I'm currently studying Physics - Principles with applications by Douglas C. Giancoli. I'm not sure about this problem (statics) so I need some help here...

A 7.5 m long ladder of mass 15.0 kg leans steeply (60 deg) againts a smooth wall (so the force exerted by the wall, Fwall, is perpendicular to the wall). The ground is rough. Calculate the components of force excerted by the ground on the ladder at its base, and determine what the coefficient of friction at the base of the ladder must be if the ladder is not to slip when a 70 kg person is 3/4 of the way up the ladder.

Here's my analysis:

Now take an easier case where there is no wall. The the ladder will undergo rotational motion because of gravity force. I assume that the cg is in the middle of the ladder (3.75 m from each of the ends). The normal force (excerted by the ground) will balance the downward gravity force so the object won't go down the earth. Look at the figure below.

(fig 1) http://gamemania1986.netfirms.com/images/physics01.gif

http://gamemania1986.netfirms.com/images/physics01.gif

Is my analysis correct? Anything missing?

Now let's go back to the problem. It states that Fwall is perpendicular to the wall. Why is this so? Why not in other direction? Here's my analysis (without the 70 kg guy):

(fig 2) http://gamemania1986.netfirms.com/images/physics02.gif

http://gamemania1986.netfirms.com/images/physics02.gif

Am I correct?

Now there's this guy.... I'm not really sure about this one... Here's my analysis:

(fig 3) http://gamemania1986.netfirms.com/images/physics03.gif

http://gamemania1986.netfirms.com/images/physics03.gif

Is Fground-x (in the 2 last figures) the friction force needed? If so, is the miu required 339.5 N/833 N = 0.4?

Thanks a lot!!!

aaargh... I hate this kind of physics. statics/mechanics. Not my cup of tea.
I leave it to others. :D
sorry. Just wanted to express that.

Originally posted by gamemania1986
Is my analysis correct? Anything missing?


Your analysis is correct--I got the same thing you got.


Now let's go back to the problem. It states that Fwall is perpendicular to the wall. Why is this so? Why not in other direction?


In the absence of friction (which is what you have here), the wall is not capable of exerting any component of force on the rod that is parallel to the wall. Thus, the force of contact is perpendicular to the wall.

Looks good to me.