Two massege 8kg and 12kg are connected at two ends of a light inextensible string that goes over a frictionless pulley . Find the acceleration of the masses and the tension in the string when the masses are released.
Let m1 = 8 kg, m2 = 12 kg and tension in string = T
Mass m2 being heavy will move down with acceleration and mass m1 will move upward.
Applying Newtons second law of motion to each mass:
>For mass m1:
The equation of motion will be:
T – m1xg = ma …(i)
>For mass m2:
The equation of motion will be:
m2xg – T = m2xa …(ii)
Adding (i) & (ii),
(m2 – m1)g = (m1 + m2)a
a=[(m2 – m1)/(m1 + m2)g] …(iii)
= [(12 – 8)/(12 + 8) 10]
= 2 m/s^2
Therefore, acceleration of masses is 2 m/s^2
Now, substituting value of a in (ii),
m2xg – T = m2[(m2 – m1)/(m1 + m2)]g
T = [m2 – (m2^2 – m1 x m2)/(m1 + m2)]g
= [(2 x m1 x m2)/(m1 + m2)]g
= [(2 x 12 x 8)/(12 + 8)] x 10
= 96 N
Hence, the tension in the string is 96 N.
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