An 85 kg person stands on a uniform ladder that is 3.9 m long and weighs 60.0 N.

Question

An 85 kg person stands on a uniform ladder that is 3.9 m long and weighs 60.0 N. The floor is rough; hence it exerts both a normal force, f1, and a frictional force, f2, on the ladder. The wall, on the other hand, is frictionless; it exerts only a normal force, f3. Use the dimensions in the figure to find the following. (a = 3.8 m.) (a) Find the forces exerted on the ladder when the person is halfway up the ladder. f 1 = N f 2 = N f 3 = N (b) Find the forces exerted on the ladder when the person is three-fourths of the way up the ladder. f 1 = N f 2 = N f 3 = N

Explanation / Answer

a) when man is half up ladder

balancing forces in x

f3 = f2 --------------1

balancing forces in y

f1 = 85g + 60 = 893 N

angle made at floor = sin inverse ( 3.8/3.9) = 77 deg

now balancing torque at floor point

f3sin77* 3.9 = 893*sin13 1.95

f3 = 103.08 N

f2 = 103.08 N

f1 = 893 N

b) when man is 3/4 up ladder

balancing forces in x

f3 = f2 --------------1

balancing forces in y

f1 = 85g + 60 = 893 N

angle made at floor = sin inverse ( 3.8/3.9) = 77 deg

now balancing torque at floor point

f3sin77* 3.9 = 833sin13*2.925 + 60sin13*1.95

f3 = 151.16 N

f2 = 151.16 N

f1 = 893 N

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