While moving in, a new homeowner is pushing a box across thefloor at a constant

Question

While moving in, a new homeowner is pushing a box across thefloor at a constant velocity. The coefficient of kineticfriction between the box and the floor is 0.41. The pushingforce is directed downward at an angle below thehorizontal. When is greater than a certain value, itis not possible to move the box, no matter how large the pushingforce is. Find that value of . answer: 68o While moving in, a new homeowner is pushing a box across thefloor at a constant velocity. The coefficient of kineticfriction between the box and the floor is 0.41. The pushingforce is directed downward at an angle below thehorizontal. When is greater than a certain value, itis not possible to move the box, no matter how large the pushingforce is. Find that value of . answer: 68o

Explanation / Answer

Let F be the force he is exerting on the box. The horizontal force he exerts on the box is equal to Fx= Fcos and the vertical (downward) force he exerts isFy = Fsin. When the box is not moving, that meansit is in equillibrium, i.e. the forces are balanced: Ffric = horizontal force (Fy)(coeff. of friction) = Fx Fsin(0.41) = Fcos tan = (1/0.41) =1.1816991o edit: Oops! I'm very sorry, I forgot to convert the angle intodegrees. The one I gave is in radians. = (1.1816991rad) (180o / rad) =67.7063711o

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