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<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy">Hi Emily</span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy">The question is quite tricky………</span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy">As he drops through a distance x, he loses GPE of mgx</span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy">The energy stored in the bar is ½ kx<sup>2</sup> and since F=kx, and F<sub>W
</sub> =mg the energy stored is ½ mgx</span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy">So he loses GPE of mgx and the bar gains EPE of ½ mgx, so where is the missing ½ mgx?</span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy">The answer depends on how he moves down.</span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> if he grabs the bar and drops, its going to go into heat</span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy">If someone slowly lowers him down as the bar deforms, they have to do work on him. The work they do is
<b><span style="font-weight:bold">average force </span></b>times x</span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><i><font size="2" color="navy" face="Arial"><span style="font-size:10.0pt;font-family:Arial;color:navy;font-style:italic">(Remember that the maximum force exerted by the bar is F=kx, the average as he moves from 0 to x is 1/2kx)</span></font></i></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy">The
<b><span style="font-weight:bold">average force</span></b> as they lower him would be ½ mg, so the person lowering him would do ½ mgx of work.</span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy">The other point to note is that if he held the bar and is was unbent, and then he let go, the bar would initially bend a distance 2x,
then oscillate and end up bent a distance x.</span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy">Try it with a mass on a spring.</span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy">Hope this is reasonably clear</span></font></p>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<div>
<p class="MsoAutoSig"><i><font size="3" color="navy" face="Times New Roman"><span style="font-size:12.0pt;color:navy;font-style:italic">Thanks, ........ Francis</span></font></i></p>
<p class="MsoAutoSig"><i><font size="3" color="navy" face="Times New Roman"><span style="font-size:12.0pt;color:navy;font-style:italic"> </span></font></i></p>
<p class="MsoAutoSig"><i><font size="3" color="navy" face="Times New Roman"><span style="font-size:12.0pt;color:navy;font-style:italic">Francis Bryden</span></font></i></p>
<p class="MsoAutoSig"><i><font size="3" color="navy" face="Times New Roman"><span style="font-size:12.0pt;color:navy;font-style:italic">HoD Physics</span></font></i></p>
<p class="MsoAutoSig"><i><font size="3" color="navy" face="Times New Roman"><span style="font-size:12.0pt;color:navy;font-style:italic">St Cuthbert's College</span></font></i></p>
<p class="MsoAutoSig"><i><font size="3" color="navy" face="Times New Roman"><span style="font-size:12.0pt;color:navy;font-style:italic">122 Market Rd</span></font></i></p>
<p class="MsoAutoSig"><i><font size="3" color="navy" face="Times New Roman"><span style="font-size:12.0pt;color:navy;font-style:italic">Epsom 1021</span></font></i></p>
<p class="MsoAutoSig"><i><font size="3" color="navy" face="Times New Roman"><span style="font-size:12.0pt;color:navy;font-style:italic">PO Box 26 020</span></font></i></p>
<p class="MsoAutoSig"><i><font size="3" color="navy" face="Times New Roman"><span style="font-size:12.0pt;color:navy;font-style:italic">ph 64 09 520 4159 x 7808</span></font></i></p>
</div>
<p class="MsoNormal"><font size="2" color="navy" face="Arial"><span style="font-size:
10.0pt;font-family:Arial;color:navy"> </span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Tahoma"><span lang="EN-US" style="font-size:10.0pt;font-family:Tahoma">-----Original Message-----<br>
<b><span style="font-weight:bold">From:</span></b> phys-teach-talk-bounces@nzip.org.nz [mailto:phys-teach-talk-bounces@nzip.org.nz]
<b><span style="font-weight:bold">On Behalf Of </span></b>Emily Hall<br>
<b><span style="font-weight:bold">Sent:</span></b> Thursday, 22 October 2009 12:08 p.m.<br>
<b><span style="font-weight:bold">To:</span></b> phys-teach-talk@nzip.org.nz<br>
<b><span style="font-weight:bold">Cc:</span></b> 'Mr Crawford'<br>
<b><span style="font-weight:bold">Subject:</span></b> Problem from Level 2 NZIP exam</span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Calibri"><span style="font-size:11.0pt"> </span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Calibri"><span style="font-size:11.0pt">Hi</span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Calibri"><span style="font-size:11.0pt"> </span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Calibri"><span style="font-size:11.0pt">I had a question about a problem from the level 2 NZIP exam we can’t seem to get straight in our minds here. The one where the guy hangs off the bar,
his energy in that is 43J and the displacement of the bar is 0.14m so what is his mass?</span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Calibri"><span style="font-size:11.0pt"> </span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Calibri"><span style="font-size:11.0pt">I worked it out and got 63kg which is what is in the marking schedule and that is all good – using E=1/2kx<sup>2</sup> and then F=-kx=mg. But then a
student came to me with conservation of energy like mgh = mg(h-0.14) + 43 if you work it out though you get an answer of ½ what the one is using the above method. We’ve gone through it several times and can’t figure out what the problem is.</span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Calibri"><span style="font-size:11.0pt"> </span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Calibri"><span style="font-size:11.0pt">Can someone explain why they aren’t the same?</span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Calibri"><span style="font-size:11.0pt"> </span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Calibri"><span style="font-size:11.0pt">Thanks</span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Calibri"><span style="font-size:11.0pt">Emily</span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="2" face="Calibri"><span style="font-size:11.0pt"> </span></font></p>
<p class="MsoNormal" style="margin-left:36.0pt"><font size="3" face="Times New Roman"><span style="font-size:12.0pt;font-family:"Times New Roman""><br>
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