Question

A block is kept on a horizontal table.The table is undergoing simple harmonic motion of frequency $3Hz$ in a horizontal plane.The coefficient of static friction between block and the table surface is $0.72$. Find the maximum amplitude (in cm) of the table at which the block does not slip on the surface.

( Take $g=10m/s^2$ and ${\pi }^2=10$ )

Answer 1

For maximum amplitude force due to friction must be equal to force on block.
So we can write

$m{\omega }^{2}A=\mu mg$

$\Rightarrow A=\frac{\mu g}{{\omega }^2}$

But $\omega =2\pi f$

$\Rightarrow A=\frac{0.72\times 10}{4{\pi }^2\times 9}$

By solving, we get,

$A=2cm$