Exercício de Dinamica Aplicada (225)

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386 
 
 
PROBLEM 12.56 
Three seconds after a polisher is started from rest, small tufts of 
fleece from along the circumference of the 225-mm-diameter 
polishing pad are observed to fly free of the pad. If the polisher is 
started so that the fleece along the circumference undergoes a 
constant tangential acceleration of 24 m/s , determine (a) the 
speed v of a tuft as it leaves the pad, (b) the magnitude of the force 
required to free a tuft if the average mass of a tuft is 1.6 mg. 
 
SOLUTION 
(a) constantta =  uniformly acceleration motion 
 Then 0 tv a t= + 
 At 3 s:=t 2(4 m/s )(3 s)=v 
 or 12.00 m/sv =  
(b) :t t t tF ma F maΣ = = 
 or 6 2
6
(1.6 10 kg)(4 m/s )
6.4 10 N
tF −
−
= ×
= ×
 
 
2
:n n n
v
F ma F m
ρ
Σ = = 
 At 3 s:=t ( )
2
6
0.225
2
3
(12 m/s)
(1.6 10 kg)
m
2.048 10 N
nF −
−
= ×
= ×
 
 Finally, 2 2
tuft
6 2 3 2(6.4 10 N) (2.048 10 N)
t nF F F
− −
= +
= × + ×
 
 or 3
tuft 2.05 10 NF −= × 