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A cup of coffee is on a table in an airplane flying at a constant altitude and a constant velocity. The coefficient of static friction between the cup and the table is 0.420 . Suddenly, the plane accelerates forward, its altitude remaining constant. What is the maximum acceleration that the plane can have without the cup sliding backward on the table? Use g = 9.81 m/s2.

The only thing I could figure out was the static friction force which came out to be 4.12 N. I'm stuck trying to figure out how to find the acceleration. Please help!

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  1. The force needed to move the cup is Force Max(F)= Coefficient of friction(U)times Mass (M)times Gravity(G)and the force exerted by the plane is Mass(M) times Acceleration(A). Set these equal to each other since the force needed to move the cup is going to be the same as the force exerted by the plane and solve for (A).
    UMG=MA
    M cancels out leaving
    UG=A
    so the acceleration of the plane is equal to the coefficient of friction multiplied by gravity.

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