Problem 11.35 An 88 kg person stands on a uniform 6.2 kg ladder that is 4.0 m lo

Question

Problem 11.35 An 88 kg person stands on a uniform 6.2 kg ladder that is 4.0 m long, as shown in the figure(Figure 1). The floor is rough; hence, it exerts both a normal force, fi, and a frictional force 2, on the ladder. The wall, on the other hand, is frictionless it exerts only a normal force f3 Figure 1 of 1 3.8 m b 0.70 m Part A using the dimensions given in the figure, find the magnitudes of fi, f2, and fa Express your answer using two significant figures kN Submit My Answers Give Up Part B Express your answer using two significant figures. kN

Explanation / Answer

Let,

M be the mass of the ladder,
L be the length of the ladder,
t be the inclination of the ladder to the horizontal.

Resolving vertically and horizontally
f1 = (M + m)g
f2 = f3

Moments about the base of the ladder
MgL cos(t) / 2 + mgb = f3 a

L = 4 m
Mg = 60.82 N
m = 88kg
a = 3.8m

sin(t) = a / L = 3.8 / 4

cos(t) = sqrt(4^2-(3.8)^2)/4 =0.31

Part A

f1 = (M+m)*g = (88+6.2)*9.81 = 0.924kN

Part B

f2*a = MgL cos(t) / 2 + mgb

f2*3. 8 = (60.82*4*0.31/2)+88*9.81*0.7 = 0.168kN

Part C

f2 = f3 = 0.168kN

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