~4! The combined mass of the piezo and brass rod, 1.8 kg,
was much larger than that of any of the balls tested, so the
energy transferred to the rod was much smaller than the incident
energy of the ball. The momentum transfer was not
entirely negligible, with the result that part of the y displacement
observed at the end of the impact could be attributed to
motion of the brass rod during the impact. The velocity of
the rod after the collision is given by V5m(v11v2)/M,
where m is the ball mass and M51.8 kg is the rod mass.
Since the average speed of the rod during the collision is
approximately V/2, the displacement in time t is approximately
Dy5m(v11v2)t/(2M). This displacement is
shown in the last column of Table I. For the baseball, tennis
ball, and steel ball, motion of the rod accounted for about
half of the final y displacement, and it also accounted for
about 5% of the energy lost by these balls. The results presented
below were not corrected for this effect, in part because
of the unknown effect of the rubber support in restricting
motion of the rod. The displacement of the rod is
significant only toward the end of the impact, and the area of
the hysteresis loop is increased by only a few % as a result.
More precise measurements could be obtained either by using
a heavier rod, or by suspending the rod horizontally to
allow for free motion of the rod during the collision. In the
latter case, an appropriate correction based on the measured
force wave form could then be made for displacement of the
rod.
~4! The combined mass of the piezo and brass rod, 1.8 kg,was much larger than that of any of the balls tested, so theenergy transferred to the rod was much smaller than the incidentenergy of the ball. The momentum transfer was notentirely negligible, with the result that part of the y displacementobserved at the end of the impact could be attributed tomotion of the brass rod during the impact. The velocity ofthe rod after the collision is given by V5m(v11v2)/M,where m is the ball mass and M51.8 kg is the rod mass.Since the average speed of the rod during the collision isapproximately V/2, the displacement in time t is approximatelyDy5m(v11v2)t/(2M). This displacement isshown in the last column of Table I. For the baseball, tennisball, and steel ball, motion of the rod accounted for abouthalf of the final y displacement, and it also accounted forabout 5% of the energy lost by these balls. The results presentedbelow were not corrected for this effect, in part becauseof the unknown effect of the rubber support in restrictingmotion of the rod. The displacement of the rod issignificant only toward the end of the impact, and the area ofthe hysteresis loop is increased by only a few % as a result.More precise measurements could be obtained either by usinga heavier rod, or by suspending the rod horizontally toallow for free motion of the rod during the collision. In thelatter case, an appropriate correction based on the measuredforce wave form could then be made for displacement of therod.
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