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].(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A Problem on Friction Coefficient

**Physics Forums | Science Articles, Homework Help, Discussion**