3 unknowns, 3 equations, failure on algebraic method

[togo]

Homework Statement

This example comes straight out of the book. Can someone show intermediate steps?

Fx = 0: -0.0933Tab - 0.0846Tac + P = 0
Fy = 0: +0.778Tab + 0.705Tac - 1962N = 0
Fz = 0: +0.622Tab - 0.705Tac = 0

Book solution: P = 235 N, Tab = 1401N, Tac = 1236N

Homework Equations

what method did they use

The Attempt at a Solution

determinants & algebraic methods failed.

 

[dynamicsolo]

Homework Statement

This example comes straight out of the book. Can someone show intermediate steps?

Fx = 0: -0.0933Tab - 0.0846Tac + P = 0
Fy = 0: +0.778Tab + 0.705Tac - 1962N = 0
Fz = 0: +0.622Tab - 0.705Tac = 0

Book solution: P = 235 N, Tab = 1401N, Tac = 1236N

Homework Equations

what method did they use

The Attempt at a Solution

determinants & algebraic methods failed.

I would suggest you check your hand calculation or calculator work more carefully. Those values does work in the equations.

Try adding the last two equations together: you should get 1.4 T_ab = 1962 N , which does give the book's answer. Now 0.622 T_ab = 0.705 T_ac , so T_ac = (0.622/0.705) T_ab . Putting these values into the first equation will let you find P .

It would help in troubleshooting if you showed what you'd done...

 

[Ray Vickson]

Homework Statement

This example comes straight out of the book. Can someone show intermediate steps?

Fx = 0: -0.0933Tab - 0.0846Tac + P = 0
Fy = 0: +0.778Tab + 0.705Tac - 1962N = 0
Fz = 0: +0.622Tab - 0.705Tac = 0

Book solution: P = 235 N, Tab = 1401N, Tac = 1236N

Homework Equations

what method did they use

The Attempt at a Solution

determinants & algebraic methods failed.

The problem is sensitive to roundoff errors. When I solve the system in Maple 14 I get Tab = 1401.42857142857, Tac = 1236.43768996960 and P = 235.355914285714. Putting these in a column vector X and computing A.X gives [0, 1962, .1137e-12] (taking N=1) which is close to the actual right-hand-sides [0,1962,0]. However, rounding off to Tab = 1401, Tac = 1236, P=235 in a vector X gives A.X = [-.2789, 1961.358, .0420], which is not particularly close to [0,1962,0]. I don't know if this is what you are getting, as you have not explained exactly what you mean by failure.

RGV

 

[togo]

Ok I posted the answer to these equations in my original post, but I wasn't trying to verify whether or not they work. They do work; what I posted is the last part of the example in my book. What I want to know is how they took on the 2nd last step those equations and somehow got that result?

There appears to be 3 unknowns: Tab, Tac, and P. In another thread on another question I tried using Cramers rule to solve a similar question using determinants. Next I tried the algebraic solution to try and arrive at the book's result, but with 3 unknowns I kept going in circles. I ended up with 2 unknowns no matter what I did.

The book just says ''solving these equations we obtain'' and then lists the result. Can someone please explain how to solve these equations? thanks.

 

[TheoMcCloskey]

togo - I would start with the last two equations. Note that they contain just two variables (Tab and Tac).

Use the last equation and solve for Tab in terms of Tac (or Tac in terms of Tab).


Next (I'll assume you solved for Tab in terms of Tac):

Substitute Tab expresion into the second equation so you get an equation soley in terms of Tac. Solve this equation for Tac.

Now, using the expresion you first solved for (Tab as a function of Tac), use the value of Tac and sove for the value of Tab.

Use the values for Tab and Tac in the first equation to solve for the value of P.

 

[vela]

The book just says ''solving these equations we obtain'' and then lists the result. Can someone please explain how to solve these equations? thanks.

dynamicsolo already told you how to solve the equations step by step.

If you still can't work it out on your own, you need to post details of your work, so we can see where you're going wrong.

 

[togo]

crap your right, sorry.