Belarusian team SPECTRUM Task №1 “Foxy Jeweler” Belarusian team SPECTRUM

Task Investigate the parameters affecting the precise weighting of solid objects with the mass of 10-100g, and find what maximal gain can be attained by unfair jeweler who sells gold or diamonds. It is assumed that the jeweler makes weighting with certified electronic scales and cannot make any change in the mechanism of the scale itself and add extra weight.

certified electronic scales Electronic scales Ohaus Explorer Pro (EP) model EP 214C with draft shield and automatic temperature calibration. To determine different errors, we used a weight m = 49.9790±0.001 We used electronic scales Ohaus Explorer Pro model EP 214C with draft shield and automatic temperature calibration. Weight of load in the experiments is 49.9790 gram. The load cell (also called a load sensoror transducer) is a piece of machined metal that bends with the load's mechanical force and converts the mechanical force into an electrical signal. The bend doesn't exceed the metal's elasticity and is measured by strain gauges bonded at points on the cell. As long as the load is applied to the proper spot on the load cell, the strain gauges provide a proportional electrical signal. Converts the mechanical force into an electrical signal

Factors affecting the accurate weighing Vibration Latitude and altitude above sea level Electromagnetic interference Weighing magnetized goods Temperature Archimedes force Changing the position of load Condensation on the load Horizontal installation of scales Wind loading Temperatur A change of temperature influences the sensitivity of weights, and thus influences factual data. A significant source of warmth for weights can be: a person entering a room, a computer switched on, air-conditioning, the influence of direct sun rays. повышении температуры завышенниыф результат температура

Archimedes force 𝐹= 𝑚∗ 𝑄 𝐴 ∗𝑔 𝑄 𝐺 = 0,000031N 𝑚 – mass of load 𝑄 𝐴 −density of air 𝑄 𝐺 – density of gold 𝑔=9.8 N/kilo Archimedes force An object in the air is affected by a buoyancy force. For example 100 grams of gold has been put on the weights. Then Archimedes force if equal to 0,000031H. As the force is insignificant it practically won’t influence the result. The density of air depends on relative humidity, temperature, and atmosphere pressure. At a change in air density of 10% indications don’t changе, but the error increases by 0.25 e Рассчитать для ста

Changing the position If we put our load on the centre of a pan and on the edge of the pan and compare results, they will be difference in 0.0042±0.0001 gram.

Condensation on the load Temperature of load: -4°C Temperature of environment: 24°C so the mass became 0.015 grams larger due to the drops of water. When condensation appears on the load, mass changes on 0.015 gram.

High humidity investigations Error:0.0185±0.005

Horizontal installation of weights If you change the slope scales readings change. This is determined by absence of alignment forces: the force exerted to the load plate and the balancing force of the platform, being read by the weights. 9 α mg Mgcosα mg

Angles

Air flow Air conditioning, fens, radiators, swing doors and employees create air flow in the room which can influence the indications of weights. But we took off draft shield and the average extra weight was 0.564±0.110 g. Air flow Air conditioning, fens, radiators, swing doors and employees create air flow in the room which can influence the indications of weights. As a rule the influence of this factor is leveled by a draft shield. But we took off draft shield and the average error was 0.564 g.

Vibration Vibration from process equipment and other sources near the weighing system can cause the load cells to measure the weight of material as well as vibration that's transmitted to them, which the cells sense as mechanical noise. We couldn’t determine the value of this parameter. Vibration. Vibration from process equipment and other sources near the weighing system can cause the load cells to measure the weight of material as well as vibration that's transmitted to them, which the cells sense as mechanical noise. You can reduce or prevent vibration effects by isolating the weighing system from vibration sources when possible or using weighing system instrumentation with algorithms that remove vibration effects. НЕ удалось оценить вклад эффекта

CONCLUSIONS Jeweler scammer can cheat the buyer using the following factors: Horizontal installation of scales Wind flow Totally an unfair jeweler can steal up to 1.6g with the weight 50g. The price of this weight, for example gold, is about 60.8$ Если мы положи м в центр тили на край, то вес не изменится

Thanks for attention

Расчеты погрешностей m=100г g=9.8Н на кг q воздуха=1,2 кг на м кубический q золота=13,6 кг на м кубический Fa=qв m qзолота g=1,2 *0.1:19300 *10=0,000062 Н S= 24цента

Latitude and altitude above sea level  При перемещении весов из Санкт-Петербурга в Москву с 59°57’ до 55°45’северной широты изменение ускорения свободного падения влечет за собой уменьшение показаний весов на 0,6 г (6,2е): за счет изменения широты на 4° -0,7 г (-7,2е) и за счет изменения высоты над уровнем моря на 150 м +0,1 г (+1е). Даже перемещение весов с одного этажа здания на другой влияет на показания.