Instead of a traditional cue, Rodrigow 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 5.640 m/s, (Ball B may bounce off the table if its velocity is > 5.640 m/s and may not reach the pocket if < 5.640 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.
OBLIQUE CENTRAL IMPACT
Instead of a traditional cue, Rodrigow 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 5.640 m/s, (Ball B may bounce off the table if its velocity is > 5.640 m/s and may not reach the pocket if < 5.640 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.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 4 images
