24-Feb-2015:Find a relationship between mass and period for an inertialbalance.

In this lab, my partner and I try to find a relationship between mass and period.

These were our tools which used to handle our purpose. We put different mass on the inertial balance. And tested the period about different mass.

We put 0, 100g, 200g, ...800g mass marker and the tape which is 152g, and the black staff which is 176g on the inertail balance. we get some different period.

There are two unknow things.

This is the graph of mass and periof.

We are going to guess that the period is related to mass by some power-law type of equation:

T=A(m+Mtray)^n

If we take the natural logarithm of each side, we will get the other function.

lnT=nln(m+Mtray)+lnA. This function looks like y=mx+b.

On this case, this is the graph of ln which is about the mass and period.

This picture is about that we try to find the mass of tray. we try to focus to find a line which is in the centre between each point.

In this last picture, comparing the lnT=nln(m+Mtray)+lnA and y=mx+b, we know the lnT is period, m is 0.6675 as same as n, and lnA is -5.050 as same as b. Then we get the A is 0.0064 because lnA=-5.05. Then we use this function to find the mass of tray. And we get that is 316.00g.

Finally, we find the whole equation that is lnT=0.6675(m+316.00g)-5.050 which is from T=0.0064(m+316.00g)^0.6675.

Finally, we put the periods which are unknow into the function, we get the two function:

0.38=0.0064(m+316g)^0.6675 or ln0.38=0.6675ln(m+316g)-5.05, and

0.40=0.0064(m+316g)^0.6675 or ln0.40=0.6675ln(m+316g)-5.05.

Then we get the mass of tape is 136g and the black staff is 174g. Maybe the friction, the tape's mass has a big error, but the black staff's is really closed.