a traditional cue, Rodrigo used a spring-powered cue in his game of billiards. When the constraints on the spring (k = 100 kN/m) are removed, the launching mechanism of the cue is triggered, and the 170-g cue ball A is launched forward. Ball A is separated from the plate when the spring becomes fully unstretched. Ball A is launched at an angle α with the horizontal, making it rebound off the cushion at an angle β. When the cue ball A hits the initially stationary 9-ball B (mB = 160 g), the latter goes snuggly into the lower left pocket. Determine the amount of compression (mm) on the spring so that the speed of ball B is exactly 5. XYZ m/s, where XYZ is the last three digits of your student number (Ball B may bounce off the table if its velocity is > 5. XYZ m/s and may not reach the pocket if < 5.XYZ m/s). The coefficient of restitution bet
Instead of a traditional cue, Rodrigo used a spring-powered cue in his game of billiards.
When the constraints on the spring (k = 100 kN/m) are removed, the launching
separated from the plate when the spring becomes fully unstretched. Ball A is launched at
an angle α with the horizontal, making it rebound off the cushion at an angle β. When the
cue ball A hits the initially stationary 9-ball B (mB = 160 g), the latter goes snuggly into the
lower left pocket. Determine the amount of compression (mm) on the spring so that the
speed of ball B is exactly 5. XYZ m/s, where XYZ is the last three digits of your student
number (Ball B may bounce off the table if its velocity is > 5. XYZ m/s and may not reach
the pocket if < 5.XYZ m/s). The coefficient of restitution between ball A and the cushion is
0.6 while between balls A and B is 0.95. Neglect the effect of friction and the size of the
balls.
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