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Calculate the effective value of [tex]g[/tex], the acceleration of gravity, at 7000 m above the Earth's surface.

Part B

Calculate the effective value of [tex]g[/tex], the acceleration of gravity, at 7000 km above the Earth's surface.

Answer :

Final answer:

The effective value of g at 7000 m above the Earth's surface is approximately 9.712 m/s^2, and at 7000 km above the Earth's surface is approximately 2.216 m/s^2.

Explanation:

To calculate the effective value of g at a certain height above the Earth's surface, we can use the formula:

g' = g * (R / (R + h))^2

Where:

  • g is the acceleration due to gravity at the Earth's surface (approximately 9.8 m/s^2)
  • R is the radius of the Earth (approximately 6,371 km)
  • h is the height above the Earth's surface

Let's calculate the effective value of g at 7000 m:

g' = 9.8 * (6371000 / (6371000 + 7000))^2

g' = 9.8 * (6371000 / 6378000)^2

g' = 9.8 * 0.997^2

g' ≈ 9.8 * 0.994 = 9.712 m/s^2

Therefore, the effective value of g at 7000 m above the Earth's surface is approximately 9.712 m/s^2.

Now, let's calculate the effective value of g at 7000 km:

g' = 9.8 * (6371000 / (6371000 + 7000000))^2

g' = 9.8 * (6371000 / 13371000)^2

g' = 9.8 * 0.476^2

g' ≈ 9.8 * 0.227 = 2.216 m/s^2

Therefore, the effective value of g at 7000 km above the Earth's surface is approximately 2.216 m/s^2.

Learn more about calculating the effective value of g at different heights above the earth's surface here:

https://brainly.com/question/30067879

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