Purpose:
The purpose of this lab was to find the mass of the inertial balance by using the relationship between the period and mass. The relationship is determined by the equation: T=A(m+Mtray)n, where T is the period, A and n is the coefficient, and the m and Mtray is the mass.
The purpose of this lab was to find the mass of the inertial balance by using the relationship between the period and mass. The relationship is determined by the equation: T=A(m+Mtray)n, where T is the period, A and n is the coefficient, and the m and Mtray is the mass.
Apparatus:
This is the apparatus set up, where the balance was attached to the table using a c-clamp and weight was added to the other end. The balance was then pushed to the side and released, which caused the balance to swing side to side with a measurable period. To measure the period we used a photo gate which counted every time the piece of tape, attached to the end of the balance, made one whole oscillation.
This is the apparatus set up, where the balance was attached to the table using a c-clamp and weight was added to the other end. The balance was then pushed to the side and released, which caused the balance to swing side to side with a measurable period. To measure the period we used a photo gate which counted every time the piece of tape, attached to the end of the balance, made one whole oscillation.
This was one
of the objects used to make sure the period and mass of this object fits the
equation.
This was the
other object used to make sure the period and mass of this object fits the
equation.
Explanation:
With the apparatus set up, we measured and recorded the period of the balance without any weights on. Then we placed a 100g mass on the edge of the balance as shown in the pictures above, and recorded the period of the balance with the weights. We repeated this step but adding an extra 100g mass with every step until we got to 800g of mass. After gathering all the data required, we measured the period two random objects with different masses. With the equation T=A(m+Mtray)n, we take the natural log of the equation which gives us
With the apparatus set up, we measured and recorded the period of the balance without any weights on. Then we placed a 100g mass on the edge of the balance as shown in the pictures above, and recorded the period of the balance with the weights. We repeated this step but adding an extra 100g mass with every step until we got to 800g of mass. After gathering all the data required, we measured the period two random objects with different masses. With the equation T=A(m+Mtray)n, we take the natural log of the equation which gives us
lnT = n ln (m+Mtray) + ln A, which looks like y=mx+b, where the m is the n and x is m+Mtray.
With this equation, we can graph a curve with ln T vs. ln (m+Mtray). With the Mtray being an
unknown, we tried different values to get an almost perfect correlation, close
to a value of 1. After finding the mass of the tray, we plugged in the values
of the two random periods to see if the mass comes out close to the true
values, and if the values are close then the mass of the tray is acceptable.
Data Table:
Data Table:
Graphs:
The picture shown above
shows the correlation of 0.999 with the mass of the tray to be 0.277kg of mass.
Also, the 4th value set was strike out because with the value set
being read, we were getting a correlation value close to 0.995 and couldn't get
0.999. Only without that value set were we able to get a correlation value
close to 1.
We noticed that the value
of the mass of the tray had a range which the highest value of the mass was
0.346kg of mass, while still giving us a correlation of 0.999.
Conclusion:
To find the mass of the
inertial balance, we had to measure the period of different masses. The period oscillates
according to the mass of the object, so the larger the mass, the slower the
period. We applied different mass ranging from no weights to 800kg of mass on
the edge of the balance, and measured reach period. With the graph of ln T vs.
ln (m+Mtray), we can find the mass of the tray with trial and error,
guessing what the closest value to the mass of the balance, which we found the
range to be between .277kg to .346kg. The range of the mass gives us an almost
perfect correlation, a value of 0.999. With two random objects to check if the
mass was correct, we plugged in the period and calculated the mass. The percent
error was a little above 2.0% and is considered acceptable.
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