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Re: Free Body Diagram



I would apply the equations of a swinging pendulum bob:

1) T - mgCOS(TH) = mv^2/R provides the centripetal acceleration (radial),
2) mgSIN(TH) = ma provides the circumferential acceleration.

At the top of the arc v=0, the centripetal acceleration vanishes, and 1)
gives what you seek:
T = mgCOS(TH)
At this instant the acceleration is circumferential in direction, and it HAS
a non-zero vertical component.

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: Tuesday, November 19, 2002 9:26 PM
Subject: Free Body Diagram


| In Giancoli chapter 6 (Energy and Work) there is a problem wherein a
| person runs towards and grabs a vertical hanging rope in order to swing
| out over the water of a lake and then release the rope to fall into the
| water. The question asks for the tension in the rope at the point in
| his swing where his velocity is zero.
|
| Now, it seems to me that one could look at the free body diagram at that
| instant and it would show the weight of the person acting down and the
| tension acting at an angle theta from the vertical (upward, at an angle
| from the vertical).
|
| If one then considers a coordinate system imposed at the end of the
| rope, one might argue that Tcos(theta) = mg in order that there is no
| vertical acceleration.
|
| On the other hand, if one uses a rotated coordinate system (with T along
| the y axis), one could argue that T=mgcos(theta) in order that there no
| acceleration along the direction of the rope.
|
| Only one of these points of view can be correct and I am searching for
| the words that my high school class will understand and will convince
| them (and me) why one is correct and the other incorrect.
|
| I'm sure that I am missing something obvious but any help in seeing it
| would be appreciated. . . .

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.