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A uniform board is leaning against a smooth vertical wall. The board is at an ange above the horizontal ground the coefficient of static friction between the ground and the lower end of the board is 0.650. Find the smallest value for the angle such that the lower end of the board does not slide along the ground.

I've tried drawing all the forces. I made the sum of the forces in the y direction equal to zero, the x direction zero, and the sum of all the torques to equal to zero. I came up with that 0.650 = the normal foce exerted by the wall divided by the force exterted by the weight of the board = the lever arm of the weight of the board in the center divided by the lever arm of the normal force of the wall. Then I used tan(theta) = 0.65 and got theta to be 33 degrees.

However this answer isn't right. the answer is 37.6 degrees. What should I do to get this answer?

smooth means that there is no friction exerted by the wall.

I've tried drawing all the forces. I made the sum of the forces in the y direction equal to zero, the x direction zero, and the sum of all the torques to equal to zero. I came up with that 0.650 = the normal foce exerted by the wall divided by the force exterted by the weight of the board = the lever arm of the weight of the board in the center divided by the lever arm of the normal force of the wall. Then I used tan(theta) = 0.65 and got theta to be 33 degrees.

However this answer isn't right. the answer is 37.6 degrees. What should I do to get this answer?

smooth means that there is no friction exerted by the wall.

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