Vectors and Forces: Aircraft Mass, Velocity & Drag Force

In summary, Cathy is asking for help with a question about an aircraft with a mass of 11000kg, which moves at a constant velocity and altitude while being powered by propellors and experiencing a drag force. She also asks for help in drawing a free body diagram and calculating the aircraft's level flight speed. The conversation then shifts to a question about a ship being pulled at a constant speed by two tugs and experiencing a drag force. Cathy asks for help in calculating the tension in each cable and the speed to which the ship decelerates when one tug breaks down. The conversation ends with Cathy asking for help in explaining why the ship veers off-course after the tug breaks down. Finally, Cathy thanks everyone for their help and
  • #1
CathyLou
173
1
Would anyone please be able to help me with the following question. I'd really appreciate it.

6. An aircraft of mass 11000kg, which moves at a constant velocity v and constant altitude, is powered by propellors and experiences a drag force.

(a) Draw a labelled free body diagram showing the four main forces acting on the aircraft. (I don't know how to draw the diagram, but I think that the 4 forces are gravity, air resistance, friction and upthrust. Is this correct?)

(b) The thrust from the propellors is 225kN and the drag force is given by 10v^2. Calculate the aircraft’s level flight speed.

Thank you.

Cathy
 
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  • #2
CathyLou said:
Would anyone please be able to help me with the following question. I'd really appreciate it.

6. An aircraft of mass 11000kg, which moves at a constant velocity v and constant altitude, is powered by propellors and experiences a drag force.

(a) Draw a labelled free body diagram showing the four main forces acting on the aircraft. (I don't know how to draw the diagram, but I think that the 4 forces are gravity, air resistance, friction and upthrust. Is this correct?)
There are indeed four forces acting but one of your forces is wrong, you need to replace that force with another. Can you figure out which one it is? Remember constant velocity implies no net force.
HINT: The answer is in the next question :wink:
CathyLou said:
(b) The thrust from the propellors is 225kN and the drag force is given by 10v^2. Calculate the aircraft’s level flight speed.
Have you any thoughts on this one? Exactly the same principles apply here as above.
 
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  • #3
Thanks for replying.

Is it friction that is wrong? If yes, does that mean that there is a lift force that opposes the force of gravity instead. Also, I don't really get what a free body diagram is. Could you please explain?

As for part b, if thrust is equal to 225kN the drag must be 225kN.

So, 10v^2 = 225kN

and 10v^2 = 225000N

so v^2 = 22500N

and v = 150m/s

Is that correct?
 
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  • #4
CathyLou said:
Is it friction that is wrong? If yes, does that mean that there is a lift force that opposes the force of gravity instead. Also, I don't really get what a free body diagram is. Could you please explain?

I've figured out how to draw a free body digaram now. :smile:
 
  • #5
CathyLou said:
Is it friction that is wrong? If yes, does that mean that there is a lift force that opposes the force of gravity instead. Also, I don't really get what a free body diagram is. Could you please explain?
Yes, friction is "wrong," i.e., air resistance is a form of friction. What you labelled as upthrust is known as lift, and the missing force that Hootenanny was talking about is the (forward) thrust.

As for part b, if thrust is equal to 225kN the drag must be 225kN.

So, 10v^2 = 225kN

and 10v^2 = 225000N

so v^2 = 22500N

and v = 150m/s

Is that correct?
That's right!
 
  • #6
CathyLou said:
I've figured out how to draw a free body digaram now. :smile:
Good for you. :)
 
  • #7
neutrino said:
Good for you. :)

:smile:

I just posted that so that no-one spent time showing me as there was no longer any need (thanks to Wikipedia!).

Cathy
 
  • #8
neutrino said:
Yes, friction is "wrong," i.e., air resistance is a form of friction. What you labelled as upthrust is known as lift, and the missing force that Hootenanny was talking about is the (forward) thrust.


That's right!

Thanks for your help!
 
  • #9
I'm also kind of stuck on the following question.

Could anyone please offer some hints?

2. A ship is pulled at a constant speed, v, of 2.5 m/s by two tugs, A and B. Each tug is connected to the ship by a cable so that the angle each of the cables makes with the direction of travel is 41 degrees. The ship experiences a drag force given by:

Drag Force (N) = 8000 x velocity^2

(a) Calculate the tension in each cable while traveling at this constant speed. (I got an answer of 66200 N for each tug but I'm not sure if that's correct).

(b) As the tugs attempt to increase the speed of the ship from 2.5m/s, tug A breaks down, with its cable to the ship becoming slack.

<i> Calculate the speed to which the ship initially decelerates, assuming the tension in the other cable remains constant. (Go backwards and work out v through friction force).

<ii> The ship also veers off-course. Explain why this happens.

I've already drawn a diagram.

Thank you.

Cathy
 
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  • #10
Right, I've figured out part a to be T = 33100 N.

Does anyone have any idea how to work out part b?

Thank you.

Cathy
 
  • #11
CathyLou said:
...
(b) As the tugs attempt to increase the speed of the ship from 2.5m/s, tug A breaks down, with its cable to the ship becoming slack.

<i> Calculate the speed to which the ship initially decelerates, assuming the tension in the other cable remains constant. (Go backwards and work out v through friction force).

<ii> The ship also veers off-course. Explain why this happens.[/COLOR]

Obviously the speed isn't constant anymore. What does this imply?
 
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  • #12
radou said:
Obviously the speed isn't constant anymore. What does this imply?

That the forces aren't balanced?
 
  • #13
I've figured out b now but I still can't work out c.

Any suggestions as to how to do it?

Thank you.

Cathy
 
  • #14
I've now got an answer to part c.

Thanks for everyone's help.

I really appreciate it.

Cathy :smile:
 

FAQ: Vectors and Forces: Aircraft Mass, Velocity & Drag Force

What is the relationship between aircraft mass and velocity?

The relationship between aircraft mass and velocity is described by Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that as the mass of an aircraft increases, the amount of force needed to accelerate it also increases, and as the velocity of the aircraft increases, the amount of force needed to maintain that velocity also increases.

How does drag force affect an aircraft's velocity?

Drag force is a resistive force that acts opposite to the direction of motion of an aircraft. As an aircraft moves through the air, it experiences drag force, which slows it down. This means that in order to maintain a constant velocity, the aircraft must exert a force that is equal and opposite to the drag force acting on it. If the drag force increases, the aircraft's velocity will decrease, and if the drag force decreases, the aircraft's velocity will increase.

What factors contribute to the drag force on an aircraft?

There are several factors that contribute to the drag force on an aircraft, including the shape and size of the aircraft, the speed at which it is traveling, the density of the air, and the presence of any external objects, such as flaps or landing gear. These factors all affect the amount of air resistance that the aircraft experiences, which in turn affects the amount of drag force acting on the aircraft.

How does air density affect an aircraft's flight?

Air density refers to the amount of air molecules in a given volume of air. As air density decreases, the air becomes less dense and offers less resistance to the movement of an aircraft. This means that at higher altitudes where the air is less dense, an aircraft will experience less drag force and can achieve higher speeds. On the other hand, at lower altitudes where the air is more dense, an aircraft will experience more drag force and may need to exert more thrust to maintain its velocity.

What role do vectors play in understanding aircraft forces?

Vectors are used to represent both the direction and magnitude of forces acting on an aircraft. By using vectors, scientists and engineers can analyze and understand the net forces acting on an aircraft, including the effects of lift, thrust, weight, and drag. Vectors also allow for the calculation of the resultant force, which is essential for determining an aircraft's acceleration and velocity.

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