Question #104973

Two blocks are con-

nected by a light string that

passes over two frictionless

pulleys.

The block of mass m 2 is

attached to a spring of force m1 constant k and m1 . m2.

If the system is released from rest, and the spring is initially not stretched or compressed, find an expression for the maximum dis- placement d of m2.

nected by a light string that

passes over two frictionless

pulleys.

The block of mass m 2 is

attached to a spring of force m1 constant k and m1 . m2.

If the system is released from rest, and the spring is initially not stretched or compressed, find an expression for the maximum dis- placement d of m2.

Expert's answer

As per the given question,

the masses of the blocks are "m_1" and "m_2" , which is connected with the string and spring system and string is passing over the pulley, let the blocks are going x distance downwards, so the spring will elongate 2x.

Hence applying the conservation of the energy

"\\Rightarrow \\dfrac{k(2x)^2}{2}=m_1gx+m_2gx"

"\\Rightarrow 2Kx^2=(m_1+m_2)gx"

So, x"x=\\dfrac{(m_+m_2)g}{2K}"

Hence the maximum elongation in the spring will be "x=\\dfrac{(m_1+m_2)g}{2K}"

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