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 1.00 m/s .

Part A

If the total mass of the two blocks is 18.0 kg , what is the mass of the more massive block? Take free fall acceleration to be 9.80 m/s2 .

Part B

What is the mass of the lighter block? Take free fall acceleration to be 9.80 m/s2 .

Explanation / Answer

(A) distance covered by the massive block = 1.1 m Speed V = 1 m/s
So V2 = u2 + 2aS where V is final velocity , u is initial , a is acceleration , S is distance
here u = 0 so a = 0.4545 m/s2
In this arrangement we know that
a = (m1 - m2)g / (m1+m2)
so m1 -m2 = (m1+m2) *a /g = 0.8339 ---------(1)
m1 +m2 = 18
on solving we get m1 = 9.4169 kg
(b) m2 = 18 - m1 = 8.583 kg

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