A u-control airplane of mass m is attached by control wires of length L and negligible mass to the "pilot" who controls the lift provided by the wing FL. The wires control the plane's elevator or angle of attack. The plane's engine keeps it moving at constant speed v in a horizontal circle.

Find the magnitude of the force of tension T in the wires when the plane is flying in a circle at an altitude such that the wires make an angle θ with the ground. Remember that the wings can provide lift only in the direction perpendicular to their area, i.e. in a direction perpendicular to the wires. Think carefully before selecting the angle of your coordinate system. Use variables m, v, L, theta, and g in your answer.

Anyone give me some hints!:>

To find the magnitude of the force of tension (T) in the wires when the plane is flying in a circle at an altitude such that the wires make an angle (θ) with the ground, we can consider the forces acting on the plane.

1. Start by drawing a free-body diagram of the forces acting on the plane: Tension force (T) in the wires, gravitational force (mg) acting vertically downwards, and the lift force (FL) acting perpendicular to the wings.

2. Since the plane is moving in a horizontal circle at a constant speed (v), it experiences a centripetal force towards the center of the circle. This force is provided by the tension force (T) in the wires. So, the magnitude of T is the centripetal force.

3. Since the wires make an angle (θ) with the ground, we need to resolve the forces into components along and perpendicular to the wires.

- The vertical component of T cancels out the gravitational force (mg) in order to keep the plane in equilibrium vertically.

- The horizontal component of T provides the centripetal force required for circular motion.

4. Use trigonometry to find the components of T:

- The vertical component of T is T*sin(θ).

- The horizontal component of T is T*cos(θ).

5. Equate the horizontal component of T to the centripetal force:

T*cos(θ) = m*v^2 / L

(Since the radius of the circular path is L and the centripetal force is m*v^2 / L)

6. Solve the equation for T:

T = (m*v^2 / L) / cos(θ)

Now, you have the expression for the magnitude of the force of tension (T) in terms of the given variables: m, v, L, and θ.

jjn