> Q. A body of mass $m$ rests on a horizontal floor with which it has a coefficient of static friction $mu$. It is desired to make the body move by applying a minimum possible force $overrightarrow{F}$ as shown in the diagram. The values of $ theta $ and $ {{F}_{min }} $ shall be respectively equal to – LIVE ANSWER TODAY

Q. A body of mass $m$ rests on a horizontal floor with which it has a coefficient of static friction $mu$. It is desired to make the body move by applying a minimum possible force $overrightarrow{F}$ as shown in the diagram. The values of $ theta $ and $ {{F}_{min }} $ shall be respectively equal to

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A body of mass $m$ rests on a horizontal floor with which it has a coefficient of static friction $mu$. It is desired to make the body move by applying a minimum possible force $overrightarrow{F}$ as shown in the diagram. The values of $ theta $ and $ {{F}_{min }} $ shall be respectively equal to

Solution:

$ mu =tan theta $ $ therefore $ $ theta ={{tan }^{-1}}mu $ $ therefore $ $ sin theta =frac{mu }{sqrt{1+{{mu }^{2}}}} $ and $ cos theta =frac{1}{sqrt{1+{{mu }^{2}}}} $ $ {{F}_{min }}=frac{mu mg}{cos theta +sin theta } $ $ =frac{mu mg}{frac{1}{sqrt{1+{{mu }^{2}}}}+frac{{{mu }^{2}}}{sqrt{1+{{mu }^{2}}}}} $ $ =frac{mu mg}{sqrt{1+{{mu }^{2}}}} $

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