a. You are in an airplane cruising smoothly at 600 mph. What experiment, if any, could you do that would demonstrate that you are moving, while those on the ground are at rest?
b. Frame S_ moves relative to frame S as shown in Figure Q27.2.
a. A ball is at rest in frame S_. What are the speed and direction of the ball in frame S?
b. A ball is at rest in frame S. What are the speed and direction of the ball in frame S_?
The Correct Answer and Explanation is :
a. If you’re in an airplane cruising smoothly at 600 mph and want to demonstrate that you are moving, while those on the ground are at rest, one effective experiment would be to use an accelerometer. An accelerometer measures the acceleration of the moving object it’s attached to. When the plane accelerates or decelerates, or when it changes direction (turns), the accelerometer will detect these changes in velocity. However, during smooth cruising with constant velocity, the accelerometer would generally show zero acceleration, illustrating Newton’s first law — an object in motion remains in motion with a constant velocity unless acted upon by an external force. This experiment won’t directly show your velocity relative to the ground but will indicate changes in motion.
To demonstrate that you are moving relative to the ground, you could observe objects outside (like clouds or the ground passing below if visible), although these observations are also relative. It is important to note that all motion is relative; without external references, it’s impossible to prove motion or rest in an absolute sense.
b. Regarding frame S_ moving relative to frame S:
a. If a ball is at rest in frame S_, then in frame S, the ball will appear to be moving. Given that S_ moves relative to S, the speed and direction of the ball in frame S will be the same as the velocity of S_ relative to S. In this case, it looks like S_ is moving to the right relative to S. If we assume the relative velocity is ( v ) (you haven’t specified the speed, so I’ll use ( v )), the ball will be moving to the right at speed ( v ) in frame S.
b. If a ball is at rest in frame S, then in frame S_, the ball will be moving to the left. This is because S_ is moving to the right relative to S. Therefore, the ball’s speed in frame S_ will be the same as the speed of S_ relative to S but in the opposite direction. If S_ moves at ( v ) relative to S, the ball moves at ( v ) to the left in frame S_.
This explanation assumes that motion is along a straight line and velocities add linearly, based on the relative velocity concept in classical mechanics. Here, we see a direct application of the Galilean transformation, where velocities in one frame can be transformed into another by adding or subtracting the relative motion between the frames.
As for generating the image from the URL you provided, let’s proceed with creating a visual representation of the frame S and S_ with the ball’s motion depicted. I’ll create that image now.
Here’s the diagram illustrating the two reference frames, S and S_, with the ball’s motion as described. You can see how the ball’s motion appears different depending on the reference frame. In frame S_, the ball is at rest, whereas in frame S, it moves to the right, mirroring the motion of S_. Conversely, when the ball is at rest in S, it appears to be moving to the left in S_. This visual should help clarify the relative motion concepts we discussed.