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A lunar module weighs 12 metric tons on the surface of the Earth. How much work is done in propelling the module from the surface of the moon to a height of 40 miles? Consider the radius of the moon to be 1100 miles (from the center of the moon) and its force of gravity to be one-sixth that of Earth. (Round your answer to the nearest integer.)

Respuesta :

Answer:

W=76.55 miles.metric tons

Explanation:

Given that

Weight on the earth = 12 tons

So weight on the moon =12/6 = 2 tons

 ( because at moon g will become g/6)

As we know that

[tex]F=\dfrac{K}{x^2}[/tex]

Here x= 1100 miles

F 2 tons

[tex]2=\dfrac{K}{1100^2}[/tex]

So

[tex]K=2.4\times 10^6[/tex]

We know that

Work = F. dx

[tex]W=\int_{x_1}^{x_2}F.dx[/tex]

[tex]W=\int_{1100}^{1140}\dfrac{2.4\times 10^6}{x^2}.dx[/tex]

[tex]W=-2.4\times 10^6\left[\dfrac{1}{x}\right]_{1100}^{1140}[/tex]

[tex]W=-2.4\times 10^6\left[\dfrac{1}{1140}-\dfrac{1}{1100}\right][/tex]

W=76.55 miles.metric tons

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