What is the gravitational potential energy of a book with a mass of 0.3 kg on a 1.0 high desk?
2 answers:
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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
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
Let's now analyze each situation to see how the momentum changes:
- mass reduced to 0.5m, speed increased to 2v
New momentum is:
--> so momentum is unchanged
- mass reduced to 0.25m, speed increased to 1.25v
New momentum is:
--> momentum has changed
- mass increased to 2m, speed increased to 2v
New momentum is:
--> 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
Learn more about momentum:
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Answer:
The correct answer is option 'c': Smaller stone rebounds while as larger stone remains stationary.
Explanation:
Let the velocity and the mass of the smaller stone be 'm' and 'v' respectively
and the mass of big rock be 'M'
Initial momentum of the system equals
Now let after the collision the small stone move with a velocity v' and the big roch move with a velocity V'
Thus the final momentum of the system is
Equating initial and the final momenta we get
Now since the surface is frictionless thus the energy is also conserved thus
Similarly the final energy becomes
\
Equating initial and final energies we get
Solving i and ii we get
Using this in equation i we get
Thus putting v = -v' in equation i we get V' = 0
This implies Smaller stone rebounds while as larger stone remains stationary.