ENG211 Dynamics and Vibrations

Aim:

To calculate the coefficient of restitution e and verify the law of conservation of angular momentum.

Apparatus:

The impact mechanism consists of an impacting mass fastened to a hanging rod (labelled the striker) and a hanging beam attached to additional weights (labelled the receiver). The impacting mass is free to move to any desired position along the impacting rod.

Both the striker and receiver are free to swing, with potentiometers coupled to each pivot in order to accurately measure the angle of deviation. Using suitable DAQ hardware and the developed LabVIEW program, potentiometer voltage signals can be easily measured, viewed and recorded.

Figure 1 outlines the basic operation of the mechanism. Figure 1 (a) illustrates the system at rest with both striker and receiver stationary and hanging vertically. Figure 1 (b) and (c) demonstrate the striker being released and impacting the stationary receiver, causing a maximum angle of movement for both striker and receiver as shown.

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Procedure:

1. Sketch the apparatus.

2. Record M2, M3 and M4. Measure l, L and the diameter of the impacting steel rod, d. Relevant parameters are illustrated in Appendix A, Figure 2 and ALL experiment parameters are listed in Appendix B.

3. With the impact mechanism completely stationary (Figure 1 (a)), zero voltage levels
on the LabVIEW program.

4. Calibrate each potentiometer to develop a voltage/angle relationship (which should be linear) for both striker and receiver.

A possible approach is to raise each in 5° increments and, for each incremental increase, hold steady for a number of seconds so that an average voltage can be approximated at that angle. This will also require a digital inclinometer. Calibrate up to approximately 75° and then save the file.

Remember to record the incremental angles that correspond to each average voltage signal so that a calibration factor can be calculated.

5. Release the striker from a small angle and allow it to swing freely for at least 10 oscillations. Repeat 3 times and save the file. This will allow us to measure the period of oscillation. Ensure that the digital inclinometer does NOT remain attached to the apparatus.

6. Repeat (5) for the receiver beam.

7. For a selected r1 and θ1, release the striker from rest and allow it to collide with the receiver. Ensure that the digital inclinometer does NOT remain attached to the apparatus.

8. Perform 5 separate tests with the impacting mass at a different location each time. For each test, release the striker with θ1 in the range 0° - 60° in approximately 10° increments. It is important to repeat part (5) for each test performed since moving the impacting mass will affect the period of oscillation.
Remember to save the data to a new file for each test performed.

9. Repeat parts (5) and (8) with a rubber pad attached to the impacting mass (the striker).

10. Perform a theoretical analysis following the outlined approach in the Analysis section.

11. Write a concise discussion outlining the main sources of error and any reasons for discrepancies between angular momentum/rotation kinetic energy before and after the impact. Discuss the results obtained for the coefficient of restitution.