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Function Plot with Vectors Template

    1: <problem>
    2: <script type="loncapa/perl">$slope=&random(0.5,0.8,0.1);
    3: $function="2+$slope*x";
    4: $massx=&random(3.5,6.5,0.1);
    5: $massy=2.1+$slope*$massx;
    6: $angle=180.*atan($slope)/$pi;
    7: $perp=$angle+90.;</script>
    8: <startouttext />
    9: A mass is sliding down the indicated incline with a constant velocity. Construct the free body diagram, making sure the forces are approximately proportionally correct. Leave unused vectors unattached.<br /> <endouttext />
   10: <functionplotresponse xaxisvisible="no" xlabel="x" gridvisible="yes" ylabel="y" id="11" xmax="10" yaxisvisible="no" xmin="0" ymin="0" ymax="10" width="450" height="450">
   11: <functionplotelements>
   12: 
   13: <backgroundplot function="$function" fixed="yes" />
   14: <plotobject label="Mass" x="$massx" y="$massy" />
   15: <plotvector label="Gravity" tailx="6" taily="1" tipx="9" tipy="1" />
   16: <plotvector label="KineticFriction" tailx="6" taily="2" tipx="9" tipy="2" />
   17: <plotvector label="StaticFriction" tailx="6" taily="3" tipx="9" tipy="3" />
   18: <plotvector label="NormalForce" tailx="6" taily="4" tipx="9" tipy="4" />
   19: 
   20: </functionplotelements>
   21: <functionplotruleset>
   22: <functionplotvectorrule index="Grav" vector="Gravity" attachpoint="Mass" angle="270" angleerror="2" />
   23: <functionplotvectorrule index="Norm" vector="NormalForce" attachpoint="Mass" angle="$perp" angleerror="3" />
   24: <functionplotvectorrule index="KFriction" vector="KineticFriction" attachpoint="Mass" angle="$angle" angleerror="2" />
   25: <functionplotvectorrule index="SFriction" vector="StaticFriction" notattachpoint="Mass" />
   26: <functionplotvectorsumrule vectors="Gravity,NormalForce,KineticFriction" length="0" lengtherror="1" index="Total" />
   27: </functionplotruleset>
   28: <hintgroup showoncorrect="no">
   29:     
   30: <hintpart on="Grav">
   31:     <startouttext />Gravity acts on the mass and points straight down.<endouttext />
   32: </hintpart>
   33: <hintpart on="SFriction">
   34:     <startouttext />The mass is sliding.<endouttext />
   35: </hintpart>
   36: <hintpart on="Total">
   37:     <startouttext />What should be the net force on the mass?<endouttext />
   38: </hintpart>
   39: </hintgroup>
   40: </functionplotresponse>
   41: </problem>