Determining Air Resistance Force on Fire Helicopter's Water Bucket

In summary, the fire helicopter was carrying a 564 kg bucket of water at the end of a 19.2 m long cable. The bucket made an angle of 46.0° with respect to the vertical and the force of air resistance on the bucket was 124366.0155 N.
  • #1
EcKoh
13
0

Homework Statement



A fire helicopter carries a 564 kg bucket of water at the end of a 19.2 m long cable. Flying back from a fire at a constant speed of 41.6 m/s, the cable makes an angle of 46.0° with respect to the vertical. Determine the force of air resistance on the bucket.

Knowns:
m = 564 kg
d1 = 19.2 m
v = 41.6 m/s
[tex]\vartheta[/tex] = 46.0


Homework Equations



For Drag:
Fd =(1/2)CdpAv2


The Attempt at a Solution



So first I started by making a triangle out of the vertical and findin the values of the sides, the first being d1:

d2 = 19.2 sin 46.0 = 13.81
d3 = 19.2 cos 46.0 = 13.38

Then I used the pythagorean theorem (a2 + b2 = c2) to check the values. I also subtracted to find the last angle of the triangle (180-90-46 = 44), but I don't think I needed that.

So now I used the drag formula (Fd =(1/2)CdpAv2). I used p =1.29 because that's what it equals at sea level, but since its a helicopter I don't know if I used the right value. How to I calculate this?

Then I made Cd 1.15 because that is the drag coefficient of a small cylinder according to my textbook. Is this right?

Next, I used the formula A=1/2bh to get A = 92.39

Plugging this in I get Fd = (1/2)(1.15)(1.29)(92.39)(41.62) = 124366.0155

And I know this is wrong. The answer should be 5.72×103 N. Where did I go wrong? And how would I go about fixing this?
 
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  • #2
You're over-complicating things and incorrectly using the formula for force due to air resistance. Drag in that formula is a function of the cross-sectional area of the bucket as seen by the wind - that is information you do not have according to your problem statement - the area of the triangle you have calculated is not relevant.

Instead, draw a free body diagram for the bucket. What are the forces acting on it? The weight of the bucket, the force due to drag, and the tension from the cable. You should be able to draw that triangle of forces - use the magnitude of the force that you know and the angle of the triangle to find the magnitude of the other force you need.
 
  • #3
Okay, I am drawing the free body diagram right now. Would I be correct to say that normal force isn't acting on the bucket?
 
  • #4
EcKoh said:
Okay, I am drawing the free body diagram right now. Would I be correct to say that normal force isn't acting on the bucket?

A normal force as a result of its contact with what surface, exactly..?
 
  • #5
Okay so I redrew it, and finally figured it out hours later. Here is my solution, please let me know if I did this right or just happened to fall upon the correct answer:

First I redrew the free body diagram just as I had before, labeling tension (T) in the rope, force of drag (Fd) pointing away from the bucket and the direction of movement, and W=mg pointing down.

Then I used the x-axis and y-axis to get two formulas:

T sin [tex]\theta[/tex] = F
T cos [tex]\theta[/tex] = mg

This allowed for me to change it to tan [tex]\theta[/tex] = F/mg

Then I plugged in 564 for mass 46 for [tex]\theta[/tex], and 9.8 for gravity, giving me an answer of 5723.58 N.

Is this the correct method?
 
  • #6
That's spot on, EcKoh. Well done. :)
 

1. What is air resistance force?

Air resistance force is the force exerted by air molecules on an object moving through the air. It is also known as drag force and it acts in the opposite direction to the object's motion.

2. How is air resistance force calculated?

The air resistance force is calculated using the formula F = 1/2 * ρ * v^2 * A * Cd, where ρ is the density of air, v is the velocity of the object, A is the object's cross-sectional area, and Cd is the drag coefficient.

3. Why is it important to determine the air resistance force on a fire helicopter's water bucket?

It is important to determine the air resistance force on a fire helicopter's water bucket because it affects the helicopter's flight and stability. Knowing the amount of drag force can help pilots adjust their flight paths and make more efficient use of fuel.

4. What factors can affect the air resistance force on a fire helicopter's water bucket?

The air resistance force on a fire helicopter's water bucket can be affected by the helicopter's speed, the shape and size of the bucket, the density of the air, and any external factors such as wind or turbulence. The angle of attack of the helicopter also plays a role in determining the air resistance force.

5. How can the air resistance force on a fire helicopter's water bucket be reduced?

The air resistance force on a fire helicopter's water bucket can be reduced by increasing the speed of the helicopter, using a more streamlined and aerodynamic bucket design, and minimizing the angle of attack. Other methods such as using airfoils or vortex generators can also help reduce air resistance force.

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