Flying in a Loop: Plane Speed & Pilot Weight

In summary, the speed of the airplane is not constant as it flies in a loop of radius 190 m. The pilot's head always points towards the center of the loop. At the top of the loop, the pilot feels weightless and the speed of the airplane is equal to the square root of the product of the acceleration and radius. At the bottom of the loop, the speed of the airplane is 300 km/h and the apparent weight of the pilot is equal to 700 N.
  • #1
PhysicStorm
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An airplane flies in a loop (a circular path in a vertical plane) of radius 190 m. The pilot's head always points toward the center of the loop. The speed of the airplane is not constant. The airplane goes slowest at the top of the loop and fastest at the bottom.


(a) At the top of the loop, the pilot feels weightless. What is the speed of the airplane at this point?

(b) At the bottom of the loop, the speed of the airplane is 300 km/h. What is the apparent weight of the pilot at this point? His true weight is 700 N.


I have tried this problem multiple times and i used the formula of
accel = v^2/r
i know that accel is also equal to net force of the pilot divided by his mass so and that at the top of the loop it is equal to force of gravity down and force of normal force from seat

the masses do cancel out using
(9.8(m)+Fn)/m = v^2/190
i might be solving for normal force wrong can someone clear it up for me please?
w/o part a correct part b is always going to be incorrect. ty for your time and effort
 
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  • #2
Why do you include the normal force coming from the chair? In normal flight this will just cancelthe gravitational force, but at the top, if the pilot is weightless there will be no force coming from the seat.
 

Related to Flying in a Loop: Plane Speed & Pilot Weight

1. How does plane speed affect flying in a loop?

Plane speed is a crucial factor in successfully executing a loop. A loop is a maneuver in which the plane flies in a vertical circle, with the nose pointing towards the ground at the top of the loop and towards the sky at the bottom. To perform a loop, the plane needs to have enough speed to generate lift and maintain its altitude. If the plane is flying too slowly, it may not have enough lift to complete the loop and may stall, potentially leading to a dangerous situation.

2. What is the ideal speed for performing a loop?

The ideal speed for performing a loop varies depending on the weight and type of the plane. Generally, the plane should be traveling at a speed that is at least 1.5 times its stall speed. This ensures that the plane has enough lift to complete the loop without stalling. However, it is essential to consult the specific aircraft's manual for the recommended speed for performing a loop.

3. How does the pilot's weight affect flying in a loop?

The pilot's weight can also play a role in successfully executing a loop. A heavier pilot will add additional weight to the plane, which can affect its performance and ability to generate lift. This means that a heavier pilot may need to fly at a slightly higher speed to complete the loop safely. Additionally, a heavier pilot may experience higher G-forces during the loop, which can be uncomfortable or even dangerous if not trained to handle them properly.

4. Are there any safety precautions to consider when flying in a loop?

Yes, there are several safety precautions that pilots should consider when flying in a loop. Firstly, they should always ensure that the plane is in good condition and has been properly maintained. They should also have a thorough understanding of the aircraft's manual and recommended speed for performing a loop. Additionally, pilots should be trained in how to handle high G-forces and be physically fit to withstand them.

5. Can any type of plane perform a loop?

Not all planes are designed to perform loops. Planes that are capable of performing loops typically have a symmetrical airfoil and are designed for aerobatic maneuvers. It is essential to consult the aircraft's manual to determine if it is suitable for performing a loop. Attempting to perform a loop in an unsuitable aircraft can be dangerous and potentially lead to a loss of control.

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