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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

===========

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.

=======================

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.

=======

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 ???

==============

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

===============

19.

F - mg = ma

F - 2 * 10 = 2 * 5

F = 30 N

==================

20.

F - mg = m a = - m g as F is upwards, and a = -g downwards

F = 0 N

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

===========

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.

=======================

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.

=======

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 ???

==============

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

===============

19.

F - mg = ma

F - 2 * 10 = 2 * 5

F = 30 N

==================

20.

F - mg = m a = - m g as F is upwards, and a = -g downwards

F = 0 N