The coefficient of static friction is 0.60 between the two blocks in figure. The

Question

The coefficient of static friction is 0.60 between the two blocks in figure. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force causes both blocks to cross a distance of 5.0 , starting from rest.

What is the least amount of time in which this motion can be completed without the top block sliding on the lower block?

http://session.masteringphysics.com/problemAsset/1383206/5/knight_Figure_08_32.jpg

The coefficient of static friction is 0.60 between the two blocks in figure. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force causes both blocks to cross a distance of 5.0 , starting from rest. What is the least amount of time in which this motion can be completed without the top block sliding on the lower block?

Explanation / Answer

s = ut + at^2/2

5 = 0 + at^2/2

t = ?10/a

so t - min , F - max.

F -0.20 x 7g= (4 + 3)a

a = (F - 13.734)/7

on 4kg : F - 0.60 x 4g = 4a

F - 23.544 = 4 x (F - 13.734)/7

3F/7 = 23.544 - 7.848

F = 36.63 N

a = 36.63 - 13.734 /7 = 3.27 m/s2

t = ?10/3.27 = 1.75 sec

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