A spherical satellite of approximately uniform density with radius 5.4 m and mass 300 kg is originally moving with velocity <2600, 0, 0>m/s, and is originally rotating with an angular speed 2 rad/s, in the direction shown in the diagram. A small piece of space junk of mass 5.1 kg is initially moving toward the satellite with velocity <−2200, 0, 0>m/s. The space junk hits the edge of the satellite as shown in the figure below, and moves off with a new velocity <−1300, 480, 0>m/s. Both before and after the collision, the rotation of the space junk is negligible.What is the rise in the internal energy of the satellite and space junk combined?

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Asked Nov 20, 2019
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A spherical satellite of approximately uniform density with radius 5.4 m and mass 300 kg is originally moving with velocity <2600, 0, 0>m/s, and is originally rotating with an angular speed 2 rad/s, in the direction shown in the diagram. A small piece of space junk of mass 5.1 kg is initially moving toward the satellite with velocity <−2200, 0, 0>m/s. The space junk hits the edge of the satellite as shown in the figure below, and moves off with a new velocity <−1300, 480, 0>m/s. Both before and after the collision, the rotation of the space junk is negligible.

What is the rise in the internal energy of the satellite and space junk combined?

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Expert Answer

Step 1

Given data:

Radius of satellite = 5.4 m

Mass of satellite = 300 kg

Velocity = 2600 m/s

Initial angular speed = 2 rad/s

Mass of junk = 5.1 kg

New velocity =  2200

Step 2

Total energy of the system after they combined

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1 E I mv2 + - Mv ....(1) 2 2 where, I is the moment of inertia is the angular momentum mis the mass of satellite M is the mass of junk

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Step 3

Moment of inertia of the satelli...

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2 5 where m= mass r= radius Plugging in the given values: 2 I -x 300 x (5.4) I 3499.2 kg.m

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