A block is kept on a horizontal rough table (μ = 0.6) executing simple harmonic motion with amplitude 3cm. Find the maximum frequency at which the block does not slip over table.

Solution

Given,
Coefficient of friction, μ = 0.6 and
Amplitude, A = 3 cm
Let m be the mass of block and ω the maximum frequency of oscillation.
The limiting friction between block and table is,

F_limiting = μmg

The maximum acceleration of table is,

a_max = ω²A

The maximum pseudo force on the block is,

F_pseudo = ma_max = mω²A

For the block not to slip over the table, the maximum pseudo force should not exceed the limiting friction.
Therefore,
$space space space space space space space space space space space space space space space space mω squared straight A equals μmg space rightwards double arrow space space straight omega equals square root of μg over straight A end root equals square root of fraction numerator 0.6 cross times 980 over denominator 3 end fraction end root equals 14 space rad divided by straight s$
$straight omega$ is the maximum frequency at which the block does not slip over the table.

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

A block is kept on a horizontal rough table (μ = 0.6) executing simple harmonic motion with amplitude 3cm. Find the maximum frequency at which the block does not slip over table.

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