This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 Excerpt: ...equal spheres was proved by Hertz to be equal to V 8(--u)q where R is the radius of either of the spheres, s the density of the sphere, q ...
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 Excerpt: ...equal spheres was proved by Hertz to be equal to V 8(--u)q where R is the radius of either of the spheres, s the density of the sphere, q and r respectively Young's modulus and Poisson's ratio for the substance of which the spheres are made. Hamburger has measured the time two spheres are in contact by making the spheres close an electric circuit whilst they are in contact and measuring the time the current is flowing. The results of his experiments are given in the following table. They relate to the collision of brass spheres 1-8 cm. in radius: The duration of the impact is several times the gravest time of vibration of the body. In order to start such vibrations with any vigour the time of collision would have to be small compared with the time of vibration. We conclude that only a small part of the energy is spent in setting the spheres in vibration. As an example of the order of magnitude of the quantities involved in the collision of spheres we quote the results given by Hertz for two steel spheres 2 5 cm. in radius meeting with a relative velocity of 1 cm. per second. The radius of the surface of contact is-013 cm. The time of contact is-00038 seconds. The maximum total pressure is 2-47 kilogrammes and the maximum pressure per unit area is 7300 kilogrammes per centimetre. In this theory and in the example of the carriages with springs we have supposed that the energy stored up in the springs is ultimately reconverted into kinetic energy, so that the total kinetic energy at the end of the impact is the same as at the beginning. This is the case of the impact of what are called perfectly elastic bodies, for which the coefficient of restitution is equal to unity. In other cases we see by equation (3) that, instead of the whole energy stored in the ..."
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