Circular Motion with Newton's Laws

[rmarkatos]

A model airplane of mass 7.50 with a speed 35m/s flies in a horizontal circle at the end of 60.0m control wire. Aerodynamic lift acts on the plane at an angle of 20 degrees West of North.

In the picture the book has the plane on the right. The weight is acting straight down, the tension is acting at angle of 20 degrees South of East and the aerodynamic lift is acting 20 degrees west of north.

Can someone set up the x and y scalar equations please. The answer is 12.8N. I have set it up 5 different ways and i can't seem to get the right answer. My teacher says always put the object on the left when doing these types of problems but it doesn't seem to work

Fx -Tcos20 - Fsin20 = mv^2/r
Fy -Tsin20 + Fcos20 - mg = 0 where T is the tension and F is the aerodynamic lift

Those are the equations based on the picture described.

 

[rmarkatos]

Fx -Tcos20 - Fsin20 = mv^2/r
Fy -Tsin20 + Fcos20 - mg = 0 where T is the tension and F is the aerodynamic lift

Those are the equations based on the picture described.

 

[Moetasim]

However, it is important to note that in circular motion, the net force must be directed towards the center of the circle. In this case, the net force is the combination of the aerodynamic lift and the tension of the control wire.

Therefore, the x and y scalar equations should be:

Fx -Tcos20 - Fsin20 = mv^2/r *cos(theta) where theta is the angle between the velocity vector and the horizontal axis.

Fy -Tsin20 + Fcos20 - mg = mv^2/r *sin(theta) where theta is the angle between the velocity vector and the vertical axis.

Solving these equations should give the correct answer of 12.8N for the net force towards the center of the circle. It is important to always consider the direction of the net force in circular motion problems, as it determines the centripetal force needed to keep the object in circular motion.