Hinged rigid beam vs mass free fall

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SUMMARY

The discussion centers on the dynamics of a hinged rigid beam and the behavior of a mass during free fall. A 50 kg mass on a hinged platform separates from the platform when the raised end is dropped, demonstrating that the free end accelerates faster than the mass itself. This phenomenon is explained through the calculation of angular acceleration using the formula α = (3g cos θ) / (2l), where θ is the angle of the rod with the horizontal. The analysis reveals that points on the rod beyond a specific distance experience vertical acceleration greater than g.

PREREQUISITES
  • Understanding of angular acceleration and torque
  • Familiarity with free fall physics and gravitational acceleration
  • Knowledge of the ASTM foam cushion drop test methodology
  • Basic principles of rigid body dynamics
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  • Study the principles of angular motion in rigid body dynamics
  • Research the effects of torque on acceleration in mechanical systems
  • Explore the ASTM standards for drop testing and material performance
  • Learn about high-speed video analysis techniques for motion studies
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Mechanical engineers, physics students, and professionals involved in material testing and dynamic analysis will benefit from this discussion.

CraigHyattOB
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Our test group had some issues with an ASTM foam cushion drop test, and I was asked to investigate. I fixed the problem, but noticed something in a high speed video. A 50 kg mass on the hinged platform separates from the platform when the raised end of the platform is dropped. I thought the old cannon balls dropped from the Tower of Pisa story says acceleration in free fall is independent of mass. Why does the free end of the platform accelerate faster than the mass? I duplicated the effect with a ruler and steel nut:
 
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Acc. is same for free falling bodies. Take torque about the stationary end of the rod and find angular acc.
## \alpha = \frac{3g\cos\theta}{2l} ##​
Here ##\theta## is the angle with horizontal of rod, so any point on the rod beyond ##\frac{2l}{3g\cos^2\theta}## will have vetical acc. more than g . So it is somewhere here that you are placing the nut.
Hope that helps
 
Thanks!
 

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