Solving Quick Momentum Problems: Equal Force and Stopping Time Comparison

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SUMMARY

The discussion centers on the comparison of stopping time and distance for two objects with equal momentum, where one object is heavier than the other. The key conclusion is that when equal forces are applied to both objects, the time to stop and the distance traveled before stopping are indeed equal. This is derived from the relationship between force, momentum, and mass, specifically using the equation F = dp/dt, which confirms that equal forces lead to equal changes in momentum over the same time period.

PREREQUISITES
  • Understanding of momentum and its formula (p = mv)
  • Familiarity with Newton's second law (F = ma)
  • Basic knowledge of calculus, particularly derivatives
  • Concept of force and its relation to mass and acceleration
NEXT STEPS
  • Study the relationship between force and momentum in more complex systems
  • Explore the implications of varying mass on stopping distances in practical applications
  • Learn about the calculus of motion, specifically how derivatives apply to force and momentum
  • Investigate real-world examples of momentum conservation in collisions
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators looking to explain concepts of momentum and force in practical scenarios.

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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 magnitude 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:

[tex] F = \frac{{dp}}{{dt}}[/tex] 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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