Question #102696
On Jupiter a day lasts for 9.9 earth hours and the circumference at the equator is 448600 km. If the measured value of gravitational acceleration at the equator is 24.6mls² , what is the true gravitational acceleration and the centrifugal acceleration. b) A ball of mass 50g is hit due south with a speed of 70 ms-1 at latitude 60 ºN. Calculate the magnitude and direction of the coriolis force on the ball.
1
Expert's answer
2020-02-24T10:16:49-0500

1)


ω=2π9.93600=0.0001762rads\omega=\frac{2\pi}{9.9\cdot 3600}=0.0001762\frac{rad}{s}

The centrifugal acceleration


gc=ω2r=(0.0001762)24486000002π=2.22ms2g_c=\omega^2r=(0.0001762)^2\frac{448600000}{2\pi}=2.22\frac{m}{s^2}

The true gravitational acceleration:


gt=g+gc=24.6+2.22=26.82ms2g_t=g+g_c=24.6+2.22=26.82\frac{m}{s^2}

2)


Fc=2mvΩsinλF_c=2mv\Omega \sin{\lambda}

Fc=2(0.05)(70)(7.3105)sin60=4.4105 NF_c=2(0.05)(70)(7.3\cdot 10^{-5}) \sin{60}=4.4\cdot 10^{-5}\ N

The missile with a south-pointing velocity is deflected to the right of its motion in the Northern Hemisphere, which is toward the west. 



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