Spring 1

Classical Mechanics Level 3

Block A of mass m m slides on a smooth slider in the system as shown. Block C of the same mass hanging from a pulley pulls block A. When the block A was ata position B, the spring was unstratched. Find the speed of the block A when A B = O B = L AB = OB = L .

Options:

  1. g L 2 − K L 2 2 m \sqrt{ \dfrac{gL}{\sqrt2} - \dfrac{KL^2\sqrt2}m }
  2. g L − K L 2 ( 2 − 1 ) 2 2 m \sqrt{ gL - \dfrac{KL^2 (\sqrt2- 1)^2}{2m}}
  3. g L − 2 L K 2 ( 2 − 1 ) 2 m \sqrt{gL - \dfrac{2LK^2 (\sqrt2 - 1)^2}m }
  4. g L 2 − K L 2 2 m \sqrt{ \dfrac{gL}2 - \dfrac{KL^2\sqrt2}m }
2 4 3 1

Radhesh Sarma by Radhesh Sarma , 22, India

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1 solution

Rohit Ner
Mar 15, 2016

Change in kinetic energy of the system equals to work done by net force acting on both the blocks. The velocity of both blocks will be same as they are held by inextensible string. 1 2 m v 2 + 1 2 m v 2 = m g L − 1 2 k x 2 x = 2 L − L v = g L − K L 2 ( 2 − 1 ) 2 2 m \begin{aligned}\frac{1}{2}m{v}^2+\frac{1}{2}m{v}^2&=mgL-\frac{1}{2}k{x}^2\\x&=\sqrt{2}L-L\\&\large\color{#3D99F6}{\boxed{v= \sqrt{ gL - \dfrac{KL^2 (\sqrt2- 1)^2}{2m}} }}\end{aligned}

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