Mass

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=2 height=90 BGCOLOR="#CC9900" TEXT="#080000" bgproperties="fixed" background="070005a0dwnjzk.png"> <div> <A HREF="lesson5.htm" TARGET="_top" TITLE="(Some) Physical Properties of Matter by "><U><B>home</B></U></A><B>     | </B><B> </B><B> </B><B>  </B><FONT SIZE="5" COLOR="#FFCC66" FACE="Arial" ><B>(Some) Physical Properties of Matter by Carl Martikean</B></FONT></div> <div> <B>Mass</B><B>   |   </B><A HREF="id33.htm" TARGET="_top" TITLE="Volume"><U><B>Volume</B></U></A><B>   |   </B><A HREF="id34.htm" TARGET="_top" TITLE="Density"><U><B>Density</B></U></A><B>   |   </B><A HREF="id36.htm" TARGET="_top" TITLE="Boiling Point"><U><B>Boiling Point</B></U></A><B>   |   </B><A HREF="id35.htm" TARGET="_top" TITLE="Melting Point"><U><B>Melting Point</B></U></A><B>   |   </B><A HREF="id37.htm" TARGET="_top" TITLE="Specific Heat"><U><B>Specific Heat</B></U></A></div> <div> </div> </td> </tr><tr> <td valign="top" width=210 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> Mass</div> <bR> </td> <td valign="top" height=390 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> Back to <A HREF="id22.htm" TARGET="_top" TITLE="Exercise"><U>Exercise</U></A>   Back to <A HREF="lesson5.htm" TARGET="_top" TITLE="(Some) Physical Properties of Matter by "><U>Home</U></A></div> <bR> <div> MEASURING MASS</div> <bR> <div> <TABLE BORDER="2" CELLPADDING="2" CELLSPACING="1" WIDTH="673" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 1100 WIDTH="333"><div> <I>1. Platform balance</I></div> <div> The platform balance is used to determine the mass of an object by comparison with known masses. Mass that is measured with a platform balance is sometimes called <FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>gravitational mass, </I></FONT>since it is measured by comparing the gravitational attraction between the earth and the objects on the balance. Figure 21 shows a singlebeam platform balance. Another type of platform balance is the triplebeam, Figure 22. Various sliding masses are suspended from the beam so that the use of separate masses is almost unnecessary. The center of the beam and the pans themselves rest on knifeedge bearings that have little friction. There is a pointer attached to the beam to show when the pans are balanced.</div> <div> <I>2. Inertia balance</I></div> <div> The inertia balance is used to compare masses by measuring the period of vibration when a mass is placed on the pan of the balance and the pan is set in horizontal motion. Mass that is measured with an inertia balance is sometimes called <FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>i</I></FONT><I>nertial</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I> </I></FONT>mass, since it is measured by comparing the resistance to a change in the motion of the object on the balance. Figure 23 is a top view of an inertia balance attached to a laboratory table. On such a balance, masses and periods of vibration are related according to the equation</div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="08e88440.jpg" border=0 width="136" height="68" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div> where m<FONT SIZE="1" COLOR="#000000" FACE="Arial" >1 </FONT>and m<FONT SIZE="1" COLOR="#000000" FACE="Arial" >2</FONT> are different masses and T<FONT SIZE="1" COLOR="#000000" FACE="Arial" >1 </FONT>and T<FONT SIZE="1" COLOR="#000000" FACE="Arial" >2</FONT> are their respective periods of vibration.</div> <div> Since m<FONT SIZE="1" COLOR="#000000" FACE="Arial" >1</FONT> and m<FONT SIZE="1" COLOR="#000000" FACE="Arial" >2</FONT> include the mass of the balance pan, it is more convenient to measure the periods of several known masses and then to plot a graph of the resulting data. The value of an unknown mass can then be read directly from the graph after the period of the unknown mass is measured. This is the method that will be used in this experiment.</div> <div> <I>3. Mass density</I></div> <div> The mass of a unit volume of a substance is called its mass density<FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>. </I></FONT><FONT SIZE="2" COLOR="#000000" FACE="Arial" >To </FONT>determine the mass density of an object, the mass and volume of the object are measured. The mass density is calculated by dividing the mass by the volume. In this experiment the mass densities of several solids will be determined from the linear measurements and mass of each.</div> <bR> </tD> <tD VALIGN=TOP WIDTH="321"><div> <IMG SRC="0903ca70.png" border=0 width="316" height="167" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <B>Courtesy of Sargent Welch Scientific Company</B></div> <DIV ALIGN="LEFT"></DIV> <div> <I>Figure 1</I></div> <bR> <div> <I><IMG SRC="09239920.jpg" border=0 width="313" height="146" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></I></div> <div> <B>Courtesy of Ohaus Scale Corporation</B></div> <DIV ALIGN="LEFT"></DIV> <div> <I>Figure 2</I></div> <bR> <div> <IMG SRC="0942e8a0.png" border=0 width="302" height="138" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <DIV ALIGN="LEFT"></DIV> <div> <I>Figure 3</I></div> <bR> <div> <I>4. Mass and weight</I></div> <div> Mass is the measure of the quantity of matter in an object. It is one of the fundamental physical quantities. Weight is the measure of the gravitational force acting on an object. Weight is measured in newtons, which is a derived quantity.</div> <div> Mass and weight are, therefore, not synonymous terms. It is incorrect to say that a given mass is equal to a certain number of newtons. However, it is correct to say that a given mass weighs a certain number of newtons at a particular location.</div> <div> In the last part of this experiment, the relationship between mass and weight will be studied by determining the masses of various objects on the platform balance and then weighing them with a spring balance. This relationship will be helpful whenever it is necessary to convert mass units into their weight equivalents and vice versa.</div> <bR> <div> <B>OBJECTIVE</B></div> <div> After completing this experiment, you should be able to use the platform and inertia balances and you should understand the relationship between mass and weight.</div> <bR> </tD> </tR> </TABLE></div> <bR> <bR> <div> <TABLE BORDER="2" CELLPADDING="2" CELLSPACING="1" WIDTH="769" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 1919 WIDTH="327"><div> <B>APPARATUS</B></div> <div> <IMG BORDER="0" SRC="Symb075c00b700f000000000.png" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">platform balance and set of masses </div> <div> <IMG BORDER="0" SRC="Symb075c00b700f000000000.png" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">inertia balance, with cylindrical mass several identical Cclamps, 100150 g each </div> <div> <IMG BORDER="0" SRC="Symb075c00b700f000000000.png" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">stopwatch or watch with sweep second hand several mass density specimens </div> <div> <IMG BORDER="0" SRC="Symb075c00b700f000000000.png" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">spring balance, 20n capacity </div> <div> <IMG BORDER="0" SRC="Symb075c00b700f000000000.png" HEIGHT="16" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">various solid objects with masses below 1 kg</div> <bR> <div> <B>PROCEDURE</B></div> <div> <I>1. Platform balance</I></div> <div> in using the balance, first see that the sliding mass is at the extreme left, or at zero. Then touch one of the pans lightly to start the beam swinging. The pans should move far enough so the pointer swings at least three spaces to either side of the center mark. If it swings farther to one side than it does to the other, the zero adjustment screw may be turned until the pointer moves as many spaces to the left as to the right. The balance is now in equilibrium and is ready for use.</div> <div> The object whose mass is to be determined with a singlebeam balance is always placed on the <I>left </I>pan of the balance. Select a mass that you judge to be greater than that of the object being measured. Place it on the <FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I>right </I></FONT>pan. If it is greater, remove it and add the <I>nextsmaller </I>mass. If this mass is less than that of the object, continue to add other masses to the right pan. Try masses <I>successively </I>from the larger to the smaller, until the last mass added is the tengram mass. Then the sliding mass, which is used to indicate mass to the nearest tenth of a gram, should be moved far enough to the right to make the pointer swing as many spaces to the right. as to the left. You do not need to wait for the pointer to come to rest. The mass of the object equals the sum of <B>all the masses on the pan plus </B>the mass <B>represented </B>by the sliding mass.</div> <div> Be careful not to jar the balance when adding or removing the larger masses. Such jarring dulls the knife edges and makes the balance less sensitive. Jarring may be avoided by supporting the pan with one hand while objects are being added to or removed from the pans. The object whose mass is being determined and the large masses should be placed near the center of the balance pan.</div> <div> Determine the masses of four solid objects, reading the balance to its greatest possible precision. Record in Data Table I. Measure the weight of each object with a spring balance and record.</div> <div> <I>2. Inertia balance</I></div> <div> Fasten one of the Cclamps to the pan of the inertia balance. Set the balance in motion, using a small (about 2 cm) vibration amplitude. Get yourself synchronized with the motion of the balance before starting the stopwatch. Start the watch on the count of "zero" and read the time of 20 vibrations to the nearest 0.01 second. Repeat this procedure two more times and average the results. Enter the average in Data Table II. In the same way,, find the average time for 20 vibrations when 2, 3, and 4 clamps are fastened to the pan. Record the results. Measure and record the mass of one Cclamp.</div> <div> Place an unknown mass on the pan of the inertia balance (after removing the Cclamps) and determine the average time for 20 vibrations. Record the average under Trial 5. For Trial 6 suspend a cylindrical mass in the hole of the balance pan by means of a string. Determine the time for 20 vibrations while holding the mass in this position. For Trial 7 place the cylindrical mass in the pan and determine the time for 20 vibrations. Record the results for Trials 5, 6, and 7.</div> <bR> <bR> </tD> <tD VALIGN=TOP WIDTH="423"><div> <B>DATA AND CALCULATIONS TABLES</B></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>DATA TABLE 1                                       TABLE 1                              CALCULATION               </B></div> <div> <TABLE BORDER="2" CELLPADDING="1" CELLSPACING="1" WIDTH="220" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="LEFT" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 30 WIDTH="62"><div> <B>TRIAL</B></div> </tD> <tD VALIGN=TOP WIDTH="69"><div> <I><B>Mass</B></I></div> <div> (kg)</div> </tD> <tD VALIGN=TOP WIDTH="69"><div> <I><B>Weight</B></I></div> <div> (n)</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="62"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="69"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="69" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="69"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="69" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="62"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="69"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="69" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="69"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="69" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="62"><div> 3</div> </tD> <tD VALIGN=TOP WIDTH="69"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="69" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="69"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="69" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="62"><div> 4</div> </tD> <tD VALIGN=TOP WIDTH="69"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="69" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="69"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="69" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></div> <div> <B> <TABLE BORDER="2" CELLPADDING="2" CELLSPACING="1" WIDTH="89" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 32 WIDTH="77"><div> <I><B>Ratio</B></I></div> <div> <B>(n/kg)</B></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="77"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="77" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="77"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="77" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="77"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="77" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="77"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="77" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></B></div> <div> <B> <TABLE BORDER="2" CELLPADDING="2" CELLSPACING="1" WIDTH="197" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="RIGHT" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 19 ><NOBR><div> Average</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="115"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="115" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 38 ><NOBR><div> Relative</div> <div> Error</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="115"><div> %</div> </tD> </tR> </TABLE></B></div> <bR> <bR> <bR> <bR> <bR> <bR> <div> <B>DATA TABLE II</B></div> <DIV ALIGN="LEFT"></DIV> <div> <B>Mass of 1 Cclamp:     kg</B></div> <div> <TABLE BORDER="2" CELLPADDING="1" CELLSPACING="1" WIDTH="303" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 44 WIDTH="55"><div> <B>TRIAL</B></div> </tD> <tD VALIGN=TOP WIDTH="93"><div> <I><B>Objects</B></I></div> <div> <I><B>in pan</B></I></div> </tD> <tD VALIGN=TOP><NOBR><div> <I><B>Number of</B></I></div> <div> <I><B>vibrations</B></I></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="49"><div> <I><B>Total</B></I></div> <div> <I><B>time</B></I></div> <div> <I><B>(s)</B></I></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="55"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="93"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="93" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="81"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="81" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="49"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="49" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="55"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="93"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="93" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="81"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="81" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="49"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="49" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="55"><div> 3</div> </tD> <tD VALIGN=TOP WIDTH="93"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="93" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="81"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="81" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="49"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="49" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="55"><div> 4</div> </tD> <tD VALIGN=TOP WIDTH="93"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="93" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="81"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="81" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="49"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="49" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="55"><div> 5</div> </tD> <tD VALIGN=TOP WIDTH="93"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="93" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="81"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="81" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="49"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="49" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="55"><div> 6</div> </tD> <tD VALIGN=TOP WIDTH="93"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="93" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="81"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="81" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="49"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="49" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="55"><div> 7</div> </tD> <tD VALIGN=TOP WIDTH="93"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="93" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="81"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="81" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="49"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="49" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></div> <bR> <div> <B>DATA TABLE III</B></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="2" CELLPADDING="1" CELLSPACING="1" WIDTH="369" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 30 WIDTH="71"><div> <B>TRIAL</B></div> </tD> <tD VALIGN=TOP WIDTH="84"><div> <I><B>Substance</B></I></div> </tD> <tD VALIGN=TOP><NOBR><div> <I><B>Dimensions or volume</B></I></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="57"><div> <I><B>Mass</B></I></div> <div> (kg)</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="84"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="84" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="132"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="132" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="57"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="57" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="84"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="84" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="132"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="132" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="57"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="57" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 3</div> </tD> <tD VALIGN=TOP WIDTH="84"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="84" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="132"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="132" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="57"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="57" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="71"><div> 4</div> </tD> <tD VALIGN=TOP WIDTH="84"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="84" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="132"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="132" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="57"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="57" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></div> <bR> <div> <B>CALCULATIONS TABLE III</B></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="2" CELLPADDING="1" CELLSPACING="1" WIDTH="369" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 43 WIDTH="59"><div> <B>TRIAL</B></div> </tD> <tD VALIGN=TOP WIDTH="70"><div> <I><B>Period</B></I></div> <div> <I><B>squared</B></I></div> <div> (s<FONT SIZE="1" COLOR="#000000" FACE="Arial" >2</FONT>)</div> </tD> <tD VALIGN=TOP WIDTH="80"><div> <I><B>Mass,</B></I></div> <div> <I><B>graphical</B></I></div> <div> (kg)</div> </tD> <tD VALIGN=TOP WIDTH="72"><div> <I><B>Mass,</B></I></div> <div> <I><B>accepted</B></I></div> <div> (kg) </div> </tD> <tD VALIGN=TOP><NOBR><div> <I><B>Relative</B></I></div> <div> <I><B>error</B></I></div> <div> (%)</div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="59"><div> 5</div> </tD> <tD VALIGN=TOP WIDTH="70"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="70" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="80"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="80" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="72"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="72" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="58"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="58" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="59"><div> 6</div> </tD> <tD VALIGN=TOP WIDTH="70"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="70" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="80"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="80" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="72"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="72" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="58"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="58" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="59"><div> 7</div> </tD> <tD VALIGN=TOP WIDTH="70"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="70" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="80"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="80" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="72"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="72" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="58"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="58" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></div> <bR> <div> <B>CALCULATIONS TABLE IV</B></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="2" CELLPADDING="1" CELLSPACING="1" WIDTH="423" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 58 ><NOBR><div> <B>TRIAL </B></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <I><B>Substance</B></I></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="65"><div> <I><B>Volume</B></I></div> <div> <B>(cm</B><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><B>3</B></FONT><B>)</B></div> </tD> <tD VALIGN=TOP WIDTH="51"><div> <I><B>Mass</B></I></div> <div> <B>(g)</B></div> </tD> <tD VALIGN=TOP><NOBR><div> <I><B>Mass</B></I></div> <div> <I><B>density,</B></I></div> <div> <I><B>experimental</B></I></div> <div> <B>(g/cm</B><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><B>3</B></FONT><B>)</B></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <I><B>Mass</B></I></div> <div> <I><B>density,</B></I></div> <div> <I><B>accepted</B></I></div> <div> <B>(g/cm</B><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><B>3</B></FONT><B>)</B></div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="46"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="67"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="67" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="65"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="65" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="51"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="51" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="91"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="91" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="68"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="68" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="46"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="67"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="67" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="65"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="65" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="51"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="51" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="91"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="91" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="68"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="68" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="46"><div> 3</div> </tD> <tD VALIGN=TOP WIDTH="67"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="67" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="65"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="65" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="51"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="51" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="91"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="91" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="68"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="68" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="46"><div> 4</div> </tD> <tD VALIGN=TOP WIDTH="67"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="67" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="65"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="65" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="51"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="51" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="91"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="91" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="68"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="68" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></div> <bR> <div> <B>CALCULATIONS TABLE IV (cont)</B></div> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="2" CELLPADDING="1" CELLSPACING="1" WIDTH="158" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 43 WIDTH="74"><div> <I><B>Absolute</B></I></div> <div> <I><B>error</B></I></div> <div> <B>(g/cm</B><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><B>3</B></FONT><B>)</B></div> </tD> <tD VALIGN=TOP WIDTH="69"><div> <I><B>Relative</B></I></div> <div> <I><B>error</B></I></div> <div> (%)</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="74"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="74" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="69"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="69" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="74"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="74" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="69"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="69" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="74"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="74" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="69"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="69" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="74"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="74" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="69"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="19" ALIGN="bottom" WIDTH="69" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></div> <bR> <div> <B>CALCULATIONS</B></div> <div> Show the calculations for the first trial in the space provided below. Enter the results of all calculations in the appropriate tables.</div> <bR> <div> 1.     Calculate the weighttomass ratio for each mass in Data Table I. Average the four values and calculate the relative error of the average, using the ratio looked up in a standard refrence as the accepted value.</div> <bR> <div> 2.     Plot a graph of Trials 14 for the inertia balance, using masses as abscissas and the periods of vibration <I>squared </I>as ordinates. Draw a smooth (best fit) line for the graph as explained. Now place the periods <I>squared</I><FONT SIZE="1" COLOR="#000000" FACE="Arial" ><I> </I></FONT>for Trials 57 on the curve and determine the graphical values of the unknown masses. Record these values in Calculations Table III. Determine the masses with a platform balance and record these values as the accepted masses. Compute the relative error.</div> <div> 3.     Using the masses and volumes of the density specimens in Data Table III, calculate the mass density for each and record in Calculations Table IV. Look up the accepted values in a standard refrence volume, and determine the absolute and relative errors. If the substance is not listed in Table 17, consult some other handbook. Be sure to observe the rules for significant figures in your calculations.</div> <bR> <bR> <bR> </tD> </tR> </TABLE></div> <div> <TABLE BORDER="2" CELLPADDING="2" CELLSPACING="1" WIDTH="769" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 19 WIDTH="757"><div> QUESTIONS</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 146 WIDTH="757"><div> 1.     Which, if any, of the three devices used in this experiment (platform balance, inertia balance, spring scale) would work in the absence of gravity? Justify your answer.</div> <bR> <bR> <bR> <bR> <bR> <bR> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 151 ><NOBR><div> 2.     Which of the three devices listed above is capable of the greatest precision? Justify your answer</div> <bR> <bR> <bR> <bR> <bR> <bR> <bR> <bR> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 168 ><NOBR><div> 3.     What conclusions can you draw from the data for Trials 6 and 7 in Data Table II?</div> <bR> <bR> <bR> <bR> <bR> <bR> <bR> <bR> <bR> </NOBR></tD> </tR> </TABLE></div> <bR> </td> </tr></table></body>