Question

A ship steams at speed v along the equator. Show that the apparent weight w of an object as weighed on the ship is given approximately by $w=w_0(1\pm 4\pi fv/g),$ where f is the frequency of rotation (revolutions / second ) of the earth. Why is there $a\pm$ sing ? Let $w_0$ be the measured weight of the object when the ship is at rest relative to the earth.

Answer 1

Apparent weight of any object on any moving object is given by

$W=m{a}_{eff}$ where $a_{eff}$ is effective acceleration experienced by body.

when ship is at rest , $a_{eff}$ is given by $g-{\omega }^{2}R$

so $W_o=m(g-{\omega }^{2}R)$

when ship is moving with velocity v , $a_{eff}$ is given by $g-{\omega }_a^{2}R$

where ${\omega }_a=v/R\pm \omega$

$\pm$ sign is because, it is not defined that in which direction ship is moving.

so $W=m(g-{\omega }_a^{2}R)$

$W=m(g-(\frac{v}{R}+\omega {)}^{2}R)$

diving both equation we get

$\frac{W}{W_o}=1\pm 2v\omega /g$

putting $\omega =2\pi f$

$\frac{W}{W_o}=1\pm 4\pi fv/g$

$W=W_o(1\pm 4\pi fv/g)$