The situation that will not affect momentum is:
mass reduced to 0.5m, speed increased to 2v
Explanation:
The momentum of an object is defined as
[tex]p=mv[/tex]
where
m is the mass of the object
v is its velocity
Let's call m the initial mass of object A and v its initial velocity, so its initial momentum is
[tex]p=mv[/tex]
Let's now analyze each situation to see how the momentum changes:
- mass reduced to 0.5m, speed increased to 2v
New momentum is:
[tex]p'=(0.5m)(2v)=mv=p[/tex] --> so momentum is unchanged
- mass reduced to 0.25m, speed increased to 1.25v
New momentum is:
[tex]p'=(0.25m)(1.25v)=0.31mv = 0.31 p[/tex] --> momentum has changed
- mass increased to 2m, speed increased to 2v
New momentum is:
[tex]p'=(2m)(2v)=4mv=4p[/tex] --> momentum has changed
- the direction of velocity reversed, speed kept at v
Since momentum is a vector, the direction also matters: therefore, if the direction of the velocity changes, the direction of the momentum changes as well, so the momentum has changed.
So the only situation that will not affect the momentum is
mass reduced to 0.5m, speed increased to 2v
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