problem05_70

University Physics with Modern Physics with Mastering Physics (11th Edition)

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5.70: It’s interesting to look at the string’s angle measured from the perpendicular to the top of the crate. This angle is of course ° 90 —angle measured from the top of the crate. The free-body diagram for the washer then leads to the following equations, using Newton’s Second Law and taking the upslope direction as positive: slope w string slope w string string slope w w string slope w cos cos ) sin ( sin 0 cos cos sin sin θ g m T θ g a m θ T θ T θ g m a m θ T θ g m = + = = + - = + - θ Dividing the two equations: slope slope string 0 cos sin tan g θ g a θ + = For the crate, the component of the weight along the slope is
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Unformatted text preview: c slope sin m g-and the normal force is . cos slope c θ g m Using Newton’s Second Law again: slope slope k c slope c k slope c cos sin cos sin θ g θ g a a m θ g m θ g m + = = +-μ which leads to the interesting observation that the string will hang at an angle whose tangent is equal to the coefficient of kinetic friction : 40 . 22 tan ) 68 90 tan( tan string k = ° = °-° = = θ...
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