<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n\nCan someone please help me? Many physics textbooks define the tension\nin a cord as "the magnitude of each of the two forces with opposite\ndirections that produce the tension." It would appear, therefore, that\ntension is not a vector, but then, when solving a problem with cords\nand pulleys, they add the tension in the cord to the force of gravity\non an object. Is this correct? What meaning can this sum have?\n\nPeter\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Can someone please help me? Many physics textbooks define the tension
in a cord as "the magnitude of each of the two forces with opposite
directions that produce the tension." It would appear, therefore, that
tension is not a vector, but then, when solving a problem with cords
and pulleys, they add the tension in the cord to the force of gravity
on an object. Is this correct? What meaning can this sum have?
Peter
Franz Heymann
Jul26-04, 07:12 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n"Peter R. Oakfield" <Poakfield@msn.com> wrote in message\nnews:a7e268ec.0407250754.4272bb2@posting.google.com...\n>\n>\n>\n>\n> Can someone please help me? Many physics textbooks define the\ntension\n> in a cord as "the magnitude of each of the two forces with opposite\n> directions that produce the tension."\n\nThe tension is a force, and as such it is a\nvector. In the case of a perfectly flexible string it acts in the\ndirection of the string itself.\n\n\n\nFranz\n\n[Moderator\'s note: One should probably keep in mind that in everyday language\na vector quantity and its norm may tend to be addressed with the same english\nword. -usc]\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Peter R. Oakfield" <Poakfield@msn.com> wrote in message
news:a7e268ec.0407250754.4272bb2@posting.google.com...
>
>
>
>
> Can someone please help me? Many physics textbooks define the
tension
> in a cord as "the magnitude of each of the two forces with opposite
> directions that produce the tension."
The tension is a force, and as such it is a
vector. In the case of a perfectly flexible string it acts in the
direction of the string itself.
Franz
[Moderator's note: One should probably keep in mind that in everyday language
a vector quantity and its norm may tend to be addressed with the same english
word. -usc]
Igor Khavkine
Jul26-04, 11:32 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nPoakfield@msn.com (Peter R. Oakfield) wrote in message news:<a7e268ec.0407250754.4272bb2@posting.google.com>...\n> Can someone please help me? Many physics textbooks define the tension\n> in a cord as "the magnitude of each of the two forces with opposite\n> directions that produce the tension." It would appear, therefore, that\n> tension is not a vector, but then, when solving a problem with cords\n> and pulleys, they add the tension in the cord to the force of gravity\n> on an object. Is this correct? What meaning can this sum have?\n\nLast time you asked a similar question, different interpretations of\ntension were discussed in the following thread:\n\nhttp://groups.google.ca/groups?th=66187fc91dd7f25\n\nWhatever tension may be when considered intrinsic to the rope, it is\nalways defined to produce a force on an object that is attached at the\nend of the rope. Force is a vector, vectors can be added, case closed.\n\nHope this helps.\n\nIgor\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Poakfield@msn.com (Peter R. Oakfield) wrote in message news:<a7e268ec.0407250754.4272bb2@posting.google.com>...
> Can someone please help me? Many physics textbooks define the tension
> in a cord as "the magnitude of each of the two forces with opposite
> directions that produce the tension." It would appear, therefore, that
> tension is not a vector, but then, when solving a problem with cords
> and pulleys, they add the tension in the cord to the force of gravity
> on an object. Is this correct? What meaning can this sum have?
Last time you asked a similar question, different interpretations of
tension were discussed in the following thread:
http://groups.google.ca/groups?th=66187fc91dd7f25
Whatever tension may be when considered intrinsic to the rope, it is
always defined to produce a force on an object that is attached at the
end of the rope. Force is a vector, vectors can be added, case closed.
Hope this helps.
Igor
Pierre Asselin
Jul27-04, 01:50 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nPeter R. Oakfield <Poakfield@msn.com> wrote:\n\n> Can someone please help me? Many physics textbooks define the tension\n> in a cord as "the magnitude of each of the two forces with opposite\n> directions that produce the tension." It would appear, therefore, that\n> tension is not a vector,\n\nThat\'s correct, the tension is a stress tensor. In three space\ndimensions the difference is inescapable, because a force is\nrepresented by a 3-component vector while a stress tensor is\nrepresented by a 3x3 matrix. In a one-dimensional setting it is\neasier to confuse the 1-component vector and the 1x1 matrix.\n\n> but then, when solving a problem with cords\n> and pulleys, they add the tension in the cord to the force of gravity\n> on an object. Is this correct? What meaning can this sum have?\n\nAh, but there is a true force acting on the *endpoint* of the rope.\nThis is analoguous to the surface tractions in 3-dimensional\nelasticity. There, the tractions are obtained by "dotting" one\ntensor index of the 3x3 stress tensor into the 3x1 vector representing\nthe surface normal.\n\n--\npa at panix dot com\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Peter R. Oakfield <Poakfield@msn.com> wrote:
> Can someone please help me? Many physics textbooks define the tension
> in a cord as "the magnitude of each of the two forces with opposite
> directions that produce the tension." It would appear, therefore, that
> tension is not a vector,
That's correct, the tension is a stress tensor. In three space
dimensions the difference is inescapable, because a force is
represented by a 3-component vector while a stress tensor is
represented by a 3x3 matrix. In a one-dimensional setting it is
easier to confuse the 1-component vector and the 1x1 matrix.
> but then, when solving a problem with cords
> and pulleys, they add the tension in the cord to the force of gravity
> on an object. Is this correct? What meaning can this sum have?
Ah, but there is a true force acting on the *endpoint* of the rope.
This is analoguous to the surface tractions in 3-dimensional
elasticity. There, the tractions are obtained by "dotting" one
tensor index of the 3x3 stress tensor into the 3x1 vector representing
the surface normal.