Application of Newton's Laws of motion

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SUMMARY

The discussion focuses on calculating the minimum force (P) required to hold a 20kg block against a vertical surface at a 30-degree angle, considering a coefficient of friction of 0.2. The correct value for P is established as 202.2 N, contrasting with an incorrect calculation of 271.5 N. Participants emphasize the importance of incorporating the frictional force, which is dependent on P, into the equations used for the analysis. The equation mg + Fr = mg cos(theta) is identified as flawed due to the omission of P.

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A block of mass 20kg is pushed against a vertical surface at an angle of 30 degrees as shown. The coefficient of friction between the surface and the block is 0.2. What is the minimum magitude of P to hold the block still?


I got 271.5 when I tried but the answer is 202.2
 

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How did you come to the 271.5?
 
Have you taken into account the fact that the frictional force will depend also on P, ie how strongly it is being pressed against the wall?
 
I came up withthe equation

mg+ Fr = mg cos theta
 
That equation does not look right. Where is P?

Also how do you determine Fr. You need another equation right?
 

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