Which component of velocity should we choose?

Asked Sep 16 '21 at 10:51

Active Sep 16 '21 at 11:09

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In the arrangement shown in the figure, the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. What is the speed with which mass m moves upward?

The textbook solution to this question says the mass m moves with u/cosθ. I have a big confusion here. If the string inclined on the left moves with 'u', similary the string on the right moves with 'u' as well, shouldn't the velocity with which the mass m moves upward be 2ucosθ? This is because the component of u along that unknown velocity of mass m will be ucosθ.

The book says: vcosθ = u ; hence, v = u/cosθ

I feel ucosθ = v

edited Sep 16 '21 at 10:56

asked Sep 16 '21 at 10:51

Swami

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Does this answer your question? Why do these two methods give different answers? – ACB Sep 16 '21 at 10:59
Another similar question: https://physics.stackexchange.com/q/594941/305718 – ACB Sep 16 '21 at 11:00
It answers but I am still looking for an easier and precise explanation. – Swami Sep 16 '21 at 12:27
@Swami What is not "easy and precise" about the other answers? – BioPhysicist Sep 16 '21 at 12:35
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This question has been asked numerous times here. The main problem with your reasoning, as already explained, is that the direction of v is constant but the direction of u is not. – Vincent Thacker Sep 16 '21 at 13:25
As for the factor of 2; note that if the left side string were removed and the junction above M were constrained to move along a vertical rail, the acceleration would change, but the relation between the two velocities would not. – R.W. Bird Sep 16 '21 at 14:55
@VincentThacker That's a neat explanation. I got it. – Swami Sep 18 '21 at 09:12

Which component of velocity should we choose?

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