The ratio of acceleration of block A placed on a smooth incline with block B placed on a rough incline is 2:1. The coefficient of kinetic friction acting on a block and the incline is ??
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Answer:
∑F
y
=0
⇒ N=10 gcosθ/m
A
=10 kg
∑F
x
=m
A
.a
A
⇒ 10 g.sinθ=10.a
A
⇒ a
A
=g sinθ−−−(i)
∑F
y
=0
N=20 g cosθ−−−−(ii)/m
B
=20 kg
∑F
x
=m
B
a
B
⇒ 20 g sinθ−fk=20 a
B
⇒ 20 g sinθ−μ
k
.20 gcosθ=20a
B
g
f
k
=μ
k
.N
=μ
k
.20 gcosθ
from (ii)
⇒ sinθ−μ
k
.cosθ=
g
a
B
⇒ a
B
=g(sinθ−mu
k
cosθ)−−−(iii)
(i)÷(iii):
a
B
a
A
=
g (sinθ−μ
k
cosθ)
g sinθ
=
sinθ(1−μ
k
.cotθ)
sinθ
⇒
1
2
=
1−μ
k
1
⇒ (1−μ
k
)2=1
θ=45
o
cot45
o
=1
⇒ 2−2μ
k
=1 ⇒
μ
k
=0.5
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