You are helping a friend move into a new apartment. A box weighing 150 lbs needs

Question

You are helping a friend move into a new apartment. A box weighing 150 lbs needs to be moved to make room for a couch. You are taller than the box, so you reach down to push it at an angle of 50o from the horizontal. The coefficient of static friction between the box and the floor is 0.50 and the coefficient of kinetic friction between the box and the floor is 0.30. (a) If you want to exert the minimum force necessary, how hard would you push to keep the box moving across the floor? (b) Suppose you bend your knees so that your push is horizontal. How hard would you push to keep the box moving across the floor?

Explanation / Answer

(A) to keeep it moving, horizontal force have to overcome with kinetic friction.

in vertical,

N - W - F sin50 = 0

N = 150 + F sin50

fk = uk N = 45 + 0.3 F sin50

in horizontal,

Fcos50 - fk = 0

F (cos50 - 0.3 sin50) = 45

F = 109 lbs ............Ans

(B) in this case , N = W = 150 lbs

fk = uk N = 45 lbs

F - fk = 0

F = 45 lbs .....Ans

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