Hello there,
If a mass, m, is placed at one end of an boat of mass M, which is located on a frictionless ocean. If the mass, m, is moved from one end of the boat to the other end, conservation of center of mass position ensures that the boat shifts a small distance in the opposite direction. The conservation of mass is given by: $$\frac{x_1\,m+x_2\,M}{m+M} = \frac{\tilde{x_1}\,m+\tilde{x_2}\,M}{m+M}$$ where each x equal the position of the masses.
How can I derive this forumla from more fundamental physics?
Thank you for your time,
Kind regards,
Marius
PS: how can I most easily do inline latex? Is it possible to do something similar to $expr$? Thanks
If a mass, m, is placed at one end of an boat of mass M, which is located on a frictionless ocean. If the mass, m, is moved from one end of the boat to the other end, conservation of center of mass position ensures that the boat shifts a small distance in the opposite direction. The conservation of mass is given by: $$\frac{x_1\,m+x_2\,M}{m+M} = \frac{\tilde{x_1}\,m+\tilde{x_2}\,M}{m+M}$$ where each x equal the position of the masses.
How can I derive this forumla from more fundamental physics?
Thank you for your time,
Kind regards,
Marius
PS: how can I most easily do inline latex? Is it possible to do something similar to $expr$? Thanks