folks what to do.

The OP was just indicating his knowledge of the fundamental speed limit.
What is your answer to @PeroK question? I believe it is quite complicated for a real helicopter..

 

[PeroK]

PeroK didnt ask me any question,where are you looking at?

I can confirm that I have not asked a question in this thread!

 

[hutchphd]

I believe the question was in fact posed by @John Mcrain and I perpetuated the mistake...vis "how fast can the helicopter go" Apologies.

 

[italicus]

Sorry @PeroK, question in #3 was not asked by you.

Please stop telling folks what to do.

I’m not telling folks. Do what you want, but I repeat that this is a simple exercise of non-relativistic mechanics.

 

[hutchphd]

Sorry @PeroK, question in #3 was not asked by you.I’m not telling folks. Do what you want, but I repeat that this is a simple exercise of non-relativistic mechanics.

Manifestly not so for the OP.

.

 

[John Mcrain]

I can confirm that I have not asked a question in this thread!

now with incluced aero drag
So if we have box that fall in sky,inside is 50kg rock hanging on rope.
First box start to accelarate with accelaration little bit less then 1G because of air drag,so tension in rope will not be 100% zero,but close to zero..
When falling box reach constant speed let say 300km/h,tension at rope will be 50kg x 10=500N

 

[hutchphd]

Is there a question hidden in here? The air drag is typically modeled as $\alpha v^2$. Is there an end point to this?

 

[jbriggs444]

When If falling box reach constant speed let say 300km/h,tension at rope will be 50kg x 10=500N

For a hypothetical infinitely tall uniformly dense atmosphere and an infinitely tall uniform gravitational field, 300 km/h will never be reached. Instead, it will be approached asymptotically.

Yes, in this case, tension will approach 500 N.For a hypothetical finitely tall [it has ground at the bottom] uniformly dense atmosphere and an infinitely tall uniform gravitational field, 300 km/h will never be reached. Instead, the ball will hit the ground first.

No, in this case tension will not approach 500 N.For a hypothetical atmosphere with an exponentially increasing density as altitude decreases and a much more nearly constant gravitational field the terminal velocity will be a decreasing function of altitude. It is possible in this case for a free-fall-with-drag trajectory to be initially below terminal velocity and to then pass through and beyond terminal velocity [or, more aptly, for terminal velocity to pass below fall velocity]. It is also possible for the falling box to impact the surface before this milestone has been reached.

Yes, if terminal velocity is reached, tension will [momentarily] hit 500 N exactly.