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Wt is tension in given fig
Asked by Lashkkkuer | 28 Sep, 2022, 08:03: PM
Figure shows the tension forces acting along the rope. Let the sytem of masses is under the acceleration a.

If we write Newton's second law to the left side block of mass M, then we get

T1 - ( M g ) = ( M a ) ................................(1)

where T1 is the tension force acting along the rope between two blocks of equal masses M .

If we write Newton's second law to the right side block of mass M, then we get

(Mg) + T - T1  = ( M a ) ................................(2)

Where T is the tension force between right side block of mass M and other block of mass m.

If we write Newton's second law to the right side block of mass m, then we get

( mg ) - T = ( m a ) ................................(3)

If we add all the above equation, we get

mg = ( 2M + m ) a

Hence acceleration a =  [ m / (2M + m ) ] g  ........................(4)

Tension force T is determined from eqn.(3) as

T = m ( g - a )

If we substitute acceleration a using eqn.(4) , above expression after simplification will become

T = [ ( 2M ) / ( 2M + m ) ] g
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Asked by Lashkkkuer | 28 Sep, 2022, 08:03: PM
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