Mechanics problem involving trig and forces.

In summary, the Cessna-182 airplane of mass 1260 kg has an engine failure when flying with an airspeed of 126 km/h at an altitude of 2870 m on a calm day. The plane then glides at a constant glide angle (5.94 degrees) towards a safe landing at this constant speed of 126 km/h experiencing a drag force of 1280 N that opposes the direction in which the plane is moving.
  • #1
chrisrock
8
0
A fully loaded Cessna-182 airplane of mass 1260 kg has an engine failure when flying with an airspeed of 126 km/h at an altitude of 2870 m on a calm day. It then glides at a constant glide angle (which is the direction of flight below the horizontal) towards a safe landing at this constant speed of 126 km/h experiencing a drag force of 1280 N that opposes the direction in which the plane is moving.
Please use: g = 9.81 m s-2


[PLAIN]http://img805.imageshack.us/img805/5625 [Broken]

I would like to know what equations and values i should be using to find the glide angle of the plane.

I tried using the forces given, weight and drag, with trig but as I know that the drag force is not a component force of weight I didn't have high hopes. So of course i got the wrong answer.

Will upload the working once I draw the diagram I drew in paint.

I know the answer is 5.94 degrees.

Thanking you in advance. Been banging my head around this problem I just don't see what to use to work out the glide angle.
 
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  • #2
If something is falling, what equations do we use?

If you have a Force (be it Drag) exerted over a distance what can you get out of it?
 
  • #3
hey lok i presume we are talking about the kinematics equations. I will have a look back and report to you in a min but i don't see how i can get the angle using those equations.

actually its late in NZ so imma c this tomorrow but i think i got it, just need to manipulate the equations properly.
 
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  • #4
Well you know the speed it moves forward (or at the unknown angle) and all you have to find is the speed it is falling considering it is dropping at a constant speed attracted by gravity and slowed down to a constant speed by friction.

And then there is a bit of Trig...
 
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  • #5
Hey lok sorry for the late reply i did work it out last night. just been busy and haven't been able to put it up i will in an hour or 2 though thanks for the help.
 
  • #6
chrisrock said:
Hey lok sorry for the late reply i did work it out last night. just been busy and haven't been able to put it up i will in an hour or 2 though thanks for the help.

Np. Anytime.
 
  • #7
I used the drag force divided by the weight force, and then took the inverse sin of the answer.

Θ = sin-1 ((drag force)/(mg))


Unfortunately i can't explain y i used this as that will require me to do a diagram which i find time consuming, and as I'm short on time i can't help it SORRY !
 

1. "What is the relationship between trigonometry and mechanics?"

The use of trigonometric functions, such as sine, cosine, and tangent, is essential in solving mechanics problems involving forces. These functions help us break down forces into their components, making it easier to analyze and solve the problem.

2. "How do I use trigonometry to find the magnitude and direction of a force?"

To find the magnitude of a force, we can use the Pythagorean theorem to calculate the hypotenuse of a right triangle formed by the force and its components. The direction of the force can be determined using inverse trigonometric functions, such as arcsine and arccosine.

3. "Can you give an example of a mechanics problem involving trig and forces?"

Sure, one example is a block being pulled up an inclined plane with a force of 50 Newtons at an angle of 30 degrees above the horizontal. To find the force component pulling the block up the plane, we would use the formula Fcosθ, where θ is the angle of the force. In this case, the force component would be 50cos30 = 43.3 Newtons.

4. "How do I know if I need to use trigonometry to solve a mechanics problem?"

If the problem involves forces acting at angles, such as on an inclined plane or in a pulley system, then trigonometry will likely be needed to solve it. It is always a good idea to draw a diagram and identify the angles involved to determine if trigonometry is necessary.

5. "Are there any shortcuts for using trigonometry in mechanics problems?"

Yes, the most common shortcut is using the right triangle trigonometric ratios (sine, cosine, tangent) to find the components of a force. These ratios can also be used to find the angles of forces when given their components. Additionally, memorizing the special angles (30, 45, and 60 degrees) and their trigonometric values can save time in calculations.

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