Question

look at the attachement and answer the questyions

Answer 1

14. 
       T Cos 30 =  1 kg * a
       30 N - T cos 30 = 2 kg * a
       =>  3 a = 30      =>  a = 10 m/sec/sec
       =>  T  = 20/√3  N
       Normal reaction:    mg - T sin 30 = 1 * 10 - 20/√3 * 1/2 = 10 - 10/√3  N
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15. 
         m1 = 2 kg        m2 = 5 kg
         F - (m1 + m2) g = (m1 + m2 ) a      =>  F - 70 = 7 a
           So the pulley moves up only if  F > 70 Newtons.

     F = 70 N,  then accelerations are both 0, as the pulley still does not move up.
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16. 
       m2 g = tension    as m2 is at rest.
       m1 g Sin Ф - tension        as m1 is at rest.
         m1 Sin Ф = m2
     verify the options by substitution.
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17
       F1 = 10 N,  F2 = 20 N     
    F1 Cos 60  + F2 = 25 N     ---  in x direction
    F1 Sin 60 = 5√3 N         ---  in the y direction,  as block is at rest.
     resultant  =  √ [25² + (5√3)² ] = 26.46  N
             the result is supposed to be an integer???/
    Are you expected to write only the force in the x direction ???
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18.   m1 = 3 kg,        m2 = 2kg   
        F cos 60 =  m1 a - T
        T =  m2  a
       a = F * Cos 60  /(m1+m2)  = 1 m/s/s
     T = 2 N
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19.
           F - mg = ma
           F - 2 * 10 = 2 * 5
           F = 30 N
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20.
             F - mg  = m a = - m g          as  F is upwards, and a = -g  downwards
             F = 0 N