Part A. A plumb line is held steady while traveling in a moving train. If the ma

Question

Part A. A plumb line is held steady while traveling in a moving train. If the mass of the plumb bob is m and the mass of the string can be ignored, find the tension in the string and its angle of deflection from the local vertical if the train is accelerating forward with a constant acceleration of 0.05g. You can ignore the effects due to the earths rotation and revolution.

Part B. The orbital revolution of the moon about the earth takes about 27.32 days and is in the same direction as the earths rotation (24hrs). Use this information to prove high tides occur everywhere on earth approximately every 12 hr and 27 min.

Explanation / Answer

in frame inside the train pseudo force of -0.05mg has to be applied on bob

so in equilibrium eq. are

Tsinx = 0.05mg      and Tcosx = mg        x is the deflection from the verticl

tanx = .05

x =2.862 degree                  and T = mg/cos(2.862) = 1.00125mg

B. if moon remains stationary it would take any point on earth 12 hrs to again meet moon but moon also moves so in 12 hrs moon moves = .5*360/27.32 = 6.588 degree

which the earth would rotate in = 6.588*24/360 =.4392 hrs = 26.352 min

so any point would again meet moon in 12 hrs and 27 min approx and experience high tides

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