Dynamics Question - Simple but stuck

[Chantry09]

Homework Statement

http://img511.imageshack.us/img511/3732/dynamics01fm7.jpg

Homework Equations

F = M x A
F = u (coefficient of friction) x N

The Attempt at a Solution

http://img508.imageshack.us/img508/7526/dynamics02ry1.jpg

W sin 30 = 50000
W cos 30 = 86602.54

1Mg = 10,000KG

86,602.54 = N + P sin 20
50,000 + F = P cos 20

Im left with two unknowns, P and F, and i don't know what i need to do to get either one of them.

 

[Doc Al]

Looks to me like you have two equations and three unknowns. Get rid of F by using what you know about friction (one of your equations listed). Then you'd have two equations and two unknowns--which works out just right.

 

[Chantry09]

Are you saying i should combine the two equations into one? Like this?

u x N = M x A

Since its steadily moving up a = 0 so:

0.15 x N = 0

Surely that can't be right? If its any help, answer is listed as 6230 N, but i can't get it myself. It isn't accelerating, so a = 0, but when i put that into the equation it says F and therefore N = 0 which i know can't be right.

 

[Doc Al]

You lost me on that last post! All I'm saying is to use F = \mu N to eliminate F from your two equations. Then you can solve them together.

Also: Shouldn't 1Mg = 1,000KG (not 10,000)? (Mg is a rather odd unit!)

 

[Chantry09]

Yeah your right, I am sorry, its 1000KG. I am not quite sure how to use F = \mu N

I don't know F, and i don't know N, I only know that \mu is 0.15, and i don't know how i can work out F or N.

 

[Doc Al]

Once you eliminate F from your equations (from post #1, after you correct them) by replacing it with \mu N, you will have two equations and two unknowns (N and P). Solve those two simultaneous equations and you'll find P.

(To solve them, if that's the problem, take one of them and rewrite it to solve for N in terms of P. Then use it to replace N in the other equation. Then you'll have one equation with only P as your unknown.)