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<body lang=3Den-US>

<div style=3D'direction:ltr;border-width:100%'>

<div style=3D'direction:ltr;margin-top:0in;margin-left:0in;width:8.6347in'>

<div style=3D'direction:ltr;margin-top:0in;margin-left:.3131in;width:1.8625=
in'>

<p style=3D'margin:0in;font-family:Calibri;font-size:17.0pt'>Report</p>

</div>

<div style=3D'direction:ltr;margin-top:.0388in;margin-left:.3131in;width:1.=
5541in'>

<p style=3D'margin:0in;font-family:Calibri;font-size:10.0pt;color:gray'>Mon=
day,
March 23, 2009</p>

<p style=3D'margin:0in;font-family:Calibri;font-size:10.0pt;color:gray'>9:4=
1 PM</p>

</div>

<div style=3D'direction:ltr;margin-top:.2312in;margin-left:0in;width:6.9173=
in'><img
src=3D"page15_files/image001.png" width=3D664 height=3D488></div>

<div style=3D'direction:ltr;margin-top:.2791in;margin-left:0in;width:6.9069=
in'>

<ol style=3D'margin-left:.3125in;direction:ltr;unicode-bidi:embed;margin-to=
p:
 0in;margin-bottom:0in;font-family:Calibri;font-size:11.0pt'>
 <p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'><img
 src=3D"page15_files/image002.png" width=3D643 height=3D73></p>
 <p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>&nbsp;</p>
 <p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>The rubber ba=
nd
 chain is made of rubber bands looped together and the mass is a .15kg mass
 hanger. The drop was 4.8 m high allowing for the height of the mass hanger=
.</p>
 <p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>&nbsp;</p>
 <li value=3D1 style=3D'margin-top:0;margin-bottom:0;vertical-align:middle'=
><span
     style=3D'font-family:Calibri;font-size:11.0pt'>In order to predict the
     number of rubber bands we first had to answer:</span></li>
 <p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>&nbsp;</p>
 <p style=3D'margin:0in;margin-left:.375in;font-weight:bold;font-family:Cal=
ibri;
 font-size:11.0pt'>What is the spring constant of the bungee cord as a func=
tion
 of the number of rubber bands?</p>
 <p style=3D'margin:0in;margin-left:.375in;font-weight:bold;font-family:Cal=
ibri;
 font-size:11.0pt'>&nbsp;</p>
 <p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>To find this =
we had
 use the understand what the energy levels were at key points in the
 problem.<span style=3D'mso-spacerun:yes'>Â  </span></p>
 <p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>&nbsp;</p>
 <ol type=3Da style=3D'margin-left:.375in;direction:ltr;unicode-bidi:embed;
  margin-top:0in;margin-bottom:0in;font-family:Calibri;font-size:11.0pt'>
  <li value=3D1 style=3D'margin-top:0;margin-bottom:0;vertical-align:middle=
'><span
      style=3D'font-family:Calibri;font-size:11.0pt;font-family:Calibri;
      font-size:11.0pt'>The first key point is the top of the situation, be=
fore
      release.<span style=3D'mso-spacerun:yes'>Â  </span>Here all of the en=
ergy is
      potential (mgh)</span></li>
  <li value=3D2 style=3D'margin-top:0;margin-bottom:0;vertical-align:middle=
'><span
      style=3D'font-family:Calibri;font-size:11.0pt'>The second key point is
      where the object has fallen the length of the rubber bands.<span
      style=3D'mso-spacerun:yes'>Â  </span>At this point in time there is no
      effect from the spring.<span style=3D'mso-spacerun:yes'>Â  </span>Thi=
s is
      where the object would stop if we used a string.</span></li>
  <li value=3D3 style=3D'margin-top:0;margin-bottom:0;vertical-align:middle=
'><span
      style=3D'font-family:Calibri;font-size:11.0pt'>The third key point is=
 where
      the spring is fully extended.<span style=3D'mso-spacerun:yes'>Â  </sp=
an>This
      point </span><span style=3D'font-weight:bold;font-style:italic;font-f=
amily:
      Calibri;font-size:11.0pt'>should</span><span style=3D'font-family:Cal=
ibri;
      font-size:11.0pt'> be right above the floor.<span
      style=3D'mso-spacerun:yes'>Â  </span>At this point there is no gravit=
ational
      potential energy or kinetic energy since the object is not moving.<sp=
an
      style=3D'mso-spacerun:yes'>Â  </span>There is only spring potential e=
nergy.</span></li>
 </ol>
</ol>

</div>

<div style=3D'direction:ltr;margin-top:.1284in;margin-left:.3125in;width:6.=
6111in'><img
src=3D"page15_files/image003.png" width=3D635 height=3D470></div>

<div style=3D'direction:ltr;margin-top:.1861in;margin-left:.3125in;width:6.=
593in'>

<p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'><img
src=3D"page15_files/image004.png" width=3D640 height=3D37></p>

<p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>&nbsp;</p>

<p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>We know that t=
his is
equal to the gravitational potential energy at point 1 because of conservat=
ion
of energy.</p>

<p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>&nbsp;</p>

<p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>To fill in the
variables we need to know:</p>

<ul type=3Dcircle style=3D'margin-left:.375in;direction:ltr;unicode-bidi:em=
bed;
 margin-top:0in;margin-bottom:0in'>
 <li style=3D'margin-top:0;margin-bottom:0;vertical-align:middle'><img
     src=3D"page15_files/image005.png" width=3D601 height=3D55></li>
 <li style=3D'margin-top:0;margin-bottom:0;vertical-align:middle'><span
     style=3D'font-family:Calibri;font-size:11.0pt'>The spring constant; wi=
ll
     find below</span></li>
 <li style=3D'margin-top:0;margin-bottom:0;vertical-align:middle'><img
     src=3D"page15_files/image006.png" width=3D598 height=3D37></li>
</ul>

<p style=3D'margin:0in;margin-left:.375in;font-family:Calibri;font-size:11.=
0pt'>&nbsp;</p>

<p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>In order to fi=
nd the
spring constant, we need to test the stretched and unstretched length of ru=
bber
band chains of different lengths.<span style=3D'mso-spacerun:yes'>Â  </span=
>We
created a rubber band chain by looping the rubber bands inside of each othe=
r.<span
style=3D'mso-spacerun:yes'>Â  </span>We then held a rubber band chain up ag=
ainst a
meter stick so that it would hang freely.<span style=3D'mso-spacerun:yes'>Â 
</span>This was the unstretched length.<span style=3D'mso-spacerun:yes'>Â 
</span>We then attached the .15kg mass hanger and recorded the
&quot;stretched&quot; length.</p>

</div>

<div style=3D'direction:ltr;margin-top:.1486in;margin-left:.3131in;width:6.=
5909in'><img
src=3D"page15_files/image007.png" width=3D633 height=3D144></div>

<div style=3D'direction:ltr;margin-top:.0145in;margin-left:.2916in;width:8.=
343in'><nobr><img
src=3D"page15_files/image008.png" width=3D801 height=3D960><br>
<img src=3D"page15_files/image009.png" width=3D801 height=3D168><br>
</nobr></div>

<div style=3D'direction:ltr;margin-top:.4055in;margin-left:1.2326in;width:6=
.3319in'>

<p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>We then used a=
 TI-89
to solve for n.<span style=3D'mso-spacerun:yes'>Â  </span>This actually too=
k the
calculator a minute to process.</p>

<p style=3D'margin:0in;font-family:Calibri;font-size:11.0pt'>It returned th=
at we
needed <span style=3D'font-weight:bold'>28 rubber bands</span></p>

</div>

<div style=3D'direction:ltr;margin-top:.5361in;margin-left:.2381in;width:6.=
6791in'><nobr><img
src=3D"page15_files/image010.png" width=3D641 height=3D960><br>
<img src=3D"page15_files/image011.png" width=3D641 height=3D148><br>
</nobr></div>

</div>

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