A treatise on dynamics. Containing a considerable collection of mechanical problems / By William Whewell.

  • William Whewell
Date:
1823
Catalogue details

Licence: Public Domain Mark

Credit: A treatise on dynamics. Containing a considerable collection of mechanical problems / By William Whewell. Source: Wellcome Collection.

    50/444 (page 14)
    Cor. 1. From different distances the times of falling to the same centre are as a 2 . Hence if force oc dist. time oc l_, or is constant, if force oc 1, or is constant, time oc ,y/(dist.) 1 if force oc ——- time oc dist. (dist.) if force oc ———- time oc (dist.)2, (dist.) if force oc —:—3, time oc(dist.)'2, (dist.) if force oc ——7, time oc (dist.)L (dist.)2 Cor. 2. In all these cases the time is greater as the distance is greater; but if the force vary in a higher direct ratio than the simple power of the distance, the contrary will be the case. Thus if force oc (dist.)2, time oc —:—— (dist.)2 . 3 . 1 if force oc (dist.) , time oc —-—-. * (dist.) Cor. 3. The integration for finding the time when the force is inversely as the distance, is not properly included in this case, and is considered in the following problem. Prob. III. When the force varies inversely as the distance, to find the whole time of the descent to the centre. Let any distance SP, fig. 1, = r; hence, m mdr t a f — , vdv --, v = Q m hyp. log. - , » fjt * ^ dr 1 dr (2>»)* -y/]lypt Jog. - V dt = v