A block weighing W lb is placed upon a plane inclined at an angle theta with the horizontal Discuss what will happen if the angle of friction is a.) greater than theta; b.) equal to theta; c.) less than theta.
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The angle of friction is the maximum angle of incline (theta) for which the block will remain stationary on the plane without sliding down.
So if
the angle of friction is greater than theta, then the friction acting upward along the plane on the block will be equal to the component of weight acting downward along the plane and so the block will not slide. So will be the case where angle of friction = theta. The difference between the two cases is that if angle of friction is greater than theta, then you have the ability to increase theta further and still not have the block slide down.
If the angle of friction is less than theta, then ofcourse, the component of weight will outdo the maximum force that friction can exert on the object and so the object will slide down the plane.
So if
the angle of friction is greater than theta, then the friction acting upward along the plane on the block will be equal to the component of weight acting downward along the plane and so the block will not slide. So will be the case where angle of friction = theta. The difference between the two cases is that if angle of friction is greater than theta, then you have the ability to increase theta further and still not have the block slide down.
If the angle of friction is less than theta, then ofcourse, the component of weight will outdo the maximum force that friction can exert on the object and so the object will slide down the plane.
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Really "angle of friction"? That's a new one to me. But then they keep inventing new terms for the same old stuff all the time. That's how they rationalize their new book.
Anyway I suppose you read that K = tan(Theta) is the static coefficient where Theta is the critical value at which the block just starts to slide. So when theta > Theta the block slides and accelerates down the ramp and the coefficient of sliding friction k < K. When theta = Theta, if you're careful, nothing happens; the block just stands there like a block of wood...oh wait, it is a block of wood. And when theta < Theta, ditto, just sits there.
Anyway I suppose you read that K = tan(Theta) is the static coefficient where Theta is the critical value at which the block just starts to slide. So when theta > Theta the block slides and accelerates down the ramp and the coefficient of sliding friction k < K. When theta = Theta, if you're careful, nothing happens; the block just stands there like a block of wood...oh wait, it is a block of wood. And when theta < Theta, ditto, just sits there.