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) = ?GMmx2 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 2000 miles.W1 = GMm (mile-pounds)Next, find the limit of the work, W2, as the rocket rises infinitely far from the earth.W2 = GMm (mile-pounds). Please explain thoroughly.

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 + 2000) - 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 +2000, W2 is the integral from 4000 to infinity.

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