Purpose: Find out the theoretical maximum high and the experimental high, and compare them.
Model: I=Icm+md^2, Isω1=(Is+Ic)ω2, and ΔKE=ΔGPE
Process: We use an apparatus which can rotate with a small friction as a pivot. We place the pivot at the vary end of the meter stick. We use a support to locate a clay on the flood which can be hit be the meter stick. We wrap some tape around the other end of meter stick and the clay.
We release the meter stick from horizontal. We take a video by phone and use LoggerPro to analyse it. Then, we get:
We can get the experimental high H=0.3541m
Now, we are going to find out the theoretical high. We measure the meter stick and the clay:
Ms=161.2g=0.1612kg, Mc=38.7g=0.0387kg
Then, we calculate the moment of the stick and the clay.
Is=1/12(MsL^2+Msd1^2=0.0513516 kg.m^2
Ic=Mcd2^2=0.0375477 kg.m^2
Isys=Is+Ic=0.0888993 kg.m^2
Then, we use the energy equation:
d1=Δh
MsgΔh=1/2Isω1^2
ω1=5.462663 rad/s
Then, we use the moment equation:
Isω1=(Is+Ic)ω2
ω2=Is/(Is+Ic)ω1=3.155441 rad/s
Then, the energy again:
Hmeterstick=(48.5/98.5)*Hclay
MsgHmeterstick+McgHclay=1/2Isysω2^2
Hclay=H=0.3825 m
Now, we get:
Theoretical H=0.3825 m and Experimental H=0.3541 m
Htheoretical≈Hexperimental
There are 7% off in the experiment. It may cause by the friction on the pivot and by the clay sliding on the flood when it be hit.
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