Exercício Dinâmica - Engenharia Mecânica (95)

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815 
 
 
PROBLEM 13.189 
When the rope is at an angle of 30α = ° the 1-kg sphere A has 
a speed 0 0.6 m/s.v = The coefficient of restitution between A 
and the 2-kg wedge B is 0.8 and the length of rope 0.9 ml = 
The spring constant has a value of 1500 N/m and 20 .θ = ° 
Determine, (a) the velocities of A and B immediately after the 
impact (b) the maximum deflection of the spring assuming A 
does not strike B again before this point. 
 
SOLUTION 
Masses: 1 kg
2 kg
A
B
m
m
=
=
 
Analysis of sphere A as it swings down: 
Initial state: 030 , (1 cos ) (0.9)(1 cos30 ) 0.12058 mh lα α= ° = − = − ° = 
 
0 0
2 2
0 0
(1)(9.81)(0.12058) 1.1829 N m
1 1
(1)(0.6) 0.180 N m
2 2
AV m gh
T mv
= = = ⋅
= = = ⋅
 
Just before impact: 1 10, 0, 0h Vα = = = 
 2 2 2
1
1 1
(1) 0.5
2 2A A A AT m v v v= = = 
Conservation of energy: 0 0 1 1T V T V+ = + 
 
2
2 2 2
0.180 1.1829 0.5 0
2.7257 m /s
A
A
v
v
+ = +
=
 
 1.6510 m/sA =v 
Analysis of the impact: Use conservation of momentum together with the coefficient of restitution. 0.8.e = 
 
Note that the ball rebounds horizontally and that an impulse Tdt is applied by the rope. Also, an impulse 
Ndt is applied to B through its supports.