The two masses in the Atwood\'s machine shown in the figure are initially at res

Question

The two masses in the Atwood's machine shown in the figure are initially at rest at the same height. After they are released, the large mass,m2 , falls through a height h and hits the floor, and the small mass, m2 , rises through a height h.

Part A) Find the speed of the masses just before m2 lands, giving your answer in terms of m1, m2, g, and h. Assume the ropes and pulley have negligible mass and that friction can be ignored.
Part B) Evaluate your answer to part A for the case h= 1.8m , m1 = 3.1kg , and m2= 5.1kg.
Please show me you work! Thank you.

Explanation / Answer

By balancing the forces on the two masses, let the acceleration of the masses are a m/s^2:- =>By m2g - T = m2a -------------(i) =>T - m1g = m1a -------------(ii) =>By (i) + (ii) :- =>(m2-m1) x g = (m1+m2) x a =>a = (m2-m1)g/(m1+m2) -------------(iii) Now let the masses attain v velocity just before m2 hit the ground:- =>By v^2 = u^2 + 2ah =>v^2 = 0 +2 x (m2-m1)g/(m1+m2) x h =>v = sqrt[2gh(m2-m1)/(m1+m2)] ---------------------(iv), part B v=sqrt[2*9.8*1.8(5.1-3.1)/(8.2) =2.93m/s

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