Gravity Funny satellite

Classical Mechanics Level 3

A Geo-stationary satellite is Orbiting around the Earth at a height of 30,000 km in a circular orbit. The radius of the Earth is taken as 6,000 km.

The Geo-stationary satellite comes back to its position after one revolution in exactly 24 hours.

Let the mass of the satellite be 1000 kg. Calculate the work done 12 hours when moving under gravitational force. $(NTSE 2012-2013)$

DETAILS AND ASSUMPTIONS:

1) Take the acceleration due to gravity as $g = 9.798 \frac{m}{s^2}$

The answer is 0.

2 solutions

Sravanth C.
Feb 16, 2015

We know that the formula for work is $F \times S\cos \theta$ Here the angle between the vector i.e Force and Displacement is 90 degree.

And $\cos 90 = 0$ , therefore $F \times S\cos 90 = F \times S\times 0 = 0$

Adrian Peasey
Jun 17, 2015

Work is given by $\int \vec{F}\cdot\vec{dl}$ , and $\vec{F}$ is perpendicular to the direction of motion $\vec{dl}$ , so the dot product becomes 0 and hence $W=0$ .

Gravity Funny satellite

The answer is 0.

2 solutions

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