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 byF(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 1500 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)

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Asked Feb 4, 2020
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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 1500 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)

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