479 Horizontal Motion: The horizontal component of velocity ... - Wuala

91962_05_R1_p0479-0512 6/5/09 3:54 PM Page 500
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R1–31. The collar has a mass of 2 kg and travels along the
smooth horizontal rod defined by the equiangular spiral
r = (e u ) m, where u is in radians. Determine the tangential
force F and the normal force N acting on the collar
when if force maintains a constant angular motion
u # u = 45°, F
= 2 rad>s.
F
r
r e u
r = e u
r # = e u u #
r $ = e u (u # ) 2 + e u u #
u
At u = 45°
u # = 2 rad>s
u = 0
r = 2.1933 m
r = 4.38656 m>s
r $ = 8.7731 m>s 2
a r = r $ - r (u # ) 2 = 8.7731 - 2.1933(2) 2 = 0
a u = r u $ + 2 r # u # = 0 + 2(4.38656)(2) = 17.5462 m>s 2
tan c =
r
A dr
du B
c = u = 45°
= e u >e u = 1
©F r = m a r ; -N r cos 45° + F cos 45° = 2(0)
©F u = m a u ; F sin 45° + N u sin 45° = 2(17.5462)
N = 24.8 N
F = 24.8 N
Ans.
Ans.
500