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.
David Abineri
--
David Abineri
dabineri@choice.net
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.