A block P of mass is placed on a horizontal frictionless plane. A second block of same mass is placed on it and is connected to a spring of spring constant , the two blocks are pulled by distance . Block oscillates without slipping. What is the maximum

Question

A block P of mass $m$ is placed on a horizontal frictionless plane. A second block of same mass $m$ is placed on it and is connected to a spring of spring constant $k$ , the two blocks are pulled by distance $A$ . Block $Q$ oscillates without slipping. What is the maximum value of frictional force between the two blocks [2004]

Smart Achievers · Accepted Answer

(1)

Here acceleration is same for both $m$ and $k$ as block $A$ oscillates but does not slip. The $Q$ system oscillates with angular frequency $ω$ . The spring is stretched by $A$ .

Angular frequency of the system,

$ω = \sqrt{\frac{k}{m + m}} = \sqrt{\frac{k}{2 m}}$

Maximum acceleration of the system in SHM

$a_{\max} = A ω^{2} = A {(\sqrt{\frac{k}{2 m}})}^{2} = \frac{k A}{2 m}$

This acceleration to the lower block is provided by friction

$∴$ Maximum force of friction

$f_{\max} = m a_{\max} = m (\frac{k A}{2 m}) = \frac{k A}{2}$

Solution

1 $\frac{k A}{2}$

2 $k A$

3 $μ_{s} m g$

4 $zero$

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Solution

1 kA2

2 kA

3 μsmg

4 zero

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1 $\frac{k A}{2}$

2 $k A$

3 $μ_{s} m g$

4 $zero$