Exercício Dinâmica - Engenharia Mecânica (115)

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835 
 
 
PROBLEM 13.200 
A 2-kg block A is pushed up against a spring compressing it a 
distance 0.1 m.x = The block is then released from rest and 
slides down the 20° incline until it strikes a 1-kg sphere B 
which is suspended from a 1 m inextensible rope. The spring 
constant 800k = N/m, the coefficient of friction between A and 
the ground is 0.2, the distance A slides from the unstretched 
length of the spring 1.5 md = and the coefficient of restitution 
between A and B is 0.8. When 40 ,α = ° determine (a) the speed 
of B (b) the tension in the rope. 
 
SOLUTION 
Data: 2 kg, 1 kg, 800 N/m, 0.1 m, 1.5 mA Bm m k x d= = = = = 
 0.2, 0.8, 20 , 40 , 1.0 mk e lμ θ α= = = ° = ° = 
Block slides down the incline: 
 0yFΣ = 
 cos 0AN m g θ− = 
 
 cos
(2)(9.81)cos 20
18.4368 N
(0.2)(18.4368)
3.6874 N
A
f k
N m g
F N
θ
μ
=
= °
=
= =
=
 
Use work and energy. Datum for gV is the impact point near B. 
 2 2
1 1 1
1 1
0, ( ) (800)(0.1) 4.00 J
2 2eT V k x= = = = 
 1 1( ) ( )sin (2)(9.81)(1.6)sin 20 10.7367 Jg A AV m gh m g x d θ= = + = ° = 
 1 2 ( ) (3.6874)(1.6) 5.8998 JfU F x d→ = − + = − = − 
 2 2 2
2 2
1 1
(1)( ) 1.000 0
2 2A A A AT m v v v V= = = = 
 2
1 1 1 2 2 2: 0 4.00 10.7367 5.8998 1.000 0AT V U T V v→+ + = + + + − = + 
 2 2 28.8369 m /sAv = 
 2.9727 m/sA =v 20°