Need help with a Slope problem

[rbm003]

Need urgent help with a Slope problem

Homework Statement

A plane is traveling at a constant velocity at 30 degrees above the horizontal. Weight (W)=86 500 N; thrust (T)=103 000 N. Find the lift force and the resistance force (L= normal force, R=friction) without shifting the cartesian coordinate system

Homework Equations

sum of the forces in the x=ma, sum of the forces in the y=ma. a=0.

The Attempt at a Solution

I have set up the problem with x dir: T cos(30) - L sin(30) - Rcos(30)=ma and y dir: W - T sin(30) + L cos(30) - R sin(30)=ma and ma=0. R in the y dir is negative. Is R in the y dir equivalent to mg? I'm stuck with too many variables in my equation. Any help would be greatly appreciated.

 

[Astronuc]

W = mg and it acts directly downward. Lift acts vertically. Resistance (Drag) acts in opposition to motion, or against the thrust.

See - http://www.grc.nasa.gov/WWW/K-12/airplane/forces.html

http://www.grc.nasa.gov/WWW/K-12/airplane/presar.html

Since the fluid is in motion, we can define a flow direction along the motion. The component of the net force perpendicular (or normal) to the flow direction is called the lift; the component of the net force along the flow direction is called the drag. These are definitions. In reality, there is a single, net, integrated force caused by the pressure variations along a body. This aerodynamic force acts through the average location of the pressure variation which is called the center of pressure.

By convention take T and L to be positive, and R and W (= mg) to be negative.

See also - http://www.grc.nasa.gov/WWW/K-12/airplane/cruise.html
which gives the condition for straight (horizontal) flight.

 

[rbm003]

I understand the concepts as you explained them. My problem is that I connot tilt the x,y axis to solve the problem with information I have. Therefore, I am trying to use trig functions to solve for T and R, which are not directly on the x and y axis. The only compnent that is on the x and y-axis is W. Since R in the y direction is negative, can I use mg to solve R (in the y direction) sin (30)?

 

[rbm003]

Anyone?

 

[Astronuc]

What does the text say about lift (L). According to NASA's site, L is vertical and balance against weight. The thrust (T) and drag or resistance (R) are oriented along the axis of the aircraft.

So that would imply L = W and T = R for cruising or constant velocity.

 

[rbm003]

Thank you! That is exactly the information I needed! The problem worked out great.