A ladder with a length of 12.7m and a weight of 539.0N rests against a frictionl

Question

A ladder with a length of 12.7m and a weight of 539.0N rests against a frictionless wall, making an angle of 56 degrees with the horizontal.

1) Find the horizontal force exerted on the base ofthe ladder by earth when an 822.0N firefighter is 3.37m from the bottom of the ladder.

2) Find the vertical force exerted on the base of the ladder by earth when an 822.0N firefighter is 3.37m from the bottom of the ladder.

3) If the ladder is just on the verge of slipping when the firefighter is 7.36m up, what is the coefficient of static friction between the ladder and the ground?

Explanation / Answer

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

Rw[12.7sin56] - 539[(12.7/2)cos56] - 822[3.37cos56] = 0

Rw (10.53)=1913.92+1549.04
Rw=328.86 N
Sum horizontal forces to zero shows that the horizontal floor reaction is 328.86 N toward the wall

Sum vertical forces to zero to find the floor vertical force

Fv - 539-822= 0

Fv = 1361 N upward

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

Rw[12.7sin56] - 539[(12.7/2)cos56] - 822[7.36cos56] = 0

Rw (10.52) = 1913.92 N +3383.07 N

Rw = Fh = 503.51 N

The vertical reaction remains the same

Fv = 1361 N upward

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

? = Fh / Fv

? = 503.5 / 1361

? = 0.3699

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