Pertaining to checkpoint 11.3(b) in section 11.2 on page 261 the answer given on page A-41 is No.
However, the correct answer is yes. This is obvious to anyone who has ever done the experiment.
The explanation on page A-41 misses a fundamental physics principle:
Acceleration is not motion.
Motion is not position.
We agree that when the rope is horizontal, the bucket is subject to a vertical acceleration. However, acceleration is not the end of the world. Nothing in the diagram or in the statement of the problem requires steady purely-rotational motion. The fact is, the rope can be horizontal. With modest effort you can keep it horizontal for a half-second or more.
To summarize, to paraphrase an old VW advertisement: You can definitely do it, although you can't do it indefinitely.
Let's not quibble about "exactly" horizontal. When I say horizontal, I mean that the average slope is so small as to be irrelevant to the dynamics of the system.
Suggestions:
You could reword the problem to restrict attention to steady, purely-horizontal motion.
Perhaps better, you could leave the question as-is, and make it a lesson in real-world problem-solving. Change the answer to cover both the restricted case and the unrestricted case. Often the best way to deal with an underspecified problem is to write down the entire solution-set, along with a few words of explanation.
Just because the methods presented in chapter 11 are restricted to motion in the plane does not mean that real-world problems will magically restrict themselves accordingly.
Pertaining to checkpoint 11.3(b) in section 11.2 on page 261 the answer given on page A-41 is
No.However, the correct answer is yes. This is obvious to anyone who has ever done the experiment.
The explanation on page A-41 misses a fundamental physics principle:
We agree that when the rope is horizontal, the bucket is subject to a vertical acceleration. However, acceleration is not the end of the world. Nothing in the diagram or in the statement of the problem requires steady purely-rotational motion. The fact is, the rope can be horizontal. With modest effort you can keep it horizontal for a half-second or more.
To summarize, to paraphrase an old VW advertisement: You can definitely do it, although you can't do it indefinitely.
Let's not quibble about "exactly" horizontal. When I say horizontal, I mean that the average slope is so small as to be irrelevant to the dynamics of the system.
Suggestions:
Just because the methods presented in chapter 11 are restricted to motion in the plane does not mean that real-world problems will magically restrict themselves accordingly.