# A box of mass m rests on a rough, horizontal surface with a coefficient of static friction μs. If a force F with arrowp is applied to the box at an angle θ as shown, what is the minimum value of θ for which the box will not move regardless of the magnitude of F with arrowp? (Use any variable or symbol stated above as necessary

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1. There is some frictional force that acts against the applied Force F to prevent the motion of the box.
F can be divided into its vertical component, Fsinθ, and its horizontal component, Fcosθ. The horizontal component is the one that acts against the frictional force and can cause the box to move.

As F goes on increasing, there will eventually come a time when Fcosθ is larger than the frictional force, for any non-zero value of cosθ.

But when θ is equal to 90 degrees, then there is no horizontal component, as Fcosθ is equal to zero. Hence, at this angle (when the force is directed into the ground), the box will not move regardless of the value of F, because cosθ is zero.

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