document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117104>Question 117104</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 6000 lb SUV is being winched up a ramp onto a flatbed trailer. If the ramp is at a 25 degree angle, how much force will be required by the winch to pull the SUV up the ramp? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85167 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This was previously answered as the posting to problem 117069 (answer 85147). To save you the<BR>\n" );
document.write( "trouble of looking that answer up, here it is again:<BR>\n" );
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document.write( "In this forum it's pretty hard to do drawings that support geometric problems such as this one.<BR>\n" );
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document.write( "So, let's just say that for a weight on a ramp that goes up at an angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > the <BR>\n" );
document.write( "portion of the weight W that acts perpendicular to the ramp is given by the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5Bn%5D+=+W%2Acos%28alpha%29 ALIGN=MIDDLE  ALT=\"W%5Bn%5D+=+W%2Acos%28alpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the portion of the weight W that acts parallel to and down the ramp is given by the <BR>\n" );
document.write( "equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5Bt%5D+=+W%2Asin%28alpha%29 ALIGN=MIDDLE  ALT=\"W%5Bt%5D+=+W%2Asin%28alpha%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In this problem, the weight W is the weight of the SUV which is given as 6000 lbs and the<BR>\n" );
document.write( "angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the ramp is 25 degrees.<BR>\n" );
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document.write( "The winch will have to generate enough force to overcome the portion of the weight of the<BR>\n" );
document.write( "SUV that acts parallel to and down the ramp. [This assumes the rolling friction of the vehicle<BR>\n" );
document.write( "is negligible.] So the winch will have to produce an amount of force equal to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5Bt%5D+=+W%2Asin%28alpha%29+=+6000%2Asin%2825%29+=+6000%2A+0.422618261+=+2535.71 ALIGN=MIDDLE  ALT=\"W%5Bt%5D+=+W%2Asin%28alpha%29+=+6000%2Asin%2825%29+=+6000%2A+0.422618261+=+2535.71\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Once the vehicle is in motion the winch will have to pull with a force of 2535.71 lbs <BR>\n" );
document.write( "parallel to the ramp to keep the SUV rolling up the ramp at a steady rate of movement.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. If you expect to do many of<BR>\n" );
document.write( "these problems, you might want to memorize these two \"ramp\" equations.<BR>\n" );
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