Solution: Normal Force for Plane Taking Off at 45 Degrees

In summary, the problem involves finding the normal force and its direction acting on a pilot during takeoff of a plane with an acceleration of 3.5 m/s2 at an angle of 45 degrees. Using the equation Fg = FNy and substituting in the mass of the pilot, the normal force in the y-direction is found to be 490 N. Since the angle of 45 degrees means that the normal force in the x-direction is equal to the normal force in the y-direction, FNx is also equal to 490 N. Using the Pythagorean theorem, the magnitude of the normal force is calculated to be 692.96 N at an angle of 45 degrees west of north. The acceleration of the
  • #1
Quincy
228
0

Homework Statement


An airplane is taking off at an acceleration of 3.5 m/s2at an angle of 45 degrees relative to the horizontal. Find the Normal force and its direction that is acting on the pilot if the mass of the pilot is 50 kg.



Homework Equations





The Attempt at a Solution



Fg = FNy
(50)(9.8) = FNy
FNy = 490 N

Since there is an angle of 45 degrees, FNy = FNx, So FNx = 490 N

FNx2 + FNy2 = FN2

FN = 692.96 N at an angle of 45 degrees west of north.
 
Last edited:
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  • #2
Do you think the acceleration of the plane will affect the normal force?

(And be careful when quoting your angle at the end!)
 
  • #3
The pilot gets 2 forces from accelerations: gravity and takeoff. Also, this won't be a compass direction problem, it will be a left/right up/down problem.
 

FAQ: Solution: Normal Force for Plane Taking Off at 45 Degrees

What is normal force in the context of a plane taking off at a 45 degree angle?

Normal force is the force that acts perpendicular to the surface of an object. In the case of a plane taking off at a 45 degree angle, the normal force is the force exerted by the runway on the plane in the upward direction.

How is normal force calculated for a plane taking off at a 45 degree angle?

The normal force for a plane taking off at a 45 degree angle can be calculated using the formula F = mg cosθ, where F is the normal force, m is the mass of the plane, g is the acceleration due to gravity, and θ is the angle of the plane's takeoff.

Is the normal force the same as the weight of the plane?

No, the normal force and weight are not the same. The weight of the plane is a downward force caused by gravity, while the normal force is an upward force exerted by the runway. In this scenario, the normal force is smaller than the weight of the plane due to the angle of takeoff.

What factors can affect the normal force for a plane taking off at a 45 degree angle?

The normal force for a plane taking off at a 45 degree angle can be affected by the weight and mass of the plane, the angle of takeoff, and the coefficient of friction between the plane's wheels and the runway surface.

How does the normal force impact the takeoff of a plane at a 45 degree angle?

The normal force is an essential component of a plane's takeoff at a 45 degree angle. It helps to counteract the weight of the plane and provide the necessary upward force for the plane to lift off the ground. Without sufficient normal force, the plane would not be able to take off successfully.

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