Hello Everyone!
I am having some difficulty understanding question 214 regarding friction. The question asks:
"A block rests on a flat board. One end of the board is slowly lifted until the block begins to slide. If the block begins to slide when the board is at angle θ with the horizontal, which of the following represents the coefficient of static friction between the block and the board?"
The answer is sinθ /cosθ and EK's explanation is that the maximum static frictional force is given by μmgcosθ. The maximum static frictional force occurs just before the block begins to move. At that moment the block is in static equilibrium, so the net force is zero. That means the force up the plane is equal to the force down the plane. The force down the plane is mgsinθ. The force up the plane is static friction thus μmgcosθ=mgsinθ, so μ=sinθ/cosθ.
What I don't understand is why the static frictional force would be equal to mgcosθ. I understand why the force down the plane is mgsinθ, but if its static force is equivalent to the force down the plane, why does it equal mgcosθ?
I am having some difficulty understanding question 214 regarding friction. The question asks:
"A block rests on a flat board. One end of the board is slowly lifted until the block begins to slide. If the block begins to slide when the board is at angle θ with the horizontal, which of the following represents the coefficient of static friction between the block and the board?"
The answer is sinθ /cosθ and EK's explanation is that the maximum static frictional force is given by μmgcosθ. The maximum static frictional force occurs just before the block begins to move. At that moment the block is in static equilibrium, so the net force is zero. That means the force up the plane is equal to the force down the plane. The force down the plane is mgsinθ. The force up the plane is static friction thus μmgcosθ=mgsinθ, so μ=sinθ/cosθ.
What I don't understand is why the static frictional force would be equal to mgcosθ. I understand why the force down the plane is mgsinθ, but if its static force is equivalent to the force down the plane, why does it equal mgcosθ?
