6 (A) F Y = − F − F N COS Θ + N SIN Θ = 0 (1)Y F X = F N SIN Θ + N C...

1-6

(a)

F _y = − F − f N cos θ + N sin θ = 0 (1)

F _x = f N sin θ + N cos θ − T

r = 0

F = N (sin θ − f cos θ ) Ans .

T = N r ( f sin θ + cos θ )

Combining

T = Fr 1 + f tan θ

tan θ − f = KFr Ans . (2)

(b) If T → ∞ detent self-locking tan θ − f = 0 ∴ θ cr = tan ^{− 1} f Ans .

(Friction is fully developed.)

Check: If F = 10 lbf, f = 0.20, θ = 45 ^◦ , r = 2 in

N = 10

− 0 . 20 cos 45 ^◦ + sin 45 ^◦ = 17 . 68 lbf

T

r = 17 . 28(0 . 20 sin 45 ^◦ + cos 45 ^◦ ) = 15 lbf

f N = 0 . 20(17 . 28) = 3 . 54 lbf

θ cr = tan ^{− 1} f = tan ^{− 1} (0 . 20) = 11 . 31 ^◦