A block of mass 90 kg sits on a slope with an angle of inclination 12° above the horizontal. The coefficients of friction between the block and the slope are µk = 0.03 and µs = 0.2.
a. What is the maximum frictional force that will allow the block to stay in place?
b. At what angle of inclination will the block start to slide down the slope?
My Question: I am not looking for these two questions to be answered, however, the question has caused me to doubt my understanding of static and kinetic friction re: incline planes.
When i calculated the the angle at which the block would begin to slide, using the arc tangent of 0.2 i got an angle less than 12 degrees. However, the question is suggesting that the block is at rest with when the incline plane is at 12 degrees. What is my conceptual error in thinking?
My next question:
Wouldnt the minimum angle of the incline plane (tan inverse of 0.2) be needed in answering the first question? that is, having it placed in the formula for the static friction formula = 0.2 x 90kg x 9.81 x cos of (tan inverse of 0.2)? assuming that tan inverse of 0.2 was found already? Is there something wrong with the question or how am i thinking is conceptual flawed?
My Final Question: Is it that the maximum frictional force that allow the block to stay in place is based on whatever angle the incline plane is set at? So, for example, if the incline plane is lowered to an angle of 5 degrees, the max friction force will be adjusted, even though the block would slide at 11.31 degrees? Is it that if lowered to 5 degrees, that the max friction force to overcome would be different?
In other words: If a block is at rest on the incline plane at an angle of 30 degrees, would the maximum frictional force that would allow the block to stay in place be calculated using 30 degrees, OR would we have to find the minimum angle of the incline plane needed for the block to slide before we can determine the maximum frictional force? That is, find that minimum angle and then substitute it in the formula for fs(max) = UsMgcos (minimum angle needed for block to slide)?
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