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The northwest face of Half Dome, a large rock in Yosemite National Park, makes an angle of

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The northwest face of Half Dome, a large rock in Yosemite National Park, makes an angle of θ = 7.0° with the vertical. Suppose a rock climber lying horizontal on the top is trying to support her unfortunate friend of equal mass who is hanging from a rope over the edge, as shown in Figure. If the friction is negligible (the top is icy!), at what acceleration will they slide down before the top partner manages to grab someone's hand and stop?

The northwest face of Half Dome, a large rock in Yosemite

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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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