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Author Topic: Determining accleration due to gravity  (Read 11486 times)
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They are the same unit if you break N down and look at it. N/kg is considered gravitational force while m/s2 is an acceleration, but in reality they are the same thing and both work in any formula.
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Yes, I understand the maths.... just saying I'd never seen acceleration expressed in those units before.
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just saying I'd never seen acceleration expressed in those units before.
You have, you just haven't done the algebra before

N/kg = (kg m s-2) / kg = (kg m s-2) / kg = m s-2
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You have, you just haven't done the algebra before

No, I haven't seen acceleration expressed in those units before. By that I mean, nobody has ever said to me, nor have I ever read, that acceleration comes in N/kg....

I do understand the units' equivalency, and indeed have understood this stuff since  about 1971.... I doubt if I'd have graduated as a civil engineer without having understood the relationship between force, mass and acceleration...  smiley-cool
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They are the same unit if you break N down and look at it. N/kg is considered gravitational force while m/s2 is an acceleration, but in reality they are the same thing and both work in any formula.

A kilo of mass experiences 9.8 Newton of weight. That was part of my middle school physics class. In high school when I learned F=ma, then a was given in m/s/s.

To correct age-old problem of engineers don't know physics, I have to clarify that accelerometer is a wrong term. The measured quantity is actually force. Imagine Spring scale and weight on scale. You will read force when the scale is at rest. You will NOT read force when you drop the scale and weight together. The real term should be something like a micromachined capacitive force sensor that outputs acceleration units.
 
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There are far easier ways to measure the acceleration due to gravity using Arduino.  You can buy a photointerrupter like http://www.digikey.com/scripts/DkSearch/dksus.dll?WT.z_header=search_go&lang=en&keywords=425-1935-5-ND&x=0&y=0&cur=USD, build the simple circuit shown in the data sheet.  Then get a piece of plexiglas maybe 2" x 10" and use electrical tape to make uniformly spaced opaque strips that are perpendicular to the long axis.  Take the signal from the photointerrupter and input that into one of the interrupt pins for timing purposes.

Dropping the plexiglass strip through photointerrupter, lets call it a photogate, from the times displayed by the Arduino on the computer screen or LCD you can determine the acceleration due to gravity.

You may find that the plexiglass hits the photogate and this will increase the uncertainty of the measurement and you can either accept that or break the photogate and mount the two pieces on another frame to make a larger fixture so the plexiglass will hit it less often.

I have left out some steps as there is a derivation needed utilizing some kinematics to be worked out but it is not too bad. 
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There are far easier ways to measure the acceleration due to gravity using Arduino
How is that "far easier" than using an accelerometer?
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There are far easier ways to measure the acceleration due to gravity using Arduino
How is that "far easier" than using an accelerometer?
I share the same doubt with AWOL. If you really want an easy method, define what equipment you have first. The easiest one that requires no electronics would be using your own pulse as a time reference as Galileo probably did in his time, or use your watch/clock. Then hang a pendulum (any heavy and compact object will do, such as a key or a stack of coins taped together) with a known string length L. Watch it oscillate say 100 periods and solve the simple T=2*PI*sqrt(L/g) equation to get g. The period should be fairly close to 2 seconds for 1m string. For those in the US, I know for sure you will have 5,6,7 foot references (relatively accurate) right outside most bank branches. You don't even have to own a tape measure.
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with a known string length L
A pendulum should be rigid.
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with a known string length L
A pendulum should be rigid.
a) Why?  A swinging chain keeps time.
b) A string under tension _is_ rigid.
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a) Why?  A swinging chain keeps time.
That would be a compound pendulum.
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with a known string length L
A pendulum should be rigid.

It just needs to be light compared with the bob and not springy. And the angle of oscillation be quite a bit less than 50 degrees with vertical.
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Why is the photogate method I described a far easier method of measuring gravity than an accelerometer?

Well there was quite a bit of discussion about using cheap off the shelf accelerometers and I never did see anyone having a solution that actually did measure the acceleration due to gravity, without first assuming what it was to begin with.  By using the photogates you can easily derive the solution for the acceleration due to gravity based on first principles, and not by assuming what the result is you are looking for.  The photogate method is used in first-year physics labs everyday, I used to have my first year students derive the solution for homework, tests, or labs.
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Why is the photogate method I described a far easier method of measuring gravity than an accelerometer?

Well there was quite a bit of discussion about using cheap off the shelf accelerometers and I never did see anyone having a solution that actually did measure the acceleration due to gravity, without first assuming what it was to begin with.  By using the photogates you can easily derive the solution for the acceleration due to gravity based on first principles, and not by assuming what the result is you are looking for.  The photogate method is used in first-year physics labs everyday, I used to have my first year students derive the solution for homework, tests, or labs.

First principle is not always easy. I consider pendulum easy. You need a cheap string, some weight and a cheap watch. There is no need to set things up and there is no concern for electronics not working. photogates are fine but not cheap or easy if you compare with yarn and some deadweight.
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This reminds me of how we measured it back in high school...

It involved a battery operated bell and a huge long strip (as long as the drop from the window to the ground) of carbon paper with a weight on the end. Then dropped the weight while the bell was ringing, with the strip between the bell and the ringer lever thingy. The impact of the ringer made marks on the carbon paper, and of course the marks got further apart as the weight accelerated.

Measured the time it took to drop from the science lab window to the ground. Counted the total number of marks. That gave the number of marks per second or seconds per mark.

Measured the (varying) distance between marks. That, with the now known time between marks, gave the (varying) velocity at any instant.

And hence the acceleration....

But using a pendulum is by far the easiest way to do it... (As long as the bob is very heavy compared to the string, the whole mass may be deemed to be at the bob's CoG.) Beauty of the pendulum method is that since the period T is constant regardless of how wide the swing is, it can as suggested above be measured over 100s of swings and that reduces the impact of the reaction time when the stop watch is started and stopped.

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