Say I have an equation that goes something like this:
(200.8kg*2+3333kg+15S+78kg*14+.04kg*1000kg+20kg*28)*(9.806m/s^2) / (0.5*(1.22kg/m^3)*(1.6*52m/s)*S)=0.92
How do I go about solving for S?
First, simplify where you can: (dropping the units for convenience)
(5426.6 + 15*S)*9.806/(50.752*S) = 0.92
Multiply both sides by 50.752*S/9.806:
5426.6 + 15*S = 0.92*50.752*S/9.806
5426.6 + 15*S = 4.76155823
15*S = -5421.83844177
S = -361.455896118
The unit for S is "kg" since we have to have the same unit for any two terms we add. This also checks when I put "kg" in the denominator for S. Why S is a negative number though, I can't say. Obviously a negative mass makes no sense. What kind of problem is this from?
-Dan
C***. I dropped the S on the RHS. Let me run this again:
(5426.6 + 15*S)*9.806/(50.752*S) = 0.92
5426.6 + 15*S = 0.92*50.752*S/9.806
5426.6 + 15*S = 4.76155823*S
5426.6 = (4.76155823 - 15)*S
5426.6 = -10.23844177*S
S = -530.022060183
Shoot. I was hoping that would get rid of the negative sign.
Also, the units clearly indicate that S should be a mass, unless the "15" coefficient is supposed to be in kg?
Also, assuming S is in m^2 and the summation part of the numerator is in kg*m^2, when I do the unit division I get that the LHS has units of m^3/s, not unitless. There appears to be something wrong with the units here.
-Dan
CL=Weight/Lift
where weight is defined as: ME*2+MF+15S+MC+MP+MB
There are 5 different situations. These are the values for 1 of them:
ME=200.8kg
MF=3333kg
MC=400kg
MP=1092kg
MB=560kg
S is in m^2
lift is defined as: 0.5*P*V^2*S
Again, these are the values for the same situation above:
P=1.22kg/m^3
V=1.6(52m/s)
S is in m^2
and CL is 0.92
For what you've got here I'm now getting CL in m^2. However I note that you are saying here that you have V^2, which you didn't specify in the initial problem; this will change the numbers, which I'll get to in a minute. I'm looking at your equation and you are calling the denominator the "lift," and the units are in N as they should be. Now, if your "m"s for some reason are areal mass densities (kg/m^2) I note that the numerator is now also N. Is this a possibility? This is the possibility that makes the most sense to me and would give the numerator the interpretation of being the weight that you are trying to lift. (It's the only reason I can think of that you would multiply a "mass" by a surface area.)
(200.8*2+3333+15S+78*14+.04*1000+20*28)*(9.806) / (0.5*(1.22)*[(1.6*52)]^2*S)=0.92
(5426.6 + 15*S)*9.806/(4222.5664*S) = 0.92
(5426.6 + 15*S)/(430.610483378*S) = 0.92
5426.6 + 15*S = 396.161644707*S
5426.6 = 381.161644707*S
S = 14.237004366
which (finally!) is not negative.
-Dan