Solve Ladder Problem: 4 Equations, 5 Unknowns

[Michael94]

Homework Statement

Uniform ladder leaning 60 degrees from the ground against smooth wall (ladder: length 10' weight 60#). Vertical thrust by ground ? Horizontal Push by wall ? Coeff. of friction between ladder and ground ?

Homework Equations

Fx = 0 = F + H = 0
Fy = 0 = V + N - 60# = 0
L about ladder center of gravity = 0 = V*sin60*5' + H*cos60*5' - N*sin60*5 + F*cos60*5' = 0
Friction Coefficient = F/N
I have 4 equations and 5 unknowns. What am I missing in order to find the results ?

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

Hi Michael! Welcome to PF!

I have 4 equations and 5 unknowns.

ah, but your V and your N are the same

 

[Michael94]

I don't understand why V = N. Sum of the forces in the vertical direction w/ origin @ ladder center of gravity V + N = 60#, right ?

 

[tiny-tim]

I don't understand why V = N.

V and N are your names …

what are they supposed to be?

If V is the vertical force on the ladder from the ground, and if N is the normal force, they're just different names for the same thing, aren't they?

 

[Michael94]

I attached the ladder illustration here, maybe you are able to make better sense of the problem.

 

[venkatg]

It is a smooth wall, so V = 0. So you only have 3 unknowns (F, N, H) and 3 equations

If wall is not smooth then you need another equation that involves the elastical behavior of the ladder.

 

[tiny-tim]

Hi Michael!

Yes, venkatg is right … your V = 0.

(which is why it never occurred to me that your V was at the top of the ladder )

Moral: read every word of the given question carefully (and write your own question carefully!)