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Subject: Vectors & Scalars
Date: Wed, 29 Dec 2004 06:22:00 -0500
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<HTML><HEAD><TITLE>Vectors & Scalars</TITLE>
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<BODY text=3D#000000 vLink=3D#800080 aLink=3D#ff0000 link=3D#0000ff =
bgColor=3Dwhite>
<BLOCKQUOTE>
  <TABLE bgColor=3D#ffff00>
    <TBODY>
    <TR>
      <TD><B>Multiple Choice Online Test</B><BR>Indicate the correct =
answer by=20
        clicking on the button next to the numbers 1, 2, 3 or 4. There =
is only=20
        one correct answer per question. After you have answered=20
        <B><U>all</U></B> multiple choice questions compare your choices =
with=20
        the correct answers. </TD></TR></TBODY></TABLE>
  <HR width=3D"100%" color=3Dblue SIZE=3D3>

  <CENTER>
  <H2>Vectors and Scalars II</H2></CENTER>
  <HR width=3D"100%" color=3Dblue SIZE=3D3>
  <BR>
  <FORM name=3DF><!frage1><B>1.) Which one of the following represents a =
scalar=20
  quantity? </B>
  <UL>
    <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
      <TBODY>
      <TR>
        <TD width=3D50><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ1></TD>
        <TD>The change in momentum of a rubber ball bouncing off the=20
      floor.</TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ1></TD>
        <TD>The velocity of an airplane flying at 300 km.h<SUP>-1</SUP> =
on a=20
          bearing 040<SUP>0</SUP>.</TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D1 =
name=3DQ1></TD>
        <TD>The speed of a car travelling at 100 km.h<SUP>-1</SUP>. =
</TD></TR>
      <TR>
        <TD vAlign=3Dtop width=3D50><B>4</B><INPUT type=3Dradio =
value=3D0 name=3DQ1></TD>
        <TD>The acceleration of an object thrown vertically upwards and =
which=20
          has reached the highest point of its =
motion.</TD></TR></TBODY></TABLE>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
  </UL><!frage2>
  <TABLE>
    <TBODY>
    <TR>
      <TD><B>2.) An aircraft is flying due West in a cross-wind that =
blows=20
        from north to south. The pilot draws the following vector =
diagram to=20
        establish the aircraft's correct heading. <BR><BR>What is the =
correct=20
        label for the vector marked III in the diagram?</B> </TD>
      <TD><IMG height=3D152 alt=3D"vectors II, fig.1"=20
        src=3D"http://www.sec.org.za/tests/pmcvecIIA.gif" width=3D394 =
border=3D2>=20
    </TD></TR></TBODY></TABLE>
  <UL>
    <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
      <TBODY>
      <TR>
        <TD width=3D50><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ2></TD>
        <TD>Resultant velocity of aircraft relative to the =
ground.</TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ2></TD>
        <TD>Velocity of aircraft relative to the ground.</TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ2></TD>
        <TD>Velocity of air relative to the ground.</TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D1 =
name=3DQ2></TD>
        <TD>Velocity of aircraft relative to the =
air.</TD></TR></TBODY></TABLE>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
  </UL><!frage3><B>3.) Which one of the following statements is CORRECT? =
<BR>The=20
  direction of vector AB on the sketch can be written as a bearing of =
=85=20
  <TABLE width=3D"90%">
    <TBODY>
    <TR>
      <TD>
        <UL>
          <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
            <TBODY>
            <TR>
              <TD width=3D50><B>1</B><INPUT type=3Dradio value=3D1 =
name=3DQ3></TD>
              <TD>240<SUP>0</SUP></TD></TR>
            <TR>
              <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ3></TD>
              <TD>120<SUP>0</SUP></TD></TR>
            <TR>
              <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ3></TD>
              <TD>210<SUP>0</SUP></TD></TR>
            <TR>
              <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ3></TD>
              <TD>060<SUP>0</SUP></TD></TR></TBODY></TABLE></UL></TD>
      <TD align=3Dmiddle><IMG height=3D153 alt=3D"vectors II, fig.2"=20
        src=3D"http://www.sec.org.za/tests/pmcvecIIB.gif" width=3D352 =
border=3D2>=20
    </TD></TR></TBODY></TABLE>
  <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>

  <UL></UL><!frage4><B>4.) Three forces F<SUB>1</SUB>, F<SUB>2</SUB> and =

  F<SUB>3</SUB> act simultaneously on object O, which is in equilibrium. =

  <CENTER><IMG height=3D188 alt=3D"vectors II, fig.3"=20
  src=3D"http://www.sec.org.za/tests/pmcvecIIC.gif" width=3D263=20
  border=3D2></CENTER><B>Which ONE of the following statements is NOT =
TRUE with=20
  reference to the three forces?</B>=20
  <UL>
    <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
      <TBODY>
      <TR>
        <TD width=3D50><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ4></TD>
        <TD>The resultant of forces F<SUB>1</SUB>, F<SUB>2</SUB> and=20
          F<SUB>3</SUB> is zero.</TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ4></TD>
        <TD>The forces F<SUB>1</SUB>, F<SUB>2</SUB> and F<SUB>3</SUB> =
lie in=20
          the same plane.</TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D1 =
name=3DQ4></TD>
        <TD>Force F<SUB>3</SUB> is the resultant of forces F<SUB>2</SUB> =
and=20
          F<SUB>3</SUB>.</TD></TR>
      <TR>
        <TD vAlign=3Dtop width=3D50><B>4</B><INPUT type=3Dradio =
value=3D0 name=3DQ4></TD>
        <TD>The sum of the components of all forces in any chosen =
direction is=20
          zero.</TD></TR></TBODY></TABLE>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
  </UL><!frage5><B>5.) Three forces F1, F2 and F3 act simultaneously on =
object=20
  O, which is in equilibrium. <BR>
  <CENTER><IMG height=3D188 alt=3D"vectors II, fig.4"=20
  src=3D"http://www.sec.org.za/tests/pmcvecIIC.gif" width=3D263=20
  border=3D2></CENTER><BR>Which one of the following vector diagrams =
correctly=20
  represents the above situation?</B> <BR><BR>
  <CENTER><IMG height=3D111 alt=3D"vectors II, fig.5"=20
  src=3D"http://www.sec.org.za/tests/pmcvecIID.gif" width=3D597 =
border=3D2></CENTER>
  <UL>
    <TABLE cellSpacing=3D0 cols=3D2 border=3D0>
      <TBODY>
      <TR>
        <TD width=3D10><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ5></TD>
        <TD><B>A</B></TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D1 =
name=3DQ5></TD>
        <TD><B>B</B></TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ5></TD>
        <TD><B>C</B></TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ5></TD>
        <TD><B>D</B></TD></TR></TBODY></TABLE>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
  </UL><B>Questions 6, 7 and 8 refer to the following diagram, showing a =
number=20
  of forces acting on an object. </B>
  <P>
  <CENTER><IMG height=3D245 alt=3D"vectors II, fig.6"=20
  src=3D"http://www.sec.org.za/tests/pmcvecIIE.gif" width=3D421=20
  border=3D0></CENTER><BR><!frage6><B>6.) The resultant of force V and =
force R is=20
  force =85=20
  <UL>
    <TABLE cellSpacing=3D0 cols=3D3 width=3D"90%" border=3D0>
      <TBODY>
      <TR>
        <TD width=3D50><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ6></TD>
        <TD><B>P</B></TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D1 =
name=3DQ6></TD>
        <TD><B>Q</B></TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ6></TD>
        <TD><B>S</B></TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ6></TD>
        <TD><B>T</B></TD></TR></TBODY></TABLE>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
  </UL><!frage7><B>7.) The equilibrant of force V and force S is force =
=85 </B>
  <TABLE width=3D"100%">
    <TBODY>
    <TR>
      <TD>
        <UL>
          <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
            <TBODY>
            <TR>
              <TD width=3D50><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ7></TD>
              <TD><B>P</B></TD></TR>
            <TR>
              <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D1 =
name=3DQ7></TD>
              <TD><B>Q</B></TD></TR>
            <TR>
              <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ7></TD>
              <TD><B>U</B></TD></TR>
            <TR>
              <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ7></TD>
              =
<TD><B>T</B></TD></TR></TBODY></TABLE></UL></TD></TR></TBODY></TABLE>
  <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>

  <UL></UL><!frage8><B>8.) If force P is 100 N and angle <FONT=20
  face=3Dsymbol>q</FONT> =3D 30<SUP>0</SUP>, than the magnitude of force =
V is =85 </B>
  <UL>
    <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
      <TBODY>
      <TR>
        <TD width=3D50><B>1</B><INPUT type=3Dradio value=3D1 =
name=3DQ8></TD>
        <TD>50,0 Newton</TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ8></TD>
        <TD>57,7 Newton</TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ8></TD>
        <TD>86,6 Newton</TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ8></TD>
        <TD>88,9 Newton</TD></TR></TBODY></TABLE>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
  </UL><BR><!frage9><B>
  <TABLE>
    <TBODY>
    <TR>
      <TD vAlign=3Dtop><B>9.) Three horizontal forces of equal magnitude =
act on=20
        a box at rest as shown in the diagram. <BR>The box =85</B> </B>
        <UL>
          <TABLE cellSpacing=3D0 cols=3D2 width=3D"90%" border=3D0>
            <TBODY>
            <TR>
              <TD width=3D50><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ9></TD>
              <TD>accelerates towards the north-east.</TD></TR>
            <TR>
              <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ9></TD>
              <TD>accelerates towards the south-east.</TD></TR>
            <TR>
              <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D1 =
name=3DQ9></TD>
              <TD>accelerates towards the south-west.</TD></TR>
            <TR>
              <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ9></TD>
              <TD>does not =
accelerate.</TD></TR></TBODY></TABLE></UL></TD>
      <TD>
        <CENTER><IMG height=3D207 alt=3D"vectors II, fig.7"=20
        src=3D"http://www.sec.org.za/tests/pmcvecIIF.gif" width=3D320=20
        border=3D2></CENTER></TD></TR></TBODY></TABLE>
  <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>

  <UL></UL><!frage10>10.) In which one of the following vector diagrams =
is the=20
  resultant of the three vectors zero? <BR><BR>
  <CENTER><IMG height=3D132 alt=3D"vectors II, fig.8"=20
  src=3D"http://www.sec.org.za/tests/pmcvecIIG.gif" width=3D599 =
border=3D2></CENTER>
  <UL>
    <TABLE cellSpacing=3D0 cols=3D2 width=3D100 border=3D0>
      <TBODY>
      <TR>
        <TD width=3D50><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ10></TD>
        <TD><B>A</B></TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ10></TD>
        <TD><B>B</B></FONT></TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ10></TD>
        <TD><B>C</B></TD>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D1 =
name=3DQ10></TD>
        <TD><B>D</B></TD></TR></TBODY></TABLE>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
  </UL>
  <HR color=3Dblue SIZE=3D5>

  <CENTER>
  <TABLE cellSpacing=3D0 cols=3D1 width=3D"60%" border=3D1>
    <CAPTION><B>Results</B></CAPTION>
    <TBODY>
    <TR>
      <TD>
        <CENTER><INPUT type=3Dhidden value=3Dfalse =
name=3Dbearbeitet><INPUT onclick=3Dshow() type=3Dbutton value=3D"See =
your results" name=3DButton></CENTER></TD></TR>
    <TR>
      <TD>
        <CENTER><TEXTAREA name=3Dergebnis rows=3D3 readOnly =
cols=3D50></TEXTAREA></CENTER></TD></TR>
    <TR>
      <TD>
        <CENTER><INPUT onclick=3Dshowcorrect() type=3Dbutton =
value=3D"What are the correct answers?" =
name=3DButton></CENTER></TD></TR></TBODY></TABLE></CENTER></FORM>
  <TABLE cellPadding=3D5 width=3D"60%" border=3D1>
    <TBODY>
    <TR>
      <TD><FONT color=3D#9933ff>Hint: You can do the test offline as =
well. Just=20
        click "file" from the menu, then "save" to a destination of your =
choice.=20
        But remember to open file either with windows explorer or =
internet=20
        explorer. Netscape might not be able to reload pictures offline. =

      </FONT></TD></TR></TBODY></TABLE><B>
  <DIV align=3Dright><A href=3D"http://www.sec.org.za/trmc.html">click =
here for more=20
  multiple choice questions</A></DIV></B></BLOCKQUOTE>
<TABLE cellSpacing=3D0 cellPadding=3D3 width=3D"90%" align=3Dcenter =
bgColor=3D#99ffff=20
border=3D0 valign=3D"center">
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    <TD align=3Dmiddle width=3D"16%"><A=20
      =
href=3D"http://www.sec.org.za/index.html"><B><SMALL>Home</SMALL></B></A><=
/TD>
    <TD align=3Dmiddle width=3D"17%"><A=20
      =
href=3D"http://www.sec.org.za/trmat.html"><B><SMALL>Maths</SMALL></B></A>=
</TD>
    <TD align=3Dmiddle width=3D"17%"><A=20
      =
href=3D"http://www.sec.org.za/trphy.html"><B><SMALL>Physics</SMALL></B></=
A></TD>
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href=3D"http://www.sec.org.za/trchem.html"><B><SMALL>Chemistry</SMALL></B=
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    <TD align=3Dmiddle width=3D"17%"><A=20
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href=3D"http://www.sec.org.za/trbio.html"><B><SMALL>Biology</SMALL></B></=
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href=3D"http://www.sec.org.za/aidscont.html"><B><SMALL>HIV/AIDS</SMALL></=
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<CENTER><SMALL><B>=A9 Science Education Centre=20
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