- #1
Viraam
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Homework Statement
A pendulum having a bob of mass ##m## is hanging in a ship sailing along the equator from east to west. If the ship sails at speed v what is the tension in the string?. Angular speed of Earth's rotation is ## \omega ## and radius of the Earth is ## R ##
Homework Equations
## T = mg - R\omega'^2##
The Attempt at a Solution
If the ship were still, the tension in the string would be given by
## T_0 = mg - mR\omega^2##
However since the ship moves in the direction opposite to Earth's rotation, the angular velocity of Earth with respect to the ship would be ## \omega + \frac{v}{R}##
Therefore the tension would be
## T = mg - mR(\omega + \frac{v}{R})^2 \\
T \approx T_0 - 2m\omega v
##
Doubt: The answer key says that ## T \approx T_0 + 2m\omega v ## which means the relative angular velocity was taken as ## \omega - \frac{v}{R} ## . But isn't that the relative angular velocity when the ship sails from west to east. Where did I go wrong?