# Math Help - variable in the numerator and denominator

1. ## variable in the numerator and denominator

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?

2. Originally Posted by strangiatotheme
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

3. Originally Posted by topsquark
Ummm...looking at your units, they don't make any sense. Supposedly S is a mass, since each term in the numerator has to have the same unit (though its being negative I have a hard time explaining). Given that unit for S the units in your denominator seem to claim that the 0.92 has some units tacked onto it but you didn't write them. I'm very confused by what the units are doing. What kind of problem is this from?

-Dan
Whoops, sorry...the .92 is unitless, it's the coefficient of lift. S is surface area. So I'm still a bit confused, after you multiply 50.752*S on both sides, what happes to that S?

4. Originally Posted by strangiatotheme
Whoops, sorry...the .92 is unitless, it's the coefficient of lift. S is surface area. So I'm still a bit confused, after you multiply 50.752*S on both sides, what happes to that S?
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

5. Looking over the assignment sheet again, it looks like I messed up typing the first equation. It should be 1.6*52m/s^2. Also, the 15 should be kg/m^2. It looks like I end up with just m...?

6. Originally Posted by strangiatotheme
Looking over the assignment sheet again, it looks like I messed up typing the first equation. It should be 1.6*52m/s^2. Also, the 15 should be kg/m^2. It looks like I end up with just m...?
Now I'm getting:
(kg/m^2)*m^2*m/s^2
(kg/m^3)*(m/s^2)

which is the same as m^3, a volume.

What specifically is the equation you are using? Maybe that will help.

-Dan

7. 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

8. Originally Posted by strangiatotheme
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

9. Originally Posted by topsquark
(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
Oh man do I feel stupid. All I had to do was subtract! Thanks Dan, I'm working out the other 4 problems right now...