Question

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.)

Answer 1

W=76.55 miles.metric tons

Step-by-step 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

`F=(K)/(x^2)`

Here x= 1100 miles

F 2 tons

`2=(K)/(1100^2)`

So

`K=2.4* 10^6`

We know that

Work = F. dx

`W=\int_(x_1)^(x_2)F.dx`

`W=\int_(1100)^(1140)(2.4* 10^6)/(x^2).dx`

`W=-2.4* 10^6\left[(1)/(x)\right]_(1100)^(1140)`

`W=-2.4* 10^6\left[(1)/(1140)-(1)/(1100)\right]`

W=76.55 miles.metric tons