Two equation but one variable to solve

[lnadolny]

Hi Guys, previously you help me so I have hope that you will explain me where is problem here:

First of all I trying to find x value is in Meters. Of course i don't care about the value of mass and Na because it will reduce during the solving.

I don't know why I have x.distance as undefined? And why can't get the result that should be : 0.5 m

[AlanStevens]

You don't really need a solve block here, but if you insist, then:

I've assumed NA and mass are fixed.  If NA is an unknown variable as well then you need to solve for both NA and xdistance together even if you are ultimately interested only in xdistance.  If both NA and mass are also unknowns then not only do you need to solve for all three together you need to supply a third equation.

Alan

[lnadolny]

Thanks for your hints.

1. I don't put the variable in brackets it was, a matrix not a bracket I just learned here that matrix don't care about the units. So why it was a problem?

There is no information about NA and mass there are not fixed. And in reality you don't need the 3eq because based on those 2eq you will see that distance x don't depend on value of mass and g. So how to solved with 2 equations?

Because answer is X=0.5m

[AlanStevens]

Lukasz Nadolny wrote:

There is no information about NA and mass there are not fixed. And in reality you don't need the 3eq because based on those 2eq you will see that distance x don't depend on value of mass and g. So how to solved with 2 equations?

Because answer is X=0.5m

If NA and mass are not fixed, you will need two equations (both involving NA and mass) to find them.  Having found them you can separately find the corresponding value of xdistance using the equation that includes all of them.  However, that means you need two equations just to solve for NA and mass, and three equations to solve for NA, mass and xdistance, even if you are only interested in xdistance.

3 unknowns require three equations.

Alan

[lnadolny]

Thats how i solved by hand:

So it's easily seen that it will reduce the m and g during the calculation. How to implement those things in Mathcad?

[AlanStevens · Accepted solution]

Like so:

You are only solving for two parameters.  mass is just there to keep the units consistent; you could replace its magnitude by virtually any value.

With two unknowns you must solve for both.  You need a 2x1 vector to which to assign the results as they have different units.

Alan

[lnadolny]

Thank you but what i have wrong in my Mathcad? That I received 1N and 1m  (I correct the subsricpt a to capital letter for variable Na.)

[AlanStevens]

Firstly, you have Find(Na,...) instead of Find(NA,...).

Secondly, both equalities need to be inside the solve block (i.e. between the Given and the Find.

Thirdly, get rid of the symbolic right arrows.

Alan

[lnadolny]

Would you mind then I ask what is wrong here ?

[AlanStevens]

See below:

If you don't make Friction a function of Nforce it will simply stay at its initial value and won't change as Nforce changes through the iterations of the solver.

Alan

[lnadolny]

Thank you. You're really good . Why we actually need to wrote a function for friction depend on our one of unknowns?

[AlanStevens]

Lukasz Nadolny wrote:

Thank you. You're really good . Why we actually need to wrote a function for friction depend on our one of unknowns?

Because the friction force changes as Nforce changes.  You wouldn't have to create the function if you simply replaced Friction by Nforce*mu within the solve block.

‌

Alan