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A house is built on the top of a hill with a nearby slope at angle

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A house is built on the top of a hill with a nearby slope at angle θ = 45o(Figure). An engineering study indicates that the slope angle should be reduced because the top layers of soil along the slope might slip past the lower layers. If the coefficient of static friction between two such layers is 0.5, what is the least angleФthrough which the present slope should be reduced to prevent slippage?

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New slope Original slope-

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Fundamentals of Physics

Fundamentals of Physics

ISBN: 978-0471758013

8th Extended edition

Authors: Jearl Walker, Halliday Resnick

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Static friction and kinetic friction are two types of friction that occur when two objects are in contact with each other. Static friction is the force that must be overcome to initiate motion between two surfaces that are in contact with each other but are not moving relative to each other. It is caused by the interlocking of rough surfaces at the microscopic level, and it increases as the force pushing the surfaces together increases. Once motion between the surfaces starts, the static friction is no longer present. Kinetic friction, also known as sliding friction, is the force that opposes the motion of two surfaces that are in contact with each other and are moving relative to each other. It is caused by the rubbing of the surfaces against each other and the resistance of the molecules in the surfaces to being moved. Kinetic friction is generally less than static friction, but it can still be a significant force, especially at high speeds. Both static and kinetic friction can be quantified using a coefficient of friction, which is a dimensionless number that represents the ratio of the frictional force between two surfaces to the normal force (the force perpendicular to the surfaces). The coefficient of static friction is typically greater than the coefficient of kinetic friction for a given pair of surfaces, because it takes more force to overcome the interlocking of the surfaces at rest than to maintain motion once it has started.

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