Answer:
A) 1236 N
B) Nw = µ_s•N
C) d_max = 1.525 m
Explanation:
From the question, "smooth vertical wall" means that there is no friction there and thus the only vertical forces are the weights of the ladder and painter and the normal force at the floor.
a) Mass of ladder = 14 kg
Mass of painter = 8M = 8 * 14 = 112 kg
Thus, magnitude of normal force is;
N = total mass x acceleration due to gravity = (14 + 112)9.8
N = 1236 N
(b) Sum of the moments about the base of the ladder:
ΣH = 0
Nw - µ_s•N = 0
Nw = µ_s•N
c) Since they are the only two horizontal forces in play, we know that
Nw = Ff where Ff is the friction force at the floor.
Ff = µ_s*N = 0.39 × 1236
Ff = 482.04 N
So, to find maximum distance painter can stand without slipping, we'll use the formula ;
Nw(Lsinθ) = (Mgcosθ)(L/2) + (8Mgcosθ * d_max)
Plugging in the relevant values, we have;
482.04(2.7*sin55) = ((14 × 9.8cos55)*(2.7/2)) + (8*14*9.8cos55 * d_max)
1066.133 = 106.238 + 629.5575*d_max
629.5575*d_max = 1066.133 - 106.238
629.5575*d_max = 959.895
d_max = 959.895/629.5575
d_max = 1.525 m
