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A beam of 10 Kg and length 12 meter starts to fall from initial vertical position with one end hinged.

When Beam's center of mass is dropped 5 meter from earlier position, Beam hits an object with its far end.

The object compresses by 0.05 meter.

To calculate impact force, I have taken full mass into account. So Impact Force X displacement 0.05 meter = mass 10 Kg X g 9.81 X h 5 meter Impact Force = 9810 N

I have two questions about my method

  1. If Beam weight is 10 Kg on weighing scale; Does it mean mass m is 10 Kg or weight mg is 10 kg? if mg is 10 then force will be only 981 N. ( sorry for the dumb question)

  2. As we see only head of beam makes an impact with the object. So should I consider full mass for impact force calculation? Or a factor of it?

  3. Will it make any difference if instead of beam, a flat disk of same height and weight is falling? All condition remaining same.

Please help me. Basically I have to make sure that the object being hit is safe.

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John Rennie
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Sheldon
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1 Answers1

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1st step is to calculate the kinetic energy at the moment of impact from the difference in potential energy.

The problem then is to find the impulse needed to stop the beam, considering the hinge will produce a reaction impulse also. In regards to your 2nd question, only a fraction of the mass participates in the contact. This is because the point of contact is off-center. The calculation is $m_{\rm eff} = 1 / \left( \tfrac{1}{m} + \tfrac{d^2}{I}\right)$ where $d$ is the distance to the center of mass, and $I$ the mass moment of inertia of the beam.

Finally somehow you need to translate the impulse into a force, considering the elastic properties of the beam and the time of impact. this last part is really hard to estimate since there are so many factors that go into this.

John Alexiou
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