document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032664>Question 1032664</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Chaz is using a rope tied to his tractor to remove an old tree stump from a field.  Which method given below, a or b, will result in the greatest force applied to the stump?  Assume that the tractor will exert the same amount of force using either method. \r<BR>\n" );
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document.write( "Explain your answer by showing an example using real numbers.  Note that the length of the rope does not change between each scenario.\r<BR>\n" );
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document.write( "a.	 Tie the rope to the stump and pull.<BR>\n" );
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document.write( "b.	Tie one end to the stump and the other end to a nearby pole.  Then, pull on the rope perpendicular to it at a point about halfway between the two. \r<BR>\n" );
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document.write( "(p.s.)I do school online and its hard to get help from anyone. I know that i have to do something with the geometric/algebraic Vectors but im not sure what to do from there. Anything would helpful :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #647338 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=647338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. The amount of force <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F ALIGN=MIDDLE  ALT=\"F\"   DISABLED_style= \"max-width:90%; height:auto;\" >  that the tractor can exert is applied to the stump.<BR>\n" );
document.write( "b. How close is that nearby pole, how tight is the rope, and how is it tied?<BR>\n" );
document.write( "I envision something like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%281100%2C300%2C-5.5%2C5.5%2C-0.5%2C2.5%2C%0D%0Ared%28arrow%280%2C1%2C0%2C2%29%29%2Cgreen%28triangle%28-5%2C0%2C5%2C0%2C0%2C1%29%29%2C%0D%0Alocate%282.3%2C0.2%2Cgreen%285ft%29%29%2Clocate%28-2.7%2C0.2%2Cgreen%285ft%29%29%2C%0D%0Alocate%280.02%2C0.6%2Cgreen%281ft%29%29%2Cgreen%28triangle%28-2.5%2C0.5%2C-2.55%2C0.55%2C-2.45%2C0.55%29%29%2C%0D%0Alocate%28-2.8%2C0.85%2Cgreen%280.5F%29%29%2C%0D%0Agreen%28triangle%28-5%2C0%2C0%2C0%2C0%2C1%29%29%2Cgreen%28rectangle%280%2C0%2C0.1%2C0.1%29%29%2C%0D%0Agreen%28triangle%280%2C1%2C-2.5%2C1%2C-2.5%2C0.5%29%29%2Clocate%28-2.4%2C1.2%2Cgreen%282.5F%29%29%2C%0D%0Ablue%28arrow%280%2C1%2C2.5%2C0.5%29%29%2Cblue%28arrow%280%2C1%2C-2.5%2C0.5%29%29%2C%0D%0Alocate%280.1%2C2.05%2CF%29%2Clocate%28-2.2%2C0.55%2CR%29%2C%0D%0Agreen%28arrow%280%2C1%2C-2.5%2C1%29%29%2Cgreen%28arrow%28-2.5%2C1%2C-2.5%2C0.5%29%29%2C%0D%0Alocate%282.5%2C0.7%2CR%29%2Ccircle%28-5%2C0%2C0.08%29%2Ccircle%285%2C0%2C0.08%29%2C%0D%0Alocate%28-5.2%2C-0.1%2Cstump%29%2Clocate%285%2C-0.1%2Cpole%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The forces shown are the forward pull of the tractor (F), and the reaction forces of the stump and the pole, jointly pulling the tractor backwards.<BR>\n" );
document.write( "The rope is a physics-problem rope that has no mass, and transmits 100% of the force applied, without stretching.<BR>\n" );
document.write( "As neither one (tractor, pole or stump) is moving, the net force on the middle of the rope is zero.<BR>\n" );
document.write( "The forward component of each force is<BR>\n" );
document.write( "F for the tractor pull,<BR>\n" );
document.write( "-0.5F for the reaction of the stump,<BR>\n" );
document.write( "-0.5F for the reaction of the pole,<BR>\n" );
document.write( "0.5F for the forwards pulling action on the stump, and<BR>\n" );
document.write( "0.5F for the forwards pulling action on the pole.<BR>\n" );
document.write( "The rightwards components of the forces are<BR>\n" );
document.write( "0 for the pull of the tractor because it is pulling straight ahead,<BR>\n" );
document.write( "-2.5F for the reaction of the stump pulling the tractor to the left,<BR>\n" );
document.write( "2.5F for the reaction of the pole pulling the tractor to the right (cancelling the leftwards pull from the stump),<BR>\n" );
document.write( "2.5F for the rightwards action pull on the stump, and<BR>\n" );
document.write( "-2.5 for the leftwards action pull on the pole.<BR>\n" );
document.write( "The 2.5F to 0.5F ratio of sideways to backwards R force component magnitudes is the same as the ratio of the 5ft and 1ft corresponding sides of the similar green triangle. </SPAN>\n" );
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