18_Coll_Spheres

18_Coll_Spheres - INDIANA UNIVERSITY, DEPARTMENT OF...

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Unformatted text preview: INDIANA UNIVERSITY, DEPARTMENT OF PHYSICS, P309 LABORATORY Laboratory #18: Hertz Contact between Colliding Elastic Spheres Goal: Verify Hertz's equation for the contact time during a collision between two elastic spheres. (A) Physics: When two elastic bodies are pressed against each other, their surfaces deform. For simple geometric shapes, like spheres, the amount of deformation can be calculated from the laws of elasticity. The dynamics of a collision between two bodies can then be described theoretically. In particular, the contact time can be calculated. Heinrich Hertz carried out such a calculation more than 100 years ago [HER95]. The theoretical arguments are worked out in [LAN59] for the case of a collision of two spheres of radii r 1 , r 2 , and masses m 1 , m 2 , colliding with relative velocity v . The contact time is found to be 5 1 2 2 94 . 2 = v k . (1) Here, & is the so-called reduced mass of the two spheres, 2 1 2 1 m m m m +...
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This note was uploaded on 01/20/2012 for the course P 309 taught by Professor Urheim during the Spring '11 term at Indiana.

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18_Coll_Spheres - INDIANA UNIVERSITY, DEPARTMENT OF...

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