# Kinetic energy and momentum of two satellites colliding

## Homework Statement

Two satellites in space collide inelastically. What happens to the kinetic energy and momentum?
a. both are conserved
b. KE conserved but momentum reduced
c. KE reduced but momentum conserved
d. both are reduced
e. KE reduced but momentum increased

## Homework Equations

elastic and inelastic collision

## The Attempt at a Solution

KE is reduced because the collision is inelastic (there is some KE transforms into other energy during collision).

Momentum is only conserved for closed system (no external force acting on object). In this case momentum is conserved because all the gravitational forces acting on each satellite are considered internal forces?

How to differentiate between internal and external force? Thanks

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haruspex
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How to differentiate between internal and external force? Thanks
the question is in regard to the system consisting of the two satellites. There are no forces on it coming from outside.

songoku
DrClaude
Mentor
KE is reduced because the collision is inelastic (there is some KE transforms into other energy during collision).

Momentum is only conserved for closed system (no external force acting on object). In this case momentum is conserved because all the gravitational forces acting on each satellite are considered internal forces?

How to differentiate between internal and external force? Thanks
Gravity is definitely an external force here. But as @haruspex said, there is no mention of the satellites orbiting something. And even if they were, I think you can neglect the action of gravity for the duration of the collision.

songoku
How can I analyze whether momentum is conserved or not?

Let say two balls moving on frictionless surface in opposite direction collide. Is the normal force acting on each ball considered external force? If yes, why momentum conserved?

How about if there is friction with same magnitude acting on both balls? Is the momentum conserved?

Thanks

haruspex
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2020 Award
Let say two balls moving on frictionless surface in opposite direction collide. Is the normal force acting on each ball considered external force?
You need to define "the system". If it includes both balls then any force the balls exert on each other is internal.
why momentum conserved?
Because action and reaction are equal and opposite. If in period δt that force is F then the impulses they exert on each other are Fδt and -Fδt, so the net momentum change is zero.

songoku
jbriggs444
Homework Helper
How about if there is friction with same magnitude acting on both balls? Is the momentum conserved?
By your hypothesis, the balls are moving in opposite directions and the frictional force on each is of equal magnitude. Accordingly, the net force imparted by friction on the system consisting of the two balls is zero. Momentum of that system is conserved (barring the existence of other forces not yet mentioned).

If the system is expanded to consist of the two balls plus the surface then the frictional forces are internal and cannot contribute to a violation of momentum conservation. Again, momentum of the system is conserved (barring the existence of other forces not yet mentioned).

[I assume that there is nothing fancy going on with top-spin, "English", a moving table or the like. So the frictional force on each ball acts opposite to the direction of that balls motion.

songoku
You need to define "the system". If it includes both balls then any force the balls exert on each other is internal.

Because action and reaction are equal and opposite. If in period δt that force is F then the impulses they exert on each other are Fδt and -Fδt, so the net momentum change is zero.
Sorry, by normal force I mean the force between the ball and the surface, not the action and reaction force between the two balls when they collide.

haruspex