Block mover
A block rests on a 10 meter long board which is attached to the ground by a hinge on one end. The other end can be lifted to any height between completely horizontal and vertical. The coefficient of static friction between the block and the board is 0.7. You slowly lift the board. The block will start moving when the angle between the hinged end of the board and the ground reaches what value? (Nearest whole angle value)
The answer is 35.
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1 solution
The force pulling the block down the incline is mgsin(A). The static friction force is mgcos(A) multiplied by the coefficient of static friction. The block will begins to move once the pulling force exceeds the frictional force. This begins to happen when the pulling force and frictional forces are equal:
mgsin(A) = mgcos(A)(coefficient of static friction)
this reduces to
sin(A) = cos(A)(coefficient of static friction)
sin(A)/cos(A) = tan(A) = coefficient of static friction.
coefficient of static friction = 0.7
inv(tan)(0.7) = 35 degrees