How Does Angle Affect Block Acceleration?

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The discussion centers on determining the angle that maximizes the acceleration of a block being pushed with a force at an angle below the horizontal. The optimal angle for maximum acceleration is identified as 20.8° above the horizontal, resulting in a maximum acceleration of 43 m/s². Participants suggest using a free body diagram to analyze the forces acting on the block, which is essential for applying Newton's second law to find the correct acceleration. One user expresses difficulty in calculating the maximum acceleration despite knowing the angle, indicating a need for clarification on the application of the relevant equations. The conversation emphasizes the importance of accurately accounting for all forces to achieve the correct acceleration value.
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finding maximum velocity??

A block of mass M = 275.0 g sits on a horizontal tabletop. The coefficients of static and kinetic friction are 0.54 and 0.38, respectively, at the contact surface between table and block. The block is pushed on with a 12.0 N external force at an angle θ below the horizontal.
(a) What angle will lead to the maximum acceleration of the block for a given pushing force?
20.8° above the horizontal

(b) What is the maximum acceleration?
43 m/s^2

those were the answer given. I know how you get the degrees but i am having trouble how to find the maximum acceleration... can you guy help me?
 
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Well, if you managed to find the angle, you should have no trouble plugging it into the equation you found for the maximum acceleration...
 


well i did. a=(sin20.8)(9.8)(12)= 41.7 m/s^2.. its close but it is not the right answer.
 


Perhaps you should start with a free body diagram of the forces, and determine the net horizontal force acting. Newton's second law then provided the acceleration.
 

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