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

Question

Two blocks with different masses are attached to either end of a light rope that passes over a light, frictionless pulley suspended from the ceiling. The masses are released from rest, and the more massive one starts to descend. After this block has descended 1.20 m, its speed is 3.00 m/s. If the total mass of the two blocks is 25.0 kg, what is the mass of the heavier block? Express your answer with the appropriate units. If the total mass of the two blocks is 25.0 kg, what is the mass of the lighter block? Express your answer with the appropriate units.

Explanation / Answer

suppose mass of bigger block is m1 and lighter block is m2, tension in the string is T then acceleration of the block can be find as -

m1 g - T = m1 a

T - m2 g = m2 a

by solving above equations-

[m1 - m2]*g = [m1 + m2]*a

a = [m1-m2]g/[m1+m2]

if the block has speed of 3.0 m/sec after descending 1.20 m then -

v2 = u2 + 2 as

9 = 2*1.20*a

a = 9/2.4

a = 3.75 m/sec2

as m1 + m2 = 25

3.75 = [m1 - m2]*9.8/25

m1 - m2 = 9.56

m1 + m2 = 25

so m1 = 17.28 kg

m2 = 7.72 kg

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