A uniform ladder of length L and mass m 1 rests against a frictionless wall. The

Question

A uniform ladder of length L and mass m1 rests against a frictionless wall. The ladder makes an angle 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 above along with the following as necessary: g.)

(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 ladder and ground? (Use any variable or symbol stated above along with the following as necessary: g.)
s =

Explanation / Answer

Sum moments about the floor contact to find the wall reaction horizontal force.

Rw[Lsin ] - m1g[(L/2)cos ] - m2g[xcos ] = 0

Rw = Wall reaction horizontal force

Sum horizontal forces to zero shows that the horizontal floor reaction is Rw N toward the wall

Sum vertical forces to zero to find the floor vertical force

Fv - m1g - m2g = 0

Fv = (m1+m2)g N upward

b) Using the same logic to find the horizontal reactions when the firefighter is higher

Rw[Lsin] - m1g[(L/2)cos] - m2g[dcos] = 0

Rw = Fh = (g cos (m1L +m2d))/Lsin N

The vertical reaction remains the same

Fv = (m1+m2)g N upward

coefficient of friction is the ratio of the maximum horizontal force to vertical force

= Fh / Fv

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