Two blocks with different mass are attached to either end of a light rope that p

Question

Two blocks with different mass are attached to either end of a light rope that passes over a light, frictionless pulley that is suspended from the ceiling. The masses are released from rest, and the more massive one starts to descend. After this block has descended a distance 1.10 m , its speed is 3.00 m/s .

a)If the total mass of the two blocks is 13.0 kg , what is the mass of the more massive block?

Take free fall acceleration to be 9.80 m/s2 .

b)What is the mass of the lighter block?

Take free fall acceleration to be 9.80 m/s2 .

Explanation / Answer

Let the masses are m1 & m2 and m2>m1
By v2 = u2 + 2as
=>(3.00)2 = 0 + 2 x a x 1.10
=>a = 9/2.2 m/s2 = 4.09m/s2
Let the tension in the string is T Newton:-
=>By balancing the forces on each mass:-
=>T - m1g = m1a ---------------(i)
& m2g - T = m2a ---------------(ii)
=>By (i) + (ii) :-
=>(m2-m1)g = (m1+m2)a
=>m2 - m1 = 13 x 4.09/9.8
=>m2 - m1 = 5.42 --------------(iii)
& m1+m2 = 13 ---------------(iv)[given]
By (iii) + (iv):-
=>m2 = 9.21 kg {answer for (A)}
=>m1 = 3.79 kg {answer for (B)}

Hope this helps. :)

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