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A force F is applied on a block of mass m in such a way that it stays in contact with another block of mass M over a frictionless surface. What is the required force for the two blocks to stay in contact? The static coefficient friction between the two block is [tex]\mu_{s}[/tex].

NOTE: mass m is not in contact with the ground, and M > m.

My solution is

Acceleration on mass m is

[tex]a_{m}=\frac{F}{m}[/tex]

Acceleration on mass M is

[tex]a_{M}=\frac{F}{M}[/tex].

Since, m > M, the reaction force on m is

[tex]F_{R}=m(\frac{F}{m}-\frac{F}{M}[/tex])

Therefore,

[tex]\mu_{s}m(\frac{F}{m}-\frac{F}{M}) \geq mg[/tex]

So the required force is

[tex]F \geq \frac{Mm}{\mu_{s}(M-m)}g[/tex]

Is this correct?

NOTE: mass m is not in contact with the ground, and M > m.

My solution is

Acceleration on mass m is

[tex]a_{m}=\frac{F}{m}[/tex]

Acceleration on mass M is

[tex]a_{M}=\frac{F}{M}[/tex].

Since, m > M, the reaction force on m is

[tex]F_{R}=m(\frac{F}{m}-\frac{F}{M}[/tex])

Therefore,

[tex]\mu_{s}m(\frac{F}{m}-\frac{F}{M}) \geq mg[/tex]

So the required force is

[tex]F \geq \frac{Mm}{\mu_{s}(M-m)}g[/tex]

Is this correct?

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