Ladder Problem

1. The problem statement, all variables and given/known data
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 ?

2. Relevant 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 ?

3. The attempt at a solution


Science Advisor
Homework Helper
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 ?


Science Advisor
Homework Helper
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? :confused:
I attached the ladder illustration here, maybe you are able to make better sense of the problem.


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.


Science Advisor
Homework Helper
Hi Michael! :smile:

Yes, venkatg :smile: is right … your V = 0.

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

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

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