A 7470-kg satelite has an elliptical orbit, as in the figure. The point on the o

Question

A 7470-kg satelite has an elliptical orbit, as in the figure. The point on the orbit that is farthest from the earth is called the apogee and is at the far right side of the drawing. The point on the orbit that is closest to the earth is called the perigee and is at the far left side of the drawing. Suppose that the speed of the satellite is 2840 m/s at the apogee and 8300 m/s at (a) Find the work done by the gravitational force when the satellite moves from the apogee to the perigee. (b) Find the work done by the gravitational force when the satellite moves from the perigee to the apogee. Section 62 points CJ10 6 P

Explanation / Answer

From the Work Energy Theorem, we know that
Work done by all forces on an object = change in the Kinetic Energy of the object

the only force given in the problem on the satellite is the force of gravity.

So the work done by the gravity = change in Kinetic Energy,
i.e,

Work done= K.E(apogee) - K.E(perigee)

we know that Kinetic energy = mv2/2

thus
word done = (1/2)(7470)(2840)2 - (1/2)(7470)(8300)2

= -227179134000 = -2.27 x 1011 Joules

(b) for this, we just need to switch the order of the kinetic energy.

Work done = word done = (1/2)(7470)(8300)2 -(1/2)(7470)(2840)2

= 2.12 x1011 Joules

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