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

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Unformatted text preview: 5.74: a) The normal force will be mg cos + F sin , and the net force along (up) the ramp is F cos - mg sin - s ( mg cos + F sin ) = F (cos - s sin ) - mg (sin + s cos ). In order to move the box, this net force must be greater than zero. Solving for F, sin + s cos F > mg . cos - s sin Since F is the magnitude of a force, F must be positive, and so the denominator of this expression must be positive, or cos > s sin , and s < cot . b) Replacing s with k with in the above expression, and making the inequality an equality, sin + k cos F = mg . cos - k sin ...
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