Combining two equations - HOOOOW?

[ks23]

combining two equations - HOOOOW?

Homework Statement

Ok i have to equations:
1: S-f-m*g*sinΘ=0
2: S*r - f*R = 0

Those 2 equations i need to solve to get an expression for S and f, and i am supposed to get this:

S =( m*g*sinΘ ) / (1-r/R)

f = (m*g*sinΘ ) / (R/r -1)

I really need something to explain this to me, i don't get it at all, and i need to be able to do this myself.. please someone explain..

 

[ssulun]

Choose an equation and determine a parameter (S or f) that you want to leave alone (which equation or parameter you choose doesn't matter). Say, you have chosen S in the first equation.

Then, leave that parameter on the left side of that equation alone.(Manipulate equation 1 so that only S will remain on the left side)

Now you can plug in that parameter in the other equation (I mean you have found the definition of the parameter when you have left it alone on the left side, and now in the other equation, you can write its definition instead of that variable.) (Instead of S in the second equation, write the right side of the equation you have obtained before)

Now, manipulate the resulting equation so that only f will remain on the left side. And there you have f.

Do the same for S or, just plug the f you have found in any of the equations and leave S alone on the left side.

 

[ks23]

ive tried all that, I've been working with this for like an hour, and its SO frustrating because it should be so simple to do. I don't know if its just because I am tired and my brain is burning up or something, but could you please write out every step for me, maybe i can see it then..

 

[ssulun]

Sorry, but it would be a violation of forum's rules.

If you write your steps, then I can point out what went wrong.

Don't let the letters confuse you, it's a basic equation system with two unknowns (S and f).

If you have time, try to rest a little and then try again.

 

[RTW69]

Solve equation 2 for f. Substitute into the f in equation 1. Factor out S. Divide through solving for S and you are there.

Next solve equation 2 for S. Substitute into the S in equation 1. Factor out f. Divide through solving for f and you are done.

 

[danbernoulli]

I wonder if perhaps you are interpreting the solutions properly. I get something that looks like

S =( m*g*sinΘ ) / ((1-r)/R)

f = (m*g*sinΘ ) / (R/(r -1))

which is quite different from
S =( m*g*sinΘ ) / (1-(r/R))

f = (m*g*sinΘ ) / ((R/r) -1)

 

[azizlwl]

Maybe just do a simple algebra as a guide

a+b=6 (1)
b=3 (2)
find a.

Get the value of b and substitute b in equation (1)

 

[vela]

I wonder if perhaps you are interpreting the solutions properly. I get something that looks like

S =( m*g*sinΘ ) / ((1-r)/R)

f = (m*g*sinΘ ) / (R/(r -1))

You made a mistake somewhere. Your solution doesn't work out unit-wise. You can't subtract r, a length, from the unit-less constant 1.

 

[vela]

I've tried all that, I've been working with this for like an hour, and it's SO frustrating because it should be so simple to do. I don't know if it's just because I'm tired and my brain is burning up or something, but could you please write out every step for me, maybe i can see it then..

That's what you should be doing here so we can see where you are going wrong.

 

[space_buster]

Just solve for S in equation 2 and then simply replace value of S in equation 1 . You'll get f , then replace the value of f in the equation you solved for S in terms of f .

 

[ks23]

sorry, i slept on it now, and solved in 2 secs. Guess i was just too tired yesterday, but thank you all for trying to help :)