# 7 repeat steps five and six for total masses of 300

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7.)Repeat steps five and six for total masses of 0.300 kg, 0.350 kg, 0.400 kg, 0.450 kg, 0.500 kg. Graphing and Other Things to Do1.) Using the data collected in the “Measuring the Spring Elongation,”construct a graph of Δyversus Mon the graph paper provided. Draw a single straight linethat appears to best fit your data. 2.)Once you have the graph drawn, calculate the slope of this graph and record the value on the data sheet.3.)Using equation (5), calculate the spring constant and record the value on the data sheet as ksp,1.4.) Using the data collected in the “Measuring the Period τ,”construct a graph of τave2versus Mtoton the graph paper provided. Draw a single straight linethat appears to best fit your data. 5.)Once you have the graph drawn, calculate the slope of this graph and record the value on the data sheet.6.)Using equation (9), calculate the spring constant and record the value on the data sheet as ksp,2.7.) Calculate the percent difference between the two values you have found for the spring constant.7-6 PHY2053 LABORATORYExperiment SevenSimple Harmonic MotionName:___________________________Date:___________________________Day and Time:___________________________
Data SheetMeasuring the Spring Elongation:0.1000.1500.2000.2500.3000.3500.050ΔyMkg()m()Slope of the graph of Δyversus M:slope=____________________________________ mkg1.Recall,Δy=gkspM,(13)implies thatksp,1=gslope.The data suggests the spring constant has a value of:ksp,1=____________________________________ Nm1.HI 7-1
Measuring the Period τ:Mtotkg()τaves()τave2s2()Trial Ones()Trial Twos()Trial Threes()0.3000.3500.4000.4500.5000.250Slope of the graph of τ2versus Mtot:slope=____________________________________s2kg1.Recall,τ2=4π2kspM,(24)implies thatksp,2=4π2slope.HI 7-2
The data suggests the spring constant has a value of:ksp,2=____________________________________ Nm1.The percent difference between ksp,1and ksp,2is given by% Difference=____________________________________.HI 7-3
Mkg()0.3000.2000.100The Vertical Displacementof a Spring as a Function of MassHI 7-4Δym()0.0000.4000.5000.6000.0000.0200.0400.0600.0800.1000.120
τ2s2()The Square of the Oscillator Period of a Spring as a Function of MassMtotkg()0.600HI 7-50.5000.4000.3000.2000.0000.100
PHY2053 LABORATORYA Quantitative Interlude:The Theory of Torques
THEORYConsider a stick one meterin length--these sticks are found often in physics labs. I hope it seems reasonable to you that if you wanted to balance this stick on your finger, then the place to do this would be somewhere very near the middle of the stick. (It is implicit in this line of reasoning that the material which makes up the meter stick is homogeneous. This "balancing point" is called the center of mass.) A balanced meter stick is represented below in Figure One. (Note that I have placed the originof a Cartesian coordinate system at the center of mass of the meter stick.)Figure OneNote: zˆk()Is out of the page.xˆ i ()yˆ j ()Now that we have a balanced meter stick, if I were to place a small mass Mon the stick at some arbitrary distance xfrom the balancing point, as represented in Figure Two below, then the meter stick would rotate clockwise--as we view it--about the origin of the coordinate system. In other words, the rotational state of motion of the meter stick would changedue to the added weight .
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