Momentum and stopping distance

AI Thread Summary
When two objects have the same momentum but different masses, the heavier object will stop in a shorter distance when subjected to the same retarding force. This is because the kinetic energy (KE) of an object is inversely related to its mass when momentum is constant. The equation p = mv shows that for a constant momentum, an increase in mass results in a decrease in velocity, leading to lower kinetic energy. Consequently, with less kinetic energy, the heavier object requires a shorter stopping distance. Understanding the relationship between momentum, mass, and kinetic energy is crucial in solving this problem.
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Homework Statement



Two objects have different masses, but the same momenta. If you stop them with the same retarding force, which one will stop in the shorter distance. The heavier or lighter one? Or will both have the same distance?




Homework Equations





The Attempt at a Solution



Wouldn't the heavier one take more force to stop it, thus leading to a greater distance? However, the correct answer is that the heavier one will stop in the shorter distance. Explain, thanks!
 
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What's the equation which relates momentum to mass and velocity?
 
retarding force X distance moved = change in kinetic energy.
Can you find the relation between momentum and kinetic energy?
 
p=mv

change in KE=fd

KE=1/2m(v^2)


KE=p^2/2m

So basically, the greater the mass, the smaller the KE. And the smaller the KE, the smaller the distance. ok...thanks.
 

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