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.
My attempt:
I took a little piece of block with mass Δm, we know that Δm=mΔℓL.
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
μmgΔℓL=ma
a=μgΔℓL
I have this equation, but I don't know how to relate it with time.
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