A robotic pool cue is designed to carefully impart enough energy to a cue ball for the
Question:
A robotic pool cue is designed to carefully impart enough energy to a cue ball for the precision needed when playing billiards. The robotic pool cue consists of a pool cue and a spring (with a spring constant k = 18 lb/in.) that can be depressed a specific distance x and suddenly released, providing a known amount of energy to the pool cue. Energy is stored in the spring until the cue is launched forward. The pool cue then impacts the cue ball (which has a weight of 6 ounces, or roughly 0.375 lb), imparting kinetic energy on the cue ball. The robotic pool cue configuration is shown below.
There are three energy states involved in this problem.
Energy State | Description | Spring Energy | KE of Pool Cue | KE of Cue Ball |
1 | Spring is at max compression, nothing is moving | Max | 0 | 0 |
2 | Spring is fully restored, pool cue is at maximum speed | 0 | Max | 0 |
3 | The pool cue impacts the cue ball, causing a change in momentum. Energy is transferred from the cue to the cue ball. | 0 | 0 | Max |
The impact between the pool cue and the cue ball involves some energy loss (because it is not a perfectly elastic impact). As such, there is an efficiency less than 1 in the system. During one impact, the spring is compressed x = 1.13 in. Based on experimentation, it was determined that the efficiency of this system in converting spring energy to kinetic energy of the cue ball is approximately = 0.89. What can you expect the speed of the cue ball to be after impact? (answer in ft/s)