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Old Aug 16th 2016, 02:25 PM   #1
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Acceleration of elevator upwards and downwards

Having a little trouble understanding how to set up the maths for this question which is as follows:

An object is hung from a spring balance attached to the ceiling of an elevator.
The balance reads 1.2 kg when the elevator is accelerating upwards with acceleration a and reads 0.8 kg when it is accelerating downward with the same acceleration value.
Determine the mass of the object and the elevator acceleration?
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Old Aug 16th 2016, 08:05 PM   #2
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F= ma. The total force on the mass, attached to the spring is the acceleration due to gravity (9.81 m/s^2 downward) plus the signed force "caused" by the acceleration.

While the elevator is accelerating upward, that force is downward so the force "caused" by the acceleration is ma downward and the force registered by the spring balance is ma+ 9.81. Set that equal to the force registered by the spring balance, 9.81(1.2) Newtons, to get one equation.s

While the elevator is accelerating downward, the force is upward so the force "caused" by the acceleration is ma upward and the force registered by the spring balance is 9.81- ma. Set that equal to the force registered by the spring balance, 9.81(0.8) Newtons, to get another equation. Solve those two equations for m and a.
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Old Aug 17th 2016, 07:55 AM   #3
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Many thanks Halls for your help.

I will attempt this now.
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Old Aug 17th 2016, 08:11 AM   #4
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When trying to solve this I got ma = 1.962 for equation 1 and ma = 1.962 for equation 2 also. Did I make a mistake somewhere? If I did I'm not spotting it.
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Old Aug 17th 2016, 08:42 AM   #5
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I'm afraid that HallsoOfIvy's post has two fundamental errors: the force when the elevator is rising is m(g+a), and when descending is m(g-a). He wrote ma + g and ma-g, but you can tell that's not correct because the units don't work out: ma is units of force (i.e. Kg-m/s^2), and g is acceleration (m/s^2). The two equations you should be starting with are:

m(g+a) = 1.2g
m(g-a) = 0.8g

Regarding the right hand side of these equation, note that the spring balance gives readings in Kg, which strictly speaking is incorrect - a scale or balance measures force, not mass. When it gives a reading of 1.2 Kg what that really means is the spring balance is experiencing a force equivalent to 1.2 Kg under normal Earth gravity; hence the magnitude of that force is 1.2g.

Last edited by ChipB; Aug 17th 2016 at 09:08 AM.
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Old Aug 17th 2016, 08:50 AM   #6
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Thanks so much for pointing that one out Chip. It had my head rolling a bit for a while but hopefully now I can get the understanding of it.
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Old Aug 17th 2016, 11:16 AM   #7
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Oops! Thanks for pointing that out. As for "the units don't work out", I did point out that a spring balance reading of "1.2 kg" actually means that the force is "1.2g" Newtons.
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Old Aug 17th 2016, 11:56 AM   #8
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Originally Posted by HallsofIvy View Post
I did point out that a spring balance reading of "1.2 kg" actually means that the force is "1.2g" Newtons.
Yes, no problem with that at all. I was referring to "ma+9.81" and "9.81-ma."
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