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Subject: Momentum
Date: Wed, 29 Dec 2004 06:49:16 -0500
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<HTML><HEAD><TITLE>Momentum</TITLE>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
<META content=3D"Klaus Oetjen" name=3DAuthor>
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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 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=3D5>

  <CENTER>
  <H2>Momentum</H2></CENTER>
  <HR width=3D"100%" color=3Dblue SIZE=3D5>

  <FORM name=3DF><!frage1><B>1.) A cricket ball of mass 'm' travelling =
at a speed=20
  of 'v', is struck back in the opposite direction with the same speed =
'v'. The=20
  magnitude of the change in momentum of the ball 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=3DQ1></TD>
        <TD><B>2 mv</B></TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ1></TD>
        <TD><B>mv<SUP>2</SUP></B></TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ1></TD>
        <TD><B>mv</B></TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ1></TD>
        <TD><B>0</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Since  v=3Du we can say that change in mom =3D =
m(v - u) =3D m(v + v) =3D 2mv. Or if we take u as positive: change in =
mom =3D m (-v +-u)=3D -2v. Hence it was asked for the magnitude of the =
change of momentum it is still =3D2mv.")' type=3Dbutton =
value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage2>
  <TABLE>
    <TBODY>
    <TR>
      <TD vAlign=3Dtop width=3D"60%"><B>2.) A moving object X has a mass =
m and=20
        speed v. Another moving object Y will have twice the momentum of =
X if it=20
        has a mass and velocity of: </B></TD>
      <TD width=3D"40%">
        <CENTER><IMG height=3D98 alt=3D"momentum, diagram 1"=20
        src=3D"http://www.sec.org.za/tests/pmcmom1.gif" width=3D270=20
        border=3D0></CENTER></TD></TR></TBODY></TABLE></B>
  <UL>
    <TABLE cellSpacing=3D0 cellPadding=3D0 width=3D200 border=3D0>
      <TBODY>
      <TR>
        <TD width=3D50><B>&nbsp;</B></TD>
        <TD align=3Dmiddle width=3D75><B><BIG><U>mass</U></BIG></B></TD>
        <TD align=3Dmiddle =
width=3D75><B><BIG><U>velocity</U></BIG></B></TD></TR>
      <TR>
        <TD width=3D50><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ2></TD>
        <TD align=3Dmiddle width=3D75><B>1/2 m</B></TD>
        <TD align=3Dmiddle width=3D75><B>1/2 v</B></TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ2></TD>
        <TD align=3Dmiddle width=3D75><B>1/2 m</B></TD>
        <TD align=3Dmiddle width=3D75><B>2 v</B> </TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D1 =
name=3DQ2></TD>
        <TD align=3Dmiddle width=3D75><B>4 m</B></TD>
        <TD align=3Dmiddle width=3D75><B>1/2 v</B></TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ2></TD>
        <TD align=3Dmiddle width=3D75><B>4 m</B></TD>
        <TD align=3Dmiddle width=3D75><B>2 =
v</B></TD></TR></TBODY></TABLE><INPUT onclick=3D'gibfeedback("Object X =
has momentum of p=3Dmv. Twice the momentum is 2mv. Where in the table do =
we find the factor of velocity <small>x</small> mass =3D 2mv? Only in 3 =
we get 2mv after multiplication.")' type=3Dbutton value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage3>
  <TABLE cellPadding=3D4>
    <TBODY>
    <TR>
      <TD vAlign=3Dtop width=3D"60%"><B>3.) A soccer ball of mass 1 kg =
strikes a=20
        wall at right angles with a velocity of 2 m/s as shown in the =
sketch. It=20
        bounces back with a velocity of 1,5 m/s. <BR>The impulse of the =
wall on=20
        the ball (in kg.m/s) is ...=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=3DQ3></TD>
              <TD><B>0,5 to the right</B></TD></TR>
            <TR>
              <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ3></TD>
              <TD><B>0,5 to the left</B></TD></TR>
            <TR>
              <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ3></TD>
              <TD><B>3,5 to the right</B></TD></TR>
            <TR>
              <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D1 =
name=3DQ3></TD>
              <TD><B>3,5 to the left</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Similar to question 1 since impulse =3D change =
in momentum. The magnitude we get from u=3D+2m/s -take towards wall as =
positive-; v=3D-1,5m/s: impulse =3D m(-2 -+1,5)=3D -3,5m. Negative since =
direction is away from wall which is to the left.")' type=3Dbutton =
value=3DExplanation>
          <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
           </UL></B></TD>
      <TD vAlign=3Dtop width=3D"60%">
        <CENTER><IMG height=3D216 alt=3D"momentum, diagram 2"=20
        src=3D"http://www.sec.org.za/tests/pmcmom2.gif" width=3D246=20
        border=3D0></CENTER></TD></TR></TBODY></TABLE><!frage4>
  <TABLE cellPadding=3D4>
    <TBODY>
    <TR>
      <TD vAlign=3Dtop><B>4.) Two trolleys A and B are moving towards =
another as=20
        shown in the diagram at the right. They collide and come to rest =
at the=20
        point of impact. From this observation we can conclude that the =
trolleys=20
        have =85</B> </TD>
      <TD <center><IMG height=3D132 alt=3D"momentum, diagram 3"=20
        src=3D"http://www.sec.org.za/tests/pmcmom3.gif" width=3D295 =
border=3D0>
        <CENTER></CENTER></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=3DQ4></TD>
        <TD><B>equal masses.</B></TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D1 =
name=3DQ4></TD>
        <TD><B>were moving with equal and opposite =
momentum.</B></TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ4></TD>
        <TD><B>were moving with equal and opposite =
velocities.</B></TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ4></TD>
        <TD><B>were moving with equal kinetic=20
energies.</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Only having equal but opposite momentum brings =
trolleys to a stop after impact. Same masses does not consider velocity =
(in 1) and same velocity does not consider mass (in 3). One might tend =
to think that eqal kinetic energies stops them, but because of =
v<sup>2</sup> it is not the case.")' type=3Dbutton value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage5>
  <TABLE cellSpacing=3D0 cellPadding=3D0 border=3D0>
    <TBODY>
    <TR>
      <TD vAlign=3Dtop><B>5.) A snooker ball A moves at a velocity of 6 =
m/s and=20
        collides with two identical snooker balls B and C, as shown in =
the=20
        sketch. Ignore all friction. <BR>After the collision =85 =
</B></TD>
      <TD>
        <CENTER>&nbsp;<IMG height=3D101 alt=3D"momentum, diagram 4"=20
        src=3D"http://www.sec.org.za/tests/pmcmom4.gif" width=3D376=20
        border=3D0></CENTER></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=3D1 =
name=3DQ5></TD>
        <TD><B>balls A and B are stationary and C moves at 6 =
m/s.</B></TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ5></TD>
        <TD><B>balls A and B are stationary and C moves at 3 =
m/s.</B></TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ5></TD>
        <TD><B>ball A is stationary and B and C move at 3 =
m/s.</B></TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ5></TD>
        <TD><B>all three balls move at 2 =
m/s.</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Conservation of momentum. Momentum of A is =
transferred via B to C since A, B and C were positioned in a straight =
line (this should have been stated in the question!). Think of the =
collision as follows: A causes a small deformation in B, this =
deformation travels through the material, meets C at the boundary, =
passes deformation on to C, but C cannot pass it to another body, hence =
C starts to move at velocity at which A hits B (frictional forces =
ignored).")' type=3Dbutton value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage6>
  <TABLE cellSpacing=3D0 cellPadding=3D0 border=3D0>
    <TBODY>
    <TR>
      <TD vAlign=3Dtop><B>6.) The diagram at the right shows two blocks =
A and B,=20
        which are connected by a rubber band. The mass of A is twice the =
mass of=20
        B. <BR>The two blocks are pulled apart on a smooth horizontal =
surface=20
        and released simultaneously. When they are released, the blocks =
collide=20
        and =85</B> </TD>
      <TD vAlign=3Dtop>
        <CENTER><IMG height=3D103 alt=3D"momentum, diagram 5"=20
        src=3D"http://www.sec.org.za/tests/pmcmom5.gif" width=3D265=20
        border=3D0></CENTER></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=3DQ6></TD>
        <TD><B>both move to the right.</B></TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ6></TD>
        <TD><B>both move to the left. </B></TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D1 =
name=3DQ6></TD>
        <TD><B>both remain at rest.</B></TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ6></TD>
        <TD><B>block A remains at rest and B moves to the=20
      right.</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("This type of question is famous and appears =
often in disguise. Both remain a rest after colliding because they had =
equal but opposite momentum before the impact. The stretched rubber band =
does not accelerate both blocks in the same way. Of course the smaller =
block B gains a higher velocity. However, it has the same momentum as A =
since it has a smaller mass.")' type=3Dbutton value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage7><B>7.) Newton's second law of motion states: </B>
  <UL>
    <TABLE cellSpacing=3D0 cols=3D2 border=3D0>
      <TBODY>
      <TR>
        <TD width=3D50><B>1</B><INPUT type=3Dradio value=3D0 =
name=3DQ7></TD>
        <TD><B>For every action there is an equal and opposite=20
      reaction.</B></TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ7></TD>
        <TD><B>A body will remain at rest unless acted upon by an =
unbalanced=20
          force.</B></TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D1 =
name=3DQ7></TD>
        <TD><B>The force acting on a body equals the rate of change of=20
          momentum. </B></TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ7></TD>
        <TD><B>A body will move with uniform motion in a straight line, =
unless=20
          acted upon by an unbalanced =
force.</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Option 3 is Newton II in its original form. We =
often refer to Newton II only as F =3D ma. However, we can rewrite it =
to: F =3D m(v - u) / time =3D mv - mu / time, which is exactly what =
statement 3 says.")' type=3Dbutton value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage8><B>8.) Two vehicles move towards each other on a =
frictionless=20
  road as shown in the sketch below. The two cars collide and =
immediately come=20
  to a standstill. <BR><BR>
  <CENTER><IMG height=3D100 alt=3D"momentum, diagram 6"=20
  src=3D"http://www.sec.org.za/tests/pmcmom6.gif" width=3D621=20
  border=3D0></CENTER><BR>During the collision, the total momentum of =
the two=20
  vehicles will =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=3D0 =
name=3DQ8></TD>
        <TD><B>decrease.</B></TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D1 =
name=3DQ8></TD>
        <TD><B>stay constant.</B></TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ8></TD>
        <TD><B>firstly increase and then decrease.</B></TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ8></TD>
        <TD><B>firstly decrease and then =
increase.</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Only option 2 is in accordance with the law of =
conservation of momentum: total momentum before a collision =3D total =
momentum after a collision.")' type=3Dbutton value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage9><B>9.) An open truck is moving horizontally with a =
constant=20
  velocity along a frictionless track underneath a grain bin. Grain, =
falling=20
  vertically down, now starts falling into the truck, partly filling it =
as it=20
  moves along. What will happen to the momentum of the truck =
accumulating grain?=20
  </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><B>It will decrease.</B></TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ9></TD>
        <TD><B>It will increase.</B></TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ9></TD>
        <TD><B>It will first increase and then decrease.</B></TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D1 =
name=3DQ9></TD>
        <TD><B>It will stay the =
same.</B></TD></TR></TBODY></TABLE><INPUT onclick=3D'gibfeedback("Very =
similar to the previous question. The vertically down falling grain does =
not have a component of its velocity in the direction of the moving =
truck so it does not contribute to the velocity of the truck. However, =
the grain makes the truck not only heavier but also slower and as a =
result the momentum stays the same.")' type=3Dbutton =
value=3DExplanation>
    <SCRIPT language=3DJavaScript>zaehle()</SCRIPT>
     </UL><!frage10><B>10.) Two trolleys, X and Y, of masses 4 kg and 6 =
kg=20
  respectively, are held stationary on a horizontal surface with a =
spring=20
  compressed between them. Two barriers are situated equidistant from =
each=20
  trolley as shown in the diagram below. <BR><BR>
  <CENTER><IMG height=3D220 alt=3D"momentum, diagram 7"=20
  src=3D"http://www.sec.org.za/tests/pmcmom8.gif" width=3D434=20
  border=3D0></CENTER><BR>When the spring is released =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=3DQ10></TD>
        <TD><B>trolley X will strike the barriers first.</B></TD></TR>
      <TR>
        <TD width=3D50><B>2</B><INPUT type=3Dradio value=3D0 =
name=3DQ10></TD>
        <TD><B>trolley Y will strike the barrier first.</B> </TD></TR>
      <TR>
        <TD width=3D50><B>3</B><INPUT type=3Dradio value=3D0 =
name=3DQ10></TD>
        <TD><B>both trolleys will strike the barrier at the same=20
      time.</B></TD></TR>
      <TR>
        <TD width=3D50><B>4</B><INPUT type=3Dradio value=3D0 =
name=3DQ10></TD>
        <TD><B>the final momentum is zero and therefore the trolleys =
will not=20
          reach the barrier.</B></TD></TR></TBODY></TABLE><INPUT =
onclick=3D'gibfeedback("Do not jump for the may be tempting option 3. =
The question is similar to No.6. The stored energy of the spring causes =
greater acceleration to the trolley with less mass. Hence trolley X will =
hit the wall first. Alternatively you can look at it in this way: =
momentum before release =3D zero =3D momentum after release. For the =
moms to be the same but in opposite directions, the trolley with smaller =
mass must move at a higher velocity and as a result must hit the barrier =
before trolley Y.")' type=3Dbutton value=3DExplanation>
    <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><BR>
  <TABLE cellSpacing=3D0 cellPadding=3D3 width=3D"86%" align=3Dcenter =
bgColor=3D#99ffff=20
  border=3D0 valign=3D"center">
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    <TR>
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href=3D"http://www.sec.org.za/index.html"><B><SMALL>Home</SMALL></B></A><=
/TD>
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        =
href=3D"http://www.sec.org.za/trmat.html"><B><SMALL>Maths</SMALL></B></A>=
</TD>
      <TD align=3Dmiddle width=3D"17%"><A=20
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href=3D"http://www.sec.org.za/trphy.html"><B><SMALL>Physics</SMALL></B></=
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