Answer :
If the painter weighs 55.0 kg and the ladder weighs 12.0 kg, and the ladder starts to slide at the base when her feet are 70% of the way up the length of the ladder, The coefficient of static friction between the ladder and the floor is 0.5.
What do you mean by static friction?
The resistance people feel when they try to move something that is stationary on a surface without actually moving their bodies or the surface they are trying to move it on.
n = F[tex]_{GY}[/tex]
F[tex]_{s} ^{max}[/tex] = F[tex]_{GX}[/tex]
F[tex]_{GY}[/tex] = μ[tex]_{s}[/tex] n
F[tex]_{GX}[/tex] = μ[tex]_{s}[/tex] F[tex]_{GY}[/tex]
Sum of horizontal forces is 0 = F[tex]_{GX}[/tex] -F[tex]_{W}[/tex] = 0
∴ F[tex]_{GX}[/tex] = F[tex]_{W}[/tex]
Sum of vertical forces is 0 = F[tex]_{GY}[/tex] - mg -Mg = 0
F[tex]_{GY}[/tex] = g (m+M)
Total torque at point a (foot of ladder) = 0
hence,
mg (1.5) + Mg(2.1) - F[tex]_{W}[/tex](4) =0
mg (1.5) + Mg(2.1) = F[tex]_{W}[/tex](4)
mg (1.5) + Mg(2.1) = F[tex]_{GX}[/tex](4)
mg (1.5) + Mg(2.1) = μ[tex]_{s}[/tex] F[tex]_{GX}[/tex](4)
mg (1.5) + Mg(2.1) = μ[tex]_{s}[/tex] g(m+M) (4)
μ[tex]_{s}[/tex] = [tex]\frac{mg (1.5) + Mg(2.1)}{4g(m+M)}[/tex]
μ[tex]_{s}[/tex] = [tex]\frac{12 (1.5) + 55(2.1)}{4(12+55)}[/tex]
μ[tex]_{s}[/tex] = 0.5
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