Saturday, May 31, 2014

homework and exercises - Plank stopping time



Problem: A plank of length L and mass m lies on a frictionless floor, if the plank has an initial velocity v, what is the stopping time of the block if it meets a floor with friction constant μ.



Problem Diagram


My attempt:


I took a little piece of block with mass Δm, we know that Δm=mΔL.



Now if I apply the Newton laws in this piece, I get the following equation:


Npiece=Δmg


Thus my friction is fr=μΔmg


If I apply Newton laws to the whole plank, I get:


fr=ma

μΔmg=ma
μmgΔL=ma


a=μgΔL


I have this equation, but I don't know how to relate it with time.




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