Someone is pushing a box against an incline with a force of magnitude \"F,\" dir

Question

Someone is pushing a box against an incline with a force of magnitude "F," directed perpendicular to the incline's slope. The mass of the box is "m," the coefficient of static friction between the box and the incline is "u," and the angle of the incline is "theta." Assume that "tan theta > u", which means that the incline is steep enough that the box would slide down it without the help of the pushing force F.

a. What is the minimum value of F that would keep the box from sliding down the incline?

b. Explain briefly why pushing the crate perpendicular to the incline can keep it from sliding down along the incline.

Explanation / Answer

a)Force balance

F=inclined force-frictional force

F=mgsin? -?mgcos?

b)mgcos? act perpendicular to the inclined

while you push the crate perpendicular to the incline it increases the frictional force component

and resist from sliding down

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