Question

006 (part 1 of 2) 10.0 points A ladder rests against a vertical l There is no friction between the wall and t adder The coefficient of static friction between the ladder and the ground is0.581 ue 18-19 marder (OlsonM302K1819 2 6 A2, B, CI 7. Al. B C2 8. A2, B1, C3 9. Ai, B2, C3 10. B C3 007 (part 2 of 2) 10.0 points Determine the smallest angle θ for which the ladder remains stationary. Answer in units of

the answer to 6 is 9 I just do not know 7

Answer 1

using equilibrium of force along the horizontal direction

f = F                                                eq-1

using equilibrium of force in vertical direction

N = w                                                eq-2

static frictional force is given as

f = $\mu _{s}$ N

using eq-2

f = $\mu _{s}$ w

using eq-1

$\mu _{s}$ w = F                                   eq-3

Using equilibrium of torque about "A"

F Sin$\theta$ (AC) = (w Cos$\theta$) (AB)

given that : AB = L/2   and AC = L

using eq-3

($\mu _{s}$ w ) Sin$\theta$ (L) = (w Cos$\theta$) (L/2)

($\mu _{s}$ ) Sin$\theta$ = (Cos$\theta$) (1/2)

Sin$\theta$ /Cos$\theta$ = (0.5) /$\mu _{s}$

tan$\theta$ = 0.5/0.581

$\theta$ = 40.7 deg