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Chapter 5: Problem 11

You're on a plane undergoing a banked turn, so steep that out the window you see the ground below. Yet your pretzels stay put on the seatback tray, rather than sliding downward. Why?

Short Answer

Expert verified
The pretzels don't slide downwards because in the plane's frame of reference, the tilted tray exerts an upward normal force with a component equal to the downward gravitational force, thus cancelling it out. Additionally, the normal force contributes another component necessary for the centripetal force, allowing the pretzels to stay put.

Step by step solution

01

Concept of Forces

The forces involved in this scenario are the gravitational force, which pulls objects toward the Earth, and the normal force, which is the force exerted by the surface supporting the object and is always perpendicular to the surface.
02

Direction of Forces in a Banked Turn

When the plane makes a banked turn, the plane and tray tilt but the direction of gravity does not change - it still points vertically downwards. However, the direction of the normal force exerted by the tray also turns with the airplane, thus no longer pointing directly opposite to gravity.
03

Net Force

With the right angle of tilt, the component of the normal force opposing gravity is equivalent to the force of gravity acting on your pretzels, meaning the net force in the vertical direction is zero. As a result, your pretzels wouldn't slide downwards even though they appear to be tilted.
04

Circular Motion

For the pretzels to stay put, the net force in the horizontal direction (towards the center of the turn) also has to be zero. The other component of the normal force provides the inward force, or centripetal force, necessary for the pretzels to maintain circular motion with the plane.

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