Question

on ar rough S
is mou
mass 2K
A block of
akg
of coefficient of
frictional force on it
soving
friction
scroface
find the
0.5, find​

Answer 1

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Answer 2

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Let 'p' be the force applied too at an angle θ

From the free body diagram

R+Psinθ−mg=0

R+Psinθ+mg...(i)

μR−pcosθ=0...(ii)

Equn.(i) is μ(mg−Psinθ)−Pcosθ=0

⇒μmg=μPsinθ−Pcosθ⇒p=

μsinθ+cosθ

μmg

Applied force P should be minimum, when μsinθ+cosθ is maximum

Again, μsinθ+cosθ is maximum when its derivative is zero

∴d/dθ(μsinθ+cosθ)=0

⇒μcosθ−sinθ=0⇒θ=tan

1

μ

So, P=

μsinθ+cosθ

μmg

=

cosθ

μsinθ

+

cosθ

cosθ

μmg/cosθ

=

1+μtanθ

μmgsecθ

=

1+tan

2

θ

μmgsecθ

=

secθ

μmg

=

(1+tan

2

θ)

μmg

=

1+μ

2

μmg

Minimum force is

1+μ

2

μmg

at an angle θ=tan

−1

μ

.