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| http://iwant2study.org/ospsg/index.php/interactive-resources/physics/01-measurements/7-shmmassscale |
EJSS Mass Scale Model an orginal model by lookang
updated 08 july 2015
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| 1.00 kg scale photo by rachelle lee |
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1.00 kg scale showing reading of 0.80 kg
image scale taken from http://www.abcteach.com/free/k/kilogramblankscalergb.jpg
author: lookang
author of EJS 5: Paco.
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| 4.00 kg scale photo by rachelle lee |
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4.00 kg scale showing reading of 0.40 kg
image scale taken from http://www.abcteach.com/free/k/kilogramblankscalergb.jpg
author: lookang
author of EJS 5: Paco.
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| 5.0 kg scale photo by rachelle lee |
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5.0 kg scale showing reading of 4.0 kg
image scale taken from http://www.abcteach.com/free/k/kilogramblankscalergb.jpg
author: lookang
author of EJS 5: Paco.
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1.00 kg, 4.00 kg and 5.0 kg scale as requested by rachelle lee
image scale taken from http://www.abcteach.com/free/k/kilogramblankscalergb.jpg
author: lookang
author of EJS 5: Paco.
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| http://weelookang.blogspot.sg/2014/11/ejss-mass-scale-model.html image scale taken from http://www.abcteach.com/free/k/kilogramblankscalergb.jpg PLAY: Link1 , Link2 Download: Link1 , Link2 source: Link1 , Link2 author: lookang author of EJS 5: Paco. |
Model:
The equations that model the motion of the mass scale system are:
Mathematically, the restoring force $ F $ is given by
$ F = - k (\theta - \theta_{0}) $
where $ F $ is the restoring elastic force exerted by the spring (in SI units: N), k is the spring constant (N·m−1), and $ \theta $ is the displacement from the equilibrium position $ \theta_{0} $ (in radians).
Thus, this model assumes the following ordinary differential equations:
$ \frac{\delta \theta }{\delta t} = \omega $
$ \frac{\delta \omega }{\delta t} = -\frac{k}{m} (\theta - \theta_{0}) - b\frac{\omega}{m} $
where the terms
$ -\frac{k}{m} (\theta - \theta_{0}) $ represents the restoring force component as a result of the coil spring extending and compressing.
$ - b\frac{\omega}{m}$ represents the damping force component as a result of dampers retarding the mass's motion.
Rotation:
in order of the rotation to be sync with the typically mass scaletransformation of $ \frac{\pi}{2} $ is made for the arrows so that it starts at the top
initial angular displacement of $ 2 \pi $ so that the pointer moves towards final angle of random value say $ \pi $ which is 2.50 kg.
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