Finding Mass Using the Inertial Balance
Theory: Physics can be referred to as the study of various properties of matter and energy. Matter can best be described by looking at the mass of an object. Mass is the amount of material that is in an object. Mass can be found by using a spring scale, a balance scale, or an inertial balance. Inertia is the resistance by mass to any change in its state of motion. Scientific Law states that mass and inertial forces are directly proportional. The purpose of the inertial balance is to measure the different inertias between different masses therefore providing a mathematical and very accurate method of measuring mass. Experimentation showed that if a mass was put into some form of periodic motion, the mass could be measured fairly accurately by measuring the oscillation period and comparing it to a known mass period. The relationship m1=m2T12/T22 was discovered.
Objective: After completing the experiment, we will be able to find the mass of objects using an inertial balance and compare them to accepted measures.
Materials: C-clamps, inertial scale, a watch with a second hand, and a triple beam balance.
Procedure: 1) The class will measure the period of oscillation of their balance pans when they are empty. The accepted period will be the average of the class. To find the period, you will measure the amount of time it takes for your balance to complete 20 oscillations. The period (T) will be computed by taking your time and dividing it by 20. This will be recorded as T2.
2) You will then measure the mass of your empty pan (including all screws) and record this as m2.
3) You will then measure the mass of one c-clamp. Record this as m1 accepted.
4) Using the inertial balance, find the time it would take for 20 oscillations of the c-clamp (which should be attached to the empty pan). Divide your time by 20 and record this as T1.
5) Find the experimental mass of both the c-clamp and the empty pan by using the formula from page one. Record this as mtotal.
6) Find the difference between the mtotal and m2 and record this as m1experimental.
7) In a utopian world, m1 experimental should equal m1 accepted.
8) Find your percent error by using the following formula:
% Error = (accepted-experimental) / accepted
9) Repeat using varying amounts of c-clamps for up to three trials.
Data:
Trial # T2 M2 M1 accepted T1 Mtotal M1 experimental
1 .2 67.9 122.9 .3 152 84.1
2 .2 67.9 248.4 .35 207.9 140
3 .2 67.9 382 .45 393.74 275.84
M1 accepted M1 experimental % Error
122.9 84.1 31.6%
248.4 140 43.6%
382 275.48 27.88%
Calculations: See last page.
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