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

91962_05_R1_p0479-0512 6/5/09 3:54 PM Page 501
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*R1–32. 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
u if force maintains a constant angular motion
u # = 90°, 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 = 90°
u # = 2 rad>s
u # = 0
r = 4.8105 m
r # = 9.6210 m>s
r $ = 19.242 m>s 2
a r = r $ - r(u # ) 2 = 19.242 - 4.8105(2) 2 = 0
a u = r u $ + 2 r # u # = 0 + 2(9.6210)(2) = 38.4838 m>s 2
tan c =
r
A dr
du B
c = u = 45°
= e u >e u = 1
+ c ©F t = m a t ; -N cos 45° + F cos 45° = 2(0)
; + ©F u = m a u ; F sin 45° + N sin 45° = 2(38.4838)
N t = 54.4 N
F = 54.4 N
Ans.
Ans.
501