How Does Tension Affect Work Done in a Helicopter Rescue Scenario?

[Paul_Bunyan]

Homework Statement

OK, here's the scenario:

We have a helicopter lifting someone out of the water via a rope. The person has a mass of 79kg and he is being accelerated upwards at 0.7m/s^2.

I also need to calculate work being done by the tension in the cable and by the person's weight.

Homework Equations

So, I think the tension would be T=mg+ma, is that right?

The Attempt at a Solution

So the total tension would be the tension due to gravity (weight) plus the tension caused by the upward acceleration...?

As far as work is concerned...If the above is true, the tension in the cable would be 829.5N, and he is being lifted up a distance of 11m, parallel to the cable.

So my initial thought was that the work done by the tension in the cable would be W=829.5*11, is that right?

And then I don't think the person's weight is actually causing any movement, so there would be no work because of that, correct?

Ugh, tension confuses me sometimes...

Thanks in advance, though.

 

[Archduke]

Yep, that's right.

I don't know if you did so, but often a diagram just simplifies the whole problem so much, as you can actually see what you are doing!

 

[turdferguson]

The weight force does do work, W=Fdcos(thete). Because force is opposite of displacement (theta = 180), weight does negative work

To check your answers, remember that the new work should be the net force times displacement. The question asks for individual work, so individual forces must be used.The problem isn't very accurate however, because a person weighs less in water. there's an extra boyant force upward you can't account for because there's not enough information. You weigh less in water, making it easier to pull a person up from water than through the air. The rope could even break once the persons full weight is on the rope

 

[AngeloG]

The best thing to do is draw a force body diagram (as said above by Archduke). It makes it a lot easier.

The forces you see in the X or Y need to all equal out to M*A. Since Fx or Fy = M*A, also the sum of forces must equal m*a.

So in the picture, you have the force of gravity pulling down and the force of tension pulling up.

What do you want to call down and what do you want to call up? Naturally, you call tension vector pointing up positive and gravity negative. However, you can do the opposite. You will still end up with the same answer.

Sum of all forces = T - mg = MA.

T - mg = MA.
T = ma + mg.

Work depends on displacement.