A 50kg box that is resting on a level floor must be moved. The Coefficient of st

Question

A 50kg box that is resting on a level floor must be moved. The Coefficient of static friction between the box and the floor is 0.6. One way to move the box is to push down on it at an angle 'theta'; with the horizontal. Another method is to pull up on the box at 'theta' with the horizontal.  Calculate the force necessary to move the box by each method if 'theta' = 30 degrees and compare the answer with the results when 'theta' = 0 degrees.
My teacher went over a problem in class, but i didnt get it at all.... i need help on how to do it...

Explanation / Answer

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First of all when we push down at an angle we increase the normal force, but if we push up at an angle we decrease it.

To compare:

F=N (where N is the normal force which in this case is just W=mg), so F=mg=(0.6)(50kg)(9.81m/s2)=294.3N would be the force needed.

When the angle is changed our normal force also changes. Create a free body diagram to see the difference.

Now in the y direction we have N+FSin-mg=0, and in the x direction we have FCos-f=0 or FCos=N=(mg-FSin)=mg-FSin or FCos+FSin=mg and F(Cos+Sin)=mg ,so F=(mg)/(Cos+Sin)=212.4 N.

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