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Grade 11Mechanics

starting from rest a body slides down at 45 degree inclined plane in twice the time it takes to to slide down the same path when friction is absent.the coefficient of friction is?

Profile image of Babzz
8 Years agoGrade 11
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1 Answer

Profile image of Arun
ApprovedApproved Tutor Answer8 Years ago
Dear student
 
The normal force, N = mgsin45° 
The friction force, f = µN 
The weight force, W = mgcos45° (Not weight of object, but weight force along incline) 
The net force F = W-f 
Let F1 = Force with no friction, thus F1 = W 
Let F2 = Force with friction, thus F2 = W-f 
a1 = F1/m 
a2 = F2/m 
s = Vot + 1/2at^2 
Assume Vo = 0 (although it subtracts out anyway if it is equal to something) 
Since s is the same for both situations and t2 = 2*t1, 
1/2(a1)(t1)^2 = 1/2(a2)(2*t1)^2 
(a1)/(a2) = 4 
F1/F2 = 4 
W/(W-f) = 4 
W-f = W/4 
(3/4)W = f 
.75(mgcos45°) = µ(mgsin45°) 
µ = .75
 
 
 
Regards
Arun (askIITians forum expert)