For our first lab we were given the task to understand the relationship between mass and period for an inertia balance. This procedure required us to use an Inertia Balance, which measures inertia mass by an object's resistance to change in its motion. The objective was to pull and release the inertia balance so the computer could record a reasonable period for the oscillation of the device. Data was recorded with no mass on the tray and then repeated 8 more times, adding 100 grams to the tray each time.
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| image of inertia balance with added mass on tray |
The image above shows the set up of the apparatus clamped to the table and a photogate clamped on the opposite side that recorded the oscillation of the device as it passed through a laser sensor.
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| period of oscillation being recorded into logger pro |
The data was compiled into a data chart where we could see the relationship between the addition of mass and the length of the period for the oscillation. The data was then graphed. We were also given the task to measure the period of two unknown masses in order to see how precise our data was.
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| graph of mass and period |
Given the equation T = A(m+Mtray)^n, we took the natural logarithm of both sides in order to get an equation that looks similar to y=mx+b. we then plotted the ln T and ln of (m +Mtray) in order to determine the values of the slopes and y-intercepts.
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| data chart of mass, period, and total mass. also graph of ln of period and ln of total mass |
Finding the values of the unknowns in the equation gives us the mathematical model for the behavior of our inertia pendulum. Using this equation, we were able to estimate and verify the masses of the two unknown objects by plugging in their respective periods of oscillation.
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| high and low calculations of light unknown object and actual mass |
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| high low calculations of heavy unknown and actual mass |
The results showed that the estimated range of masses of the unknown objects were nearly consistent with the actual masses of the objects. The lab procedure proved that an increase in mass on the inertia balance equaled greater periods of oscillations.
As a side note, there were certain uncertainties that came along with the lab procedure. For one it was difficult to get consistent pull and releases on the inertia balance due to slight human errors. Even distribution of the mass and consistency of stability of the mass were also slight issues. Also, we had to find a range of masses for the unknown objects due to uncertainty in the equations we came up with for the relationship between mass and period.
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