Problem 7.40 Two blocks with different mass are attached to either end of a ligh
ID: 1265697 • Letter: P
Question
Problem 7.40 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 .40m, its speed is 4.00 m/s. Part A If the total mass of the two blocks is 18.0kg , what is the mass of the more massive block? Take free fall acceleration to be 9.80m/s^2 . Part B What is the mass of the lighter block? Take free fall acceleration to be 9.80m/s^2 .Explanation / Answer
Let the masses are m1 & m2 and m2>m1
By v^2 = u^2 + 2as
=>(4.0)^2 = 0 + 2 x a x 1.4
=>a = 5.714 m/s^2
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 = 18 x 5.714/9.8
=>m2 - m1 = 10.495 --------------(iii)
& m1+m2 = 18 ---------------(iv)[given]
By (iii) + (iv):-
=>m2 = 14.247 kg {answer for (A)}
=>m1 = 3.752 kg {answer for (B)}