Is writing P.E. = mgh and using g=+9.8 cheating?

Unless you say the positive direction is down, the positive direction is up and g = -9.8.

A negative sign has a meaning. I'm concerned by any statement that makes it sound like you can discount it, or remove it. Careful attention to the defined coordinate system is supposed to resolve these issues (but then, why your question, which puzzles me too...)

Retraction: after agreeing that you can't add work and energy together to get zero (I was thinking you were mis-using Conservation of Energy) I found

http://en.wikipedia.org/wiki/Potential_energy

which mentioned that if work was done by a Conservative Force then work equals the negative change in potential energy.

I haven't answered your question yet but I'm working on it.

I found

http://hyperphysics.phy-astr.gsu.edu/HBASE/gpot.ht...

which starts by saying potential energy is weight x height and weight, mg, is a positive value.

We could argue that weight is not your mass multiplied by the acceleration of gravity, but rather, the force of surface that resists your "downward tendency" and this force is the negative of the true "mg".

Let me guess -- you want a reference to back this up...

Got it...

http://en.wikipedia.org/wiki/Weight

weight is the magnitude of mg.

Therefore, PE = |mg|h, not mgh.

Everything is fine as long as the direction of increasing height is opposite to the direction of acceleration by gravity.

"g" usually means a SCALAR constant, and conventionally it is positive.

On the other hand, almost ever mechanics equation that includes g involve VECTOR quantites. The numbers that measure the components of the vector depend entirely on the coordinate system you use. However the underlying physics does NOT depend on what coordiate system you use, and you get the same "real world" answer in any coordinate system. (That statement is the first step towards the idea of "relativity" of course).

The force vector (weight) when gravity acts on a mass m always has MAGNITUDE mg (positive). The three components of the force vector depend on what coordinate system you choose to work in. In my job which includes modelling the dynamics of aircraft, we mostly use a coordinate system fixed to the aircraft, so "gravity" can be acting in any direction whatever, depending on the orientation of the plane relative to the ground. The weight vector usually only (0,-mg,0) when you are still on the runway.

The real "problem" here is that to when students start mechanics at the school physics level, they don't have either a strong physical understanding of what vectors "really are", and they certainly don't have the mathematical sophistication you would get from a course on vector and tensor calculus.

So the subject tends to be taught by "rules" and "formulas" rather than a deep undestanding what is going on.

That's probably an unavoidable dilemma, because you can't do much physics at all (and you certainly can't calculate anything) without some understanding of how Newtonian mechanics works. Of course the downside is that students (and also poor teachers!) may think the simplified version is "everything there is to know" about the subject, and/or they may have to unlearn some things later on.

Your PE example is a good case in point. Once you know what an irrotational vector field and its potential function is. then there's nothing to discuss about what sign should be in the formula for PE, and "PE due to gravity" is a very simple application of the general idea compared with other uses of potential functions and vector fields in physics.

But that isn't the way you start to teach conservation of mechanical energy to the average 15-year-old!

Very interesting question, i personally never use g as a negative, whether this is a bad habit i don't know but i know the answers come to what i expect. I only use negative numbers on momentum or when acceleration is negative (deceleration).

the negative sign in most of the physics problems does not mean mathematically.it only shows that work is done in opp direction which brings in vectors 2 physics.n g=+9.8

acc 2 ur prob in P.E if u take g as -ve then even in work it is -ve cause work =P.E

work=energy

work+energy can never be zero!!!

Nope, the 'g' is included in the formula to make it universally acceptable, incase you encounter environments with different gravities, like underwater, or in space. And it's positive because you're finding speed in a direction. if you were to drop a ball and told to find it's velocity upwards, then you should use -9.8. Cheers.

-Amit

Pe Mgh