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Chapter 5: Problem 3

When you are flying in a commercial jet, it may appear to you that the airplane is stationary and Earth is moving beneath you. Is this point of view valid? Discuss briefly.

Short Answer

Expert verified
The point of view of the observer inside the airplane (that the airplane is stationary while Earth is moving) is valid within the context of their inertial frame of reference. This is because they are observing the situation from an inertial reference frame where the airplane is moving with a constant velocity, making objects inside appear to be at rest. This viewpoint doesn't imply that the airplane is not moving in reality, as it is still moving at a constant velocity relative to the Earth's surface. This problem highlights the importance of considering an observer's frame of reference when discussing relative motion.

Step by step solution

01

Understand Relative Motion and Frame of Reference

To discuss this point of view, it is essential to understand relative motion and the concept of a frame of reference. Relative motion is the motion of an object with respect to another object or reference frame. A frame of reference is a system of deciding the position of an object in space, and it helps us describe motion relative to other objects.
02

Inertial Frame of Reference

Inertial frame of reference is one where the observer's reference frame is not accelerating, that is, it is either at rest or moving with a constant velocity. In an inertial reference frame, Newton's laws of motion hold, and we can regard this situation as an observer's point of view.
03

Relative Motion in A Commercial Jet

When flying in a commercial jet, the airplane is moving with a constant velocity relative to Earth's surface, which means air travelers are in an inertial frame of reference. From the perspective of a person inside the plane (an observer), they will perceive objects inside the airplane to be at rest (e.g., a cup placed on the tray table will not slide off). Therefore, the observer may feel like the airplane is stationary.
04

Earth's Motion Relative to the Airplane

While the airplane is moving in a straight line at a constant velocity, the Earth is rotating beneath it. The movement of Earth might not be noticeable by the observer within the plane because of its large size and the distance from the ground. However, the Earth's motion is happening, and it can even affect the flight path of the airplane.
05

Validity of the Point of View

The point of view of the observer inside the airplane (that the airplane is stationary while Earth is moving) is valid within the context of their inertial frame of reference. It is important to note that this viewpoint is limited to the observer's location, and it doesn't imply that the airplane is not moving in reality. The airplane is moving at a constant velocity relative to the Earth's surface, but this motion is not experienced by the observer inside the airplane because of their inertial frame of reference. This problem demonstrates the importance of considering an observer's frame of reference when discussing relative motion.

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Most popular questions from this chapter

Suppose a particle called a kaon is created by cosmic radiation striking the atmosphere. It moves by you at \(0.980 c,\) and it lives \(1.24 \times 10^{-8} \mathrm{s}\) when at rest relative to an observer. How long does it live as you observe it?

What is the rest energy of an electron, given its mass is \(9.11 \times 10^{-31} \mathrm{kg} ?\) Give your answer in joules and \(\mathrm{MeV}\)

What happens to the relativistic Doppler effect when relative velocity is zero? Is this the expected result?

A man is running on a straight road that makes \(30^{\circ}\) with the train track. The man is running in the direction on the road that is away from the track at a speed of \(12 \mathrm{m} / \mathrm{s}\). The train is moving with a speed of \(30 \mathrm{m} / \mathrm{s}\) with respect to the track. What is the speed of the man with respect to a passenger sitting at rest in the train?

If a spaceship is approaching the Earth at \(0.100 c\) and a message capsule is sent toward it at \(0.100 c\) relative to Earth, what is the speed of the capsule relative to the ship?
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