# Finding what angle is the Normal force is.

• lion_
In summary, the airplane is executing a horizontal turn and the normal force on the seat is dependent on the angle of the turn. If the plane is banked at 15 degrees when the pilot experiences only a normal force on the seat, the radius of curvature of the turn is 75 degrees.
lion_

## Homework Statement

The airplane traveling at a constant speed of 50m/s is executing a horizontal turn. If the plane is banked at ##\theta=15## when the pilot experiences only a normal force on the seat of the plane, determine the radius of curvature of the turn. Also what is the normal force of the seat on the pilot if he has a mass of 70kg.

## Homework Equations

##\Sigma F_n = ma_n=N \sin \theta ##
##\Sigma F_b= 0 = N \cos \theta= W ##
##a_n=v^2/r##

## The Attempt at a Solution

It is pretty much a plug and chug problem with the given equations. The issue I am having is that the problem uses cosine where I have sine and sine where I have cosine. Meaning that the normal force is 75 degrees from the verticle which is impossible or I must be interpreting the problem incorrectly. Please explain why this is or explain what is really happening in the picture where the plane is banking.

#### Attachments

• plane problem.png
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• plane problem.png
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Image didn't come out like I wanted too

I agree that 'banked at 15 degrees' should mean 15 degrees to the horizontal, and that leads to the equations you posted. On the other hand, banking at 75 degrees is not impossible.
The picture you attach shows the banking angle as being measured from the vertical. Did that picture accompany the question, or is it your illustration of what it would mean if it is at 15 degrees to the vertical?

I figured it out it was a little bit of common sense. First I pictured the plane flying horizontally the normal force and weight are parallel. If the plane tilts 90 degrees, then the normal force is perpendicular to the weight. So then some advanced geometry tells me if it shifts 15 degrees to the left it's going to move the normal force down 15 degrees which is 75. Picture was a bit confusing for me.

lion_ said:
it's going to move the normal force down 15 degrees which is 75
What do you mean "which is 75"? Do you mean 75 degrees to the horizontal?
lion_ said:
Picture was a bit confusing for me.
Are you saying the picture is part of the problem as provided to you? If so, it is clear that the given '15 degrees' of banking here means the plane is tilted over by 75 degrees. (I'm sure that's not standard usage though.)

## 1. What is the normal force?

The normal force is the force exerted by a surface on an object that is in contact with it. It is always perpendicular to the surface and acts in the opposite direction of the force applied by the object.

## 2. How do you find the angle of the normal force?

The angle of the normal force can be found by using trigonometric functions such as sine, cosine, and tangent. The angle can be calculated by dividing the vertical component of the normal force by the magnitude of the normal force.

## 3. Why is it important to know the angle of the normal force?

Knowing the angle of the normal force is important in understanding the stability and equilibrium of an object. It can also help in determining the direction of motion of an object and the amount of force required to keep it in place.

## 4. Can the angle of the normal force change?

Yes, the angle of the normal force can change depending on the orientation of the surface and the direction of the applied force. It is important to take into account any changes in the angle when analyzing the forces acting on an object.

## 5. How does the angle of the normal force affect the weight of an object?

The angle of the normal force does not directly affect the weight of an object. However, the normal force can counteract part of the weight of an object when it is on an inclined surface, making it easier to lift or move the object.

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