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A system of masses is shown in fig with masses and coefficients of friction indicated .Calculate the max value of F for which there is no slipping anywhere,the minimum value of F for which B slides on C,the minimum value of F for which A slips on B.

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Asked by m.nilu 16th August 2018, 7:43 PM
Answered by Expert
Answer:
1. no Slip anywhere 
 
whole system moves with acceleration a, which is given by,  a = (F-μN)/(20+30+40) = (F-88.2) / 90 m/s2 ................(1)
where μ is the friction coefficient between ground and block-A. N is the normal reaction force between the surfaces of ground and block-A
 
from the free body diagram given for block-A, we get the no slip condition for block-A is ( m× a )< f ,
where f is frictional force between the surfaces of A and B.
 
m× a < μ×m×g .........(2)
 
using (1) and (2), we can write (F-88.2) < 90×μ×g  or ( F-88.2) < 90×0.1×9.8  or F < 176.4 N .................(3)
 
Hence if the applied force F is less than 176.4 N, there will not be any slip between blocks.
 
2. Block-B sliding on Block-C
 
Free body diagram of block-B is given in figure.
we can see that if applied force exceeds sum of firctional forces f1 and f2 , block-B slides on block-C
 
F >(f1 + f2) = (0.1×20 + 0.2×50)×9.8 = 117.6 N
 
3. block-A slips on Block-B
As we already calculated for 'no slip anywhere', block-A slips if applied force exceeds 176.4 N
 
Answered by Expert 27th August 2018, 3:47 PM
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