As background for this problem, review ConceptualExample 6 . A 7200-kg satellite

Question

As background for this problem, review ConceptualExample 6. A 7200-kg satellite has an elliptical orbit, as inFigure 6.9b. The point on the orbit that is farthest from the earthis called the apogee and is at the far right of thedrawing. The point on the orbit that is closest to the earth iscalled the perigee and is at the left side of the drawing.Suppose that the speed of the satellite is 3800 m/s at the apogeeand 6920 m/s at the perigee. Find the work done by thegravitational force when the satellite moves from (a) the apogee tothe perigee and (b) the perigee to the apogee.

(a) Number Units No unitsmm/skgNJW

Explanation / Answer

The work done is the change in kinetic energy. So find KE ateach point: . apogee      KE = (1/2) mv2 = (1/2) * 7200 * 38002 =  5.1984 x 1010 Joules . perigee     KE = (1/2) mv2 = (1/2) * 7200 * 69202 =  17.2391 x 1010 Joules . Work done from apogee to perigee = KE at perigee -KE at apogee = .          =  17.2391 - 5.1984 =    1.204 x 1011 Joules . Work done from perigee to apogee would be theopposite      - 1.204 x1011 Joules

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