A rocket lifts off the pad at Cape Canaveral. According to Newton\'s Law of Grav

Question

A rocket lifts off the pad at Cape Canaveral. According to Newton's Law of Gravitation, the force of gravity on the rocket is given by F(x) = ? GMm/x^2 where M is the mass of the earth, m is the mass of the rocket, G is a universal constant, and x is the distance (in miles) between the rocket and the center of the earth. Take the radius of the earth to be 4000 miles, so that x > 4000 miles. Find the work, W1, done against gravity when the rocket rises 1600 miles. W1 = Next, find the limit of the work, W2, as the rocket rises infinitely far from the earth.

Explanation / Answer

If you are supposed to know the expression for gravitational potential energy,

U = -GMm/x,
then just plug in the appropriate values of x and subtract.
W1 is the difference U(4000 + 1600) - U(4000).
W2 is the difference U(infinity) - U(4000).

If you don't know that expression for U, then you're probably supposed to use the fact that work is the integral of F dx (which is the expression I gave above).
W1 is the integral from 4000 to 4000 +1600,
W2 is the integral from 4000 to infinity.

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