28-Feb-2015: Find a relationship between mass and period for an inertial balance.

For this lab, we are going to find a relationship between mass and period for an inertial balance. the inertial balance is a device that is used to measure inertial mass by comparing objects's resistances to changes in their motion. 

First of all,  we need to set up the equipment like the picture1, 2, and 3.  

Use a C-clamp to secure the inertial balance to the table top. Put a thin piece of masking tape on the end of the inertial balance. Set up a photogate, and make sure the tape completely passes through the beam of the photogate when the balance is oscillating. Then set up the Labpro with a power adapter, USB cable, and plug adapter plugged into the DIG/SONIC input. 

(picture 1)

(picture 2)

(picture 3)

Next, Open the computer to choose Pendulum Timer.cmbl which is under Photogates Folder. Using the software to start data collection. Right now we can collect the data when you hit the collect button and pull back and release the inertial balance.

Record the period with no mass in the tray, then repeat the record, adding 100 grams each time until you have reached 800 grams in the tray. collecting two more data when we put calculator and phone in the tray. 

There is a Data Table(picture 4).

(picture 4)

we already know that the period is related to mass by some power-law type of equation:  

T = A(m + M)^n

After we take the natural logarithm of each side we get:

ln T = n ln(m + M) + ln A, which looks like y = mx + b.

That means that there is a beautiful straight-line if we have right data.

(picture 5)

Fortunately, we almost get a straight-line like picture 5 and 6, and we also get a straight-line equation. From this equation, we know A, M, and n. 

(picture 6)

Then, Using the different M to test the minimum of lnA and lnT and maximum of lnA and lnT. Now we have min-equation and max-equation.

plug in the data of calculator to each of equations like picture 7.

(picture 7)

plug in the data of phone to each of equations like picture 8.

(picture 8)

From those two calculations, we know the first calculation is right. because the mass of calculator is between the two masses we calculated. However, there was some errors in second calculation. the mass of phone(0.130kg) is not between the two masses we calculated. We may made some mistake during the data collection.