Re: Double Atwood

[Bob Sciamanda <trebor@VELOCITY.NET>]

Hi David,
I get M = 3 kg . . . do we agree?

Re: your students' concerns:

1) It matters not that the observed objects are accelerating, so long as
we observe them from a non-accelerating frame.  It is WE, the observers,
who must not accelerate!

2) This can only be resolved by a careful examination of the geometry.  If
the 2 kg mass rises an amount x due to the fall of an amount x by the 3 kg
mass, this will be exactly canceled if the pulley B falls an equal amount
x.

Hope this is of some help. Push it if more discussion will help.

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor

----- Original Message -----
From: David Abineri <dabineri@CHOICE.NET>
To: <PHYS-L@lists.nau.edu>
Sent: Friday, October 15, 1999 8:29 PM
Subject: Double Atwood


> I wonder if someone might help with the following student comments about
> this problem given in my AP class this week.
>
> A pulley (A) is attached to the ceiling with a string passing over it.
> On the right end of the string hangs a mass M and on the left side hangs
> another pulley (B) with a string holding a mass of 2kg on one side and a
> mass of 3kg on the other side. The question is to find the mass M in
> order that the 2kg mass remains stationary when the system is released.
>
> I solved this in a pretty conventional manner making the downward
> acceleration of pulley B equal to the upward acceleration the 2kg mass.
>
> The student asks two questions:
>
> 1. Are the calculated tensions in the string around pulley B really
> correct since the system of pulley B and its masses is an accelerating
> system? Does this affect the answer to the problem?
>
> 2. Isn't pulley B behaving as a simple machine of mechanical advantage 2
> so that movements in the string around pulley A are not equal to the
> movements of the string around pulley B? Does this affect the answer to
> the problem?
>
> Any clarifying thoughts would be appreciated.
>
> Thanks,
> --
>         David Abineri     dabineri@choice.net