 # A has mass 40 kg, B is of 15 kg and F is 500 N parallel to a smooth inclined plane. The system is moving together. Show that the acc of the system is 45/11 m /s2  and the least coeff  of friction  b/w A and B is 9 (3)1/2  / 53.

13 years ago

Free body diagrams of two blocks are shown below:

on balancing forces on each block in X and y axis respectively, we have:

for A:

N -150 = 7.5a

f = uN =13a

for B:

0.866R - N =150 + 20a

433 -0.5R -uN = 34.64a   here u is coeff. of friction btn 2 blocks

on solving above equations, we have

N = 150 + 7.5a

433 - 47.64a = 0.5R

so, its     750 - 82.5a = 300 + 27.5a

450 = 110a

the acc of the system a = 45 / 11 m/sec2

the coeff. of friction is

u(150 + 20a ) = 13a

so u = 13a / (150+20a)

The coeff. of friction is    u = 0.2942 or 9.(3)1/2 / 53.

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