Circular Motion Power: Why Isn't Work Done Equal to Zero?

[Dadface]

The book answer above uses the equation:

P=Fv where F is the centripetal force

This equation can be derived from:

Work = force * distance=Fdx

Power=Work/time =Fdx/dt

With many problems we can write dx/dt=v but I think it is incorrect to do so in this case because the radius remains constant and dx remains at zero.

 

[Infinitum]

http://img402.imageshack.us/img402/2748/soklan.jpg

The answer from the book.
http://img151.imageshack.us/img151/1207/salahq.jpg

I think there is a mistake here. Power is given as a dot-product,

P = F\cdot v

I don't know how they are assumed to be in the same direction.

 

[TSny]

Perhaps the problem meant to say that the tangential acceleration varies as ...

Then the answer stated in the problem would be correct.

 

[Infinitum]

Perhaps the problem meant to say that the tangential acceleration varies as ...

Then the answer stated in the problem would be correct.

If that is the case, then it would definitely be correct

 

[D H]

Perhaps the problem meant to say that the tangential acceleration varies as ...

Then the answer stated in the problem would be correct.

Nice explanation, but wrong. The Indian education system apparently works (at least in part) by teaching the test. Old tests, to be precise. Perhaps India's copyright laws make those old tests a quick and easy source of homework questions for authors of Indian textbooks. In any case, this question is replicated over and over in many Indian physics texts. See the following google books search:

http://www.google.com/search?q=A+pa...ius+r+such+that+its+centripetal+acceleration"

Many just keep the question in its original form, a multiple choice question with choices 2πmk²r²t, mk⁴r²t⁵/3, mk²r²t, and zero. Some change the choices, others make the question open ended (not multiple choice). A small number of those books provide solutions -- including some erroneous ones (e.g., the book that is the subject of this thread). Apparently it is easy for authors to get their hands on the old test questions, but not on the old test answers.

 

[Saitama]

Nice explanation, but wrong. The Indian education system apparently works (at least in part) by teaching the test. Old tests, to be precise. Perhaps India's copyright laws make those old tests a quick and easy source of homework questions for authors of Indian textbooks. In any case, this question is replicated over and over in many Indian physics texts. See the following google books search:

http://www.google.com/search?q=A+pa...ius+r+such+that+its+centripetal+acceleration"

Many just keep the question in its original form, a multiple choice question with choices 2πmk²r²t, mk⁴r²t⁵/3, mk²r²t, and zero. Some change the choices, others make the question open ended (not multiple choice). A small number of those books provide solutions -- including some erroneous ones (e.g., the book that is the subject of this thread). Apparently it is easy for authors to get their hands on the old test questions, but not on the old test answers.

A good book is present in the link you gave D H, the book is "The Pearson Guide to Objective Physics for the IIT-JEE 2012". You can see the question in the preview and the answer is given the same as OP. Scroll down a few pages after the question and you will see the answer key.
Click Me

I think there is a mistake here. Power is given as a dot-product,
P=F⋅v
I don't know how they are assumed to be in the same direction.

Seems like the author did the same mistake as me.

 

[Ratch]

D H,

It looks like TSny found the real reason why my method did not work.

TSny,

Thanks for your insight.

ehild,

That is utterly wrong. The magnitude of an integral is not the same as the integral of the magnitude.

You are correct, I should have known better.

Ratch