8 & 9

Asked by Harshhacker2580 | 19th Apr, 2020, 07:56: AM

Expert Answer:

Case (a)
 
Free body diagram for case(a) is shown above.  F is applied force  and f is friction force
 
Let us consider friction is static so that due to applied force whole system moves with acceleration a
 
When whole system moves together with acceleration a, we have 
 
a = F / ( m1 + m2 )  = ( F / 50 )
 
By applying Newtons law on block of mass m1 ,   F - f = m1 a
 
By applying Newtons law on block of mass m2 ,   f - F +F = m2 a  i.e. f = m2a = 30(F/50) = 0.6F
 
If friction is static of nature, f ≤ μk N  or  f ≤ μk m1g  or  f = 0.6F ≤ 0.5 × 20 × 9.8 .......(1)
 
From above eqn.(1) , we get Fmax = 163.3 N
 
In case(a)-(i) , F = 160 N , hence friction is static, system moves with acceleration a = 160/50 = 3.2 m/s2
 
In case (a)-(ii), F = 175 N > Fmax
 
Hence friction is kinetic in nature, both mass blocks will move with different acceleration
 
For block of mass m1 ,  F - f = 175 - ( 0.3 × 20 × 9.8) = 20 a1  or   a1 = 5.81 m/s2
 
For block of mass m2 ,  f  = m2a2   or   (0.3 × 20 × 9.8 ) = 30 a2    or  a2 = 1.96 m/s2
-------------------------------------------------------------------------------------
 
Free body diagrams for case(b) are given above. First we get the maximum force for which whole system moves together.
 
By applying Newtons second law on mass m1 , we get  F - f = m1 a
 
By applying Newtons second law on mass m2 , we get  f - F = m2 a
 
By solving above equations we get a = 0 and f = F
 
If there is no sliding , f  < 0.5 × 20 × 9.8   or f < 98 N
 
Maximum force for no sliding is 98 N
 
Since applied force is 175 N, friction is kinetic in nature and blocks move with different acceleration
 
for block of mass m1 ,  acceleration a1 = ( F - f ) / m1 = [ 175 - (0.3×20×9.8) ] / 20 = 5.81 m/s2
 
for block of mass m2 ,  acceleration a2 = ( f - F ) / m2 = [  (0.3×20×9.8) -175 ] / 30 = - 3.87 m/s2
 
-----------------------------------------------------------------------
 
If multiple questions are asked, only first question will be answered
 



Answered by Thiyagarajan K | 19th Apr, 2020, 08:18: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.