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Tension

In the system...

Question

In the system shown above, find $a, T_{1}, T_{2}, T$ . (masses are in Kg).

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Solution

The whole system is accelerating downward from right with acceleration 'a'.
All force and tension are acting as shown in fig. or we can draw tree body diagram.
FBD
Now, applying law of motion
$F_{n e t} = m a s s \times a c c e l e r a t i o n$
For FBD is
$T_{1} - 40 = 4 a$ ...(i)
For FBD (ii)
$T = T_{1} + T_{1} = 2 T_{1}$ ...(ii)
For FBD (iii)
$30 + T_{2} - T_{1} = 3 a$ ...(iii)
For FBD (iv)
$30 - T_{2} = 3 a$ ....(iv)
Now,
Adding eqn. (i), (iii) and (iv)
we get
$(T_{1} - 40) + (30 + T_{2} - T_{1}) + (30 - T_{2}) = 4 a + 3 a + 3 a$
$\Rightarrow 20 = 10 a$
$\Rightarrow a = 2 m s^{- 2}$
From eq. (iv)
$30 - T_{2} = 3 a$
$\Rightarrow 30 - T_{2} = 6$
$T_{2} = 30 - 6 = 24 N$
From eqn. (i)
$T_{1} - 40 = 4 a$
$\Rightarrow T_{1} = 4 \times 2 + 40 = 48 N$
From eqn. (ii)
$T_{1} - 40 = 4 a$
$\Rightarrow T = 2 T_{1} \Rightarrow T = 2 \times 48$
$= 96 N$
Hence, $a = 2 m^{- 2}, T = 96 N, T_{2} = 24 N, T_{1} = 42 N$

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In the system shown above, find a,T1,T2,T. (masses are in Kg).

In the system shown above, find $a, T_{1}, T_{2}, T$ . (masses are in Kg).