# MERM Equations - Gravity or Gravity Constant



## kkelley

So - I am taking the Mechanical PE in April and started studying using the MERM. One thing that keeps coming up (and totally confusing me) is that the equations appear to be different (than from what my college textbooks have) regarding the gravity constant. This comes up in many equations (force eqn's, kinetic energy, potential energy, etc...). For example, the work done by gravity would typically be m*g*z (where z is the change in elevation) but in the MERM equation 23.9, it is m*z and the g drops out of the equation. One other example: F=ma...but the MERM has F=m*a/g (Eq. 56.12).

I am sure there is a very good explanation why these equations are seemingly all different than my college texts...could someone please explain?


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## gaidox

kkelley said:


> So - I am taking the Mechanical PE in April and started studying using the MERM. One thing that keeps coming up (and totally confusing me) is that the equations appear to be different (than from what my college textbooks have) regarding the gravity constant. This comes up in many equations (force eqn's, kinetic energy, potential energy, etc...). For example, the work done by gravity would typically be m*g*z (where z is the change in elevation) but in the MERM equation 23.9, it is m*z and the g drops out of the equation. One other example: F=ma...but the MERM has F=m*a/g (Eq. 56.12).
> I am sure there is a very good explanation why these equations are seemingly all different than my college texts...could someone please explain?


It seems your confused with US unit with the used of "g" and "g/gc".

like in F=ma/gc (for US unit); a=g= acc. due to gravity and gc= conversion from lbm to lbf.

You can understand it more if you read MERM chapter 1 explaining the use of g in SI and US unit.

Your college textbook maybe in SI unit where you dont need the "gc".


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## MechGuy

I don't have my MERM in front of me, but I am assuming that what you are describing is the gravity term "g" and the proportionality constant "g sub c" cancelling each other out. The proportionality constant gc allows you to change from lbm to lbf in english units. That's why you see it in the F=m*a/gc equation.

In English units, g = 32.2 ft/s^2 , and gc = 32.2 ft/s^2 (lbm/lbf). So numerically, g and gc cancel each other out (giving you MERM Eq 23.9 as you describe) but changes the units to lbf from lbm to allow the units to make sense.

Your college texts are probably in SI units, and the proportionality constant is not needed in SI units because you're not dealing with the lbm or lbf terms for mass, its in kg.

Does that make sense?


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## buick455

I agree with the above posts on the US customary vs SI units. The MERM does a good job in showing you both methods depending on what they are asking for on the exam and the exam is in both SI and US customary units. Also, it is important to follow units through on the exam as it can mess you up if you do not.


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## kkelley

Yes, thank you all, Chapter 1 definitely helped to explain the g/g constant. I had skipped Chapter 1 in efforts to get to the "meat" of the material and I guess I should have read it thoroughly. It still is difficult for me to modify many of the equations that seem so fundamental to me (from college). At least now it makes a bit more sense. Thanks!


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## Kephart P.E.

Don't feel like you need to solve things just the way the MERM shows them.

I didn't use the equations that MERM had listed, for some subjects I like the way Crane or my college text showed them so that is what I used for reference.


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