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to move a crate across a rough floor ,you push on it at an angle of 21degrees below the horizontal. find the force necessary to star the crate moving ,given that the mass of the crate is32kg and the coefficient of static friction between the crate and the floor is o.57.

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    The normal (downward) force on the floor is M*g + F*sin21. (F is the applied force). To start the crate moving, the force F must satisfy the inequality:

    F*cos21 >or= (M*g + F*sin21)*0.57.
    0.9336 F >or= 178.8 N - 0.2043F
    1.138F >or= 178.8 N
    F >or= 157.2 N

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