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>
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