An object takes n times as much time to side down a 45° rough incline as it takes to slide down a perfectly smooth 45° incline. The coefficient d kinetic friction between the object and the indine is given by
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d=1-1/n²
In both cases, same distance has to be travelled and both start from rest, so
a1t1²=a2t2²
But t2=nt1, so
a1=n²a2
Now a1=gsin45° and a2=gsin45° - dcos45°
So, 1=(1-d)n²
d=1-1/n²
In both cases, same distance has to be travelled and both start from rest, so
a1t1²=a2t2²
But t2=nt1, so
a1=n²a2
Now a1=gsin45° and a2=gsin45° - dcos45°
So, 1=(1-d)n²
d=1-1/n²
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