Question

A man drags a block of mass 10 kg on a rough surface. What minimum force (at some angle from horizontal ) he should apply just to move the block (\mu =\frac{1}{\sqrt{3}}).

Answer 1

SOLUTION.

Let f be the force

m be the masd

Let Φ be the angle of the force with horizontal.

So Normal force acting = mg - fsinΦ

frictional force = μ(mg - fsinΦ)

Force (horizontal) = f cosΦ

FOR THE BLOCK MOVE HORIZONTALLY

f cosΦ > μ(mg - fsinΦ)

f cosΦ + μfsinΦ > μmg

f(cosΦ + μsinΦ ) > μmg

f > μmg/cosΦ + μsinΦ

Minimum value is ( μmg/cosΦ + μsinΦ)

μ = 1/√3

Required answer

mg/cosΦ√3 + sinΦ

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Answer 2

Answer:

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