Solving Quick Momentum Problems: Equal Force and Stopping Time Comparison

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When two objects with equal momentum are brought to a stop using the same force, the time taken to stop each object is the same, despite their differing masses. The reasoning is based on the relationship between force, momentum change, and time, where equal forces result in equal changes in momentum over the same time period. The distance each object travels while stopping is also equal, as the mass cancels out in the equations governing motion. The discussion emphasizes that constant force applied to different masses with the same momentum leads to identical stopping times and distances. Understanding these principles is crucial for solving momentum-related problems in physics.
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Homework Statement



Two objects have the same momentum, object 1 is heavier than object 2. You bring each to a stop by applying a force of equal magnatude in each case. How does the time to stop each object compare and the distance.

Homework Equations


mv=p f=ma etc.


The Attempt at a Solution


I think the the time and distance are equal in both cases because if you solve each quantity for a and v in each case you get an equation where you divide the mass by sum number and set it equal to zero, so the mass cancels out. Just looking to confirm.
 
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You can also think of it in the following way with a constant force:

<br /> F = \frac{{dp}}{{dt}}<br /> thus equal forces will result in equal momenta changes over the same period of time in this case.
 
lubuntu said:
I think the the time and distance are equal in both cases
What does distance and force relate to? Is that the same for different masses that happen to have the same momentum?
 

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