A given object takes n times as much time to slide down a 45 degree rough incline as it takes to slide down a perfectly smooth 45 degree incline.What will be the coefficient of kinetic friction between object and incline ??
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Here I have taken n= √2times
from the question it is clear that
T(rough) =✓2 T(smooth)
t1= √2 t2
From the fbd
(For rough surface)
N = mgcos45...........(1). And. f = uN.........(2)
From Newton law
Net F = ma1
mg(sin45)- u mg(cos 45) =ma1
Solving......
a1 =( 1-u)g/√2
(For smooth surface)
mgsin45 = ma2
a2 = g/√2
Now from the common sense we can assume that both the block have to cover the same distance now using the equation of kinematics
S = ut + 1/2 at^2. Where u = 0 m/s
S1 = 1/2*(1-u)g/√2*(√2t)^2. (Where * means multiply)
S2= g/√2 *(t)^2
Now S1 =S2
U=1/2
from the question it is clear that
T(rough) =✓2 T(smooth)
t1= √2 t2
From the fbd
(For rough surface)
N = mgcos45...........(1). And. f = uN.........(2)
From Newton law
Net F = ma1
mg(sin45)- u mg(cos 45) =ma1
Solving......
a1 =( 1-u)g/√2
(For smooth surface)
mgsin45 = ma2
a2 = g/√2
Now from the common sense we can assume that both the block have to cover the same distance now using the equation of kinematics
S = ut + 1/2 at^2. Where u = 0 m/s
S1 = 1/2*(1-u)g/√2*(√2t)^2. (Where * means multiply)
S2= g/√2 *(t)^2
Now S1 =S2
U=1/2
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