Flatbed truck going round a circular road on an incline

[whdahl]

Homework Statement

The problem statement is in the attachments.

Homework Equations

F=ma

The Attempt at a Solution

I uploaded the solution to the problem. I have had no trouble deriving the first two equations for the summation of forces in the x, n and t directions, however I am having trouble understanding the algebra involved in the solution, specifically where it says, "Solve the first two equations for N and Fn to obtain:", then it lists the equations for N and Fn. I can't figure out how they derived those two equations for N and Fn from the first two equations.

 

[Simon Bridge]

Solve the first two equations for N and Fn to obtain:", then it lists the equations for N and Fn. I can't figure out how they derived those two equations for N

... they did exactly what was described - they too the first two equations... these were:
$$N\cos(10^\circ)-F_{n'}\sin(10^\circ) - mg = 0\\
F_{n'}\cos(10^\circ) + N\sin(10^\circ) = m\frac{2t^2}{30}$$ ... do you not know how to solve simultaneous equations?

 

[whdahl]

I know how to solve simultaneous equations, but I am not getting the solution they show in this case. Solving one of the equations for Fn or N and substituting that in the second equation will allow you to eliminate one of the variables. However I am not getting the solutions they provide, I am getting jumbles of sin squared's over cosines and tangents...

 

[Simon Bridge]

Please show your working.

 

[whdahl]

I don't see where my mistake is, but I've ended up with an extra $$cos(10)$$ in the final answer.

 

[whdahl]

Literally the moment I sent that, I found my mistake. I did not carry the $$\frac{mgsin10}{cos10}$$ over correctly.

 

[Simon Bridge]

Well done.
Note: if you put a backslash before the name of the trig function in LaTeX, it will typeset properly.
$$\frac{mg\sin\theta}{\cos\theta}=mg\tan\theta$$