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Chapter 4: Problem 10

As your plane accelerates down the runway, you take your keys from your pocket and suspend them by a thread. Do they hang vertically? Explain.

Short Answer

Expert verified
No, the keys don't hang vertically. They hang at an angle due to the combined effect of gravitational force and inertial force caused by the plane's acceleration.

Step by step solution

01

Understand the plane's movement

Before taking off, the plane accelerates forward, but it does not move up or down. The primary force that's making the plane move is applied horizontally, not vertically.
02

Analyze the forces acting on the keys

The only forces acting on the keys are the gravitational force and the tension in the thread. Gravitational force always acts vertically, while the tension force aligns with the thread.
03

Consider the effect of the plane's acceleration

Due to the plane's acceleration, the keys will 'want' to stay in their original position, due to their inertial behaviour (Newton's first law). This creates an inertial force that acts horizontally, opposite to the direction of the plane's acceleration.
04

Combine the forces

The inertial force and the gravitational force are perpendicular to each other, meaning they will create a resultant force. Because of this, the keys will not hang vertically, but at an angle. The keys, thread, and vertical line form a right triangle.
05

Conclusion

So, when the plane is accelerating down the runway, the keys do not hang vertically, because the forces acting on them create a resultant force that points at an angle to the purely vertical direction.

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