Lifting a survivor into a helicopter with a rope

In summary, the conversation revolves around two forces affecting a rope: the gravitational force and the force of air or drag. The length of the rope is decreasing with a certain velocity, and the goal is to find the angle theta that incorporates this velocity, the length of the rope, and the forces involved. The acceleration is not a major factor, but the angle and original force of air are important in finding the solution. The relevant equations to consider are not explicitly stated in the conversation.
  • #1
bolzano95
89
7
Homework Statement
A helicopter is flying horizontally with constant velocity ##v## and carries a survivor who hanging on a rope with length ##l##. Suddenly the pilot receives a message he has to pull the the survivor into the the helicopter as soon as possible. A paramedic on board starts to pull a hanging rope with such force that the length of rope is shortening with velocity ##v_k##.

What is the angle ##\theta## between the rope and vertical line?
Relevant Equations
Relevant equations are below.
CamScanner 11-21-2020 19.33.11_1.jpg

We have 2 forces affecting the rope: 1. Gravitational force of the body ##=mg## and 2. Force of air = Force of drag= ##F_{AIR}##.
The length of the rope is shortening with the velocity ##v_k##.
So to figure out the angle ##\theta## I wrote:
##R##= force of rope
##R_x = F_{AIR}##
##R_y = mg##

Now I know the acceleration is the first derivative of velocity, but don't know how to incorporate this with the angle ##\theta##, length of the rope and ##v_k##.
 
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  • #2
Acceleration is not an issue. The reason that pulling the rope up matters is that is changes the velocity of the body through the air. There will be a downward component to the drag on the hanging body.

So ##F_{AIR}## will not be exactly horizontal.
 
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  • #3
I assume we are to find θ in terms of Fg, v, vk and... something else, but what? Maybe the original FAIR, the original angle, or the coefficient of drag?
Using the original FAIR I get a quartic in tan(θ). The other choices I listed will be similar.
Perhaps you are expected to make an approximation for smallish vk.
 
  • #4
bolzano95 said:
... What is the angle ##\theta## between the rope and vertical line?
Relevant Equations:: Relevant equations are below.
What are those relevant equations that are mentioned in the OP?
 

Related to Lifting a survivor into a helicopter with a rope

What is the purpose of lifting a survivor into a helicopter with a rope?

The purpose of lifting a survivor into a helicopter with a rope is to safely and efficiently transport them from a remote or inaccessible location to a medical facility or other designated area for treatment or rescue.

How is the rope used to lift a survivor into a helicopter?

The rope is typically attached to a harness or other secure device worn by the survivor. The other end of the rope is then attached to the helicopter, which uses its winch or other lifting mechanism to hoist the survivor up into the aircraft.

What safety precautions should be taken when lifting a survivor into a helicopter with a rope?

It is important to have a trained and experienced crew operating the helicopter and handling the rope to ensure the safety of both the survivor and the rescuers. The rope and harness should also be regularly inspected and properly secured to prevent any accidents or injuries.

What factors can affect the success of lifting a survivor into a helicopter with a rope?

The success of the lift can be affected by weather conditions, the weight and condition of the survivor, the location and terrain of the rescue, and the capabilities of the helicopter and crew. It is important to carefully assess these factors before attempting a lift.

What are some alternative methods for lifting a survivor into a helicopter?

In addition to using a rope, other methods for lifting a survivor into a helicopter include using a rescue basket or stretcher, or performing a direct hoist with a harness attached to the helicopter. The most appropriate method will depend on the specific situation and the capabilities of the rescue team and equipment.

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