#1 Finding a relationship between mass and period for an inertial balance

Finding a relationship between mass and period for an inertial balance

Introduction:
 We know that object mass measurement affect inertia, then object inertia might affect the period of inertial balance. By changing mass, we can find that mass influence the period of an inertial balance. In the lab, we tried to use the inertial balance and photo gate to find relationship between mass and period. 

   Setting:  

                 Put the paper in front of the inertial balance between the photo gate that the photo gate read the period easier.

Thesis: 

      We said that the relationship between mass and period would be 

                              period             mass

                                 T      = A(Mtray+ m )^n   

      

  

y=nx+ b

            lnT=lnA + n ln(Mtay + m)                                                    y=lnT=n ln(mtray+m) + lnA                     

The job is to use the different mass to find each period by using Logger Pro to calculate the slope n and lnA.

Our date; 

We used mass from 0 to 800 adding 100grams each time then find each period with photo gate

We let   lnT=n ln(mtray+m) + lnA  

become    y     =  n  *    x    +b 

which mean using those collect point to graph can find 

slope n and the b which is lnA.

  

calculation:

     Those are two graph we use Logger Pro to draw. The closest correlation we can find is 0.9998.

Mtary=0.328 ,We found that biggest slope n= 0.7133 , and b= lnA=-0.4479
which A= e^(-0.4479)=0.639

Mtary=0.315 ,We found the smallest slope n=0.6524, and b=lnA=-0.4168
which A=e^(-0.4168)=0.659

Conclusion:

      Collect the calculation date, we get the relationship between mass and period for an inertial balance.

T= (0.649±0.010) (m+Mtary)^( 0.68285±0.05015)

The equation tell us the when our total mass is larger, the period also be larger. This is the relationship between mass and period in inertial balance.