A uniform ladder of legnth L and mass m1 rests against a frictionless wall. The

Question

A uniform ladder of legnth L and mass m1 rests against a frictionless wall.  The ladder makes an angle theta with the horizontal.  

a) find the horizontal and vertical forces the ground exerts on the base of the ladder when a firefighter of mass m2 is a distance x along the ladder from the bottom.  (use any variable or symbol stated along with g as necessary)

I cannot find the horizontal.  Please help me understand what I need to do to get this.

b)  If the ladder is just on the verge of slipping when the firefighter is a distance d along the ladder from the bottom, what is the coefficient of static friction between the ladder and ground?

Explanation / Answer

draw a picture with the angle, ?, between the bottom of the ladder and the ground.

Since there is no vertical friction force at the wall, the vertical force, Hs, does not exist. So N, the normal force exerted by the ground, is the vertical force that supports the weight of the ladder and person.

N = Wm + Ws, Wm = weight of man, Ws = weight of ladder
In your problem, Wm = m2 * g, and Ws = m1 * g.
Vertical forces the ground exerts on the base of the ladder:
N = m2 * g + M1 * g

The 2 horizontal forces = Friction force and the horizontal force that the wall exerts on the top of the ladder. In the picture, Ns, is the static friction that is caused by the Normal force that the ground exerts on the bottom of the ladder.

The wall exerts a force, on the top of the ladder, that is perpendicular to the wall, H.
H is equal in magnitude, but opposite in direction to the friction force.
H = Friction force
Friction force =

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