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

91962_05_R1_p0479-0512 6/5/09 3:53 PM Page 480
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R1–2. Cartons having a mass of 5 kg are required to move
along the assembly line with a constant speed of 8 m>s.
Determine the smallest radius of curvature, r, for the
conveyor so the cartons do not slip.The coefficients of static
and kinetic friction between a carton and the conveyor are
m s = 0.7 and m k = 0.5, respectively.
8 m/s
r
+ c ©F b = m a b ; N - W = 0
N = W
F s = 0.7W
: + ©F n = m a n ; 0.7W = W
9.81 a 82
r b
r = 9.32 m
Ans.
R1–3. A small metal particle travels downward through a
fluid medium while being subjected to the attraction of a
magnetic field such that its position is s = (15t 3 - 3t) mm,
where t is in seconds. Determine (a) the particle’s
displacement from t = 2 s to t = 4 s, and (b) the velocity
and acceleration of the particle when t = 5 s.
a)
s = 15t 3 - 3t
At t = 2 s, s 1 = 114 mm
At t = 4 s, s 3 = 948 mm
¢s = 948 - 114 = 834 mm
Ans.
b) v = ds
Ans.
dt = 45t2 - 3 2 = 1122 mm>s = 1.12 m>s
t = 5
a = dv
dt = 90t 2 = 450 mm>s 2 = 0.450 m>s 2
t = 5
Ans.
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