A 14.5 m uniform ladder weighing 520 N rests against a frictionless wall. The la

Question

A 14.5 m uniform ladder weighing 520 N rests against a frictionless wall. The ladder makes a 62.0 degree angle with the horizontal. Find the horizontal and vertical forces the ground exerts on the base of the ladder when an 810 N firefighter is 3.90 m from the bottom Magnitude of the horizontal force __________ Your response differs from the correct answer by more than 100%. Direction away from the wall towards the wall Magnitude of the vertical force ______ Direction down up If the ladder is just on the verge of slipping when the firefighter is 8.80 m up, what is the coefficient of static friction between ladder and ground? __________

Explanation / Answer

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

Rw[14.5 sin 62] - 520[(14.5/2)cos62] - 810[3.9cos62] = 0

Rw = 254 N

Sum horizontal forces to zero shows that the horizontal floor reaction is 254 N toward the wall

Sum vertical forces to zero to find the floor vertical force

Fv - 520 - 810 = 0

Fv = 1330 N upward

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

Rw[14.5 sin62] - 520[(14.5/2)cos62] - 810[8.80 cos62] = 0

Rw = Fh = 399.6 N =400N

The vertical reaction remains the same

Fv = 1330 N upward

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

= Fh / Fv

= 400 / 1330

= 0.300

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