an object of mass 5kg weighs 49N at surface of the Earth. At an altitude equal to twice the Earth's radius its weight is?
The answer is 12.3N but i dont get why
The answer is 12.3N but i dont get why
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We know that, at the Earth's surface the gravity pulls (creates weight) of 9.8 N/kg. Which means that every kg weighs 9.8 newtons.
But as the altitude increases, weight decreases. So you see that at double the altitude from the Earth's centre the object weighs less.
Let's remember the statement for surface of a sphere. From the formula A = r^2×pi×4 we see that the area of a sphere increases proportionally with the square of the radius.
And since the centre of gravity is at the Earth's core, then the effect of gravity DECREASES proportionally to the square of the radius as the distance INCREASES. And vice versa.
Having that in mind, you would square the amount the radius increased. We know that it is twice as big as it was before. 2^2 = 4
And now you know the the object weighs 49 N on the surface. So 49 / 4 = 12.3 N
But as the altitude increases, weight decreases. So you see that at double the altitude from the Earth's centre the object weighs less.
Let's remember the statement for surface of a sphere. From the formula A = r^2×pi×4 we see that the area of a sphere increases proportionally with the square of the radius.
And since the centre of gravity is at the Earth's core, then the effect of gravity DECREASES proportionally to the square of the radius as the distance INCREASES. And vice versa.
Having that in mind, you would square the amount the radius increased. We know that it is twice as big as it was before. 2^2 = 4
And now you know the the object weighs 49 N on the surface. So 49 / 4 = 12.3 N