Question

ques

Answer 1

A mass of ice, weighing 500,000 tons near the North pole moves west at a rate of 5 miles a day. Neglecting the curvature of the earth, find the magnitude and the direction of the Coriolis force. Express the magnitude in tons weight. Take g=32m/s^2
\[F=2mv\omega=2m\frac{v^2}{r}\]
\[m=5\times 10^8 Kg\]
\[v=0.0931ms^{-1}\]\[\therefore v^2=0.008674m^2s^{-2}\]
\[r=64 \times 10^5 m\]
\[F=\frac{2 \times 5 \times 10^8 \times 0.008674}{64 \times 10^5}N\]
\[F=\frac{0.008674 \times 10^9}{64 \times 10^5}N=\frac{0.008674 \times 10^4}{64}N=\frac{86.74}{64}N=1.4N\]
Now
\[1N=1kg.1ms^{-2}=10^{-3} tonne.\frac{g}{32}=\frac{10^{-3}}{32}.tonne.wt\]
\[F=1.4 \times \frac{10^{-3}}{32} tonne.wt=0.00004375 tonne.wt\]
But answer is
\[0.7 tonne.wt\]

Answer 2

first of all, there's something very odd going on with the units here

it all seems to be in imperial, and the answer they want is also expressed as ton weight, not tonne weight

and g = 32m/s/s?!?! g in imperial is 32 ft /s/s

if you start by checking that is not the problem, then happy to have a look at the mechanics

"In American English, a ton is a unit of measurement equaling 2,000 pounds. In non-U.S. measurements, a ton equals 2,240 pounds. A tonne, also known as a metric ton, is a unit of mass equaling 1,000 kilograms."

Answer 3

Oh, so a ton is different from a tonne?I didn't know there was such a unit, and I think the reason for such a value of g is maybe because we're at the north pole, should that make such a huge difference?

Answer 4

Ah, so THAT's why it's called a metric ton, to differentiate it from the imperial ton