The block of mass `m_1` shown in figure is fastened to the spring and the block of mass `m_2` is placed asgainst ilt. A. Find the compression of the spring in the equilibrium position. b.The blocks are pushed a further distance `(2/k)(m_1+m_2)gsintheta` against the spring and released. Find the position where the two blocks separate. c. What is the common speed of blocks at the time of separation?

The block of mass `m_1` shown in figure is fastened to the spring and

1.	The block of mass `m_1` shown in figure is fastened to the spring and the block of mass `m_2` is placed asgainst ilt. A. Find the compression of the spring in the equilibrium position. b.The blocks are pushed a further distance `(2/k)(m_1+m_2)gsintheta` against the spring and released. Find the position where the two blocks separate. c. What is the common speed of blocks at the time of separation?
Answer» Correct Answer - `rarr x=((m_1+m_2)gsintheta)/k` `x_1=2/k(m_1+m_2)gsintheta` `v=sqrt({3/k(m_1+m_2)})gsintheta` `a`. At the equilibrium condition `kx=(m_1+m_2)gsin theta` `rarr x=((m_1+m_2)gsintheta)/k` `b`. `x_1=2/k(m_1+m_2)gsintheta` given When the system is released it will start to make SHM. where , `omega=sqrt(k/(m_1+m_2))` when the blocks lose contact `p=0` So `m_2gsintheta=m_2x_2xxk/(m_1+m_2)` `rarr x_2=((m_1+m_2)gsintheta)/k` so the blocks will lose contact with each other when the springs attain its natural length. `c`.Let the common speed attained you both the block be v `1/2(m_1+m_2)v^2-0` `=1/1k(x_1+x_2)^2-(m_1+m_2)gsintheta(x+x_1)` `[x+x_1=`total compression] `rarr 1/2(m_1+m_2)v^2` `=1/2k(3/k)(m_1+m_2)gsintheta-(m_1+m_2)gsintheta-(x_1+x_2)` `rarr 1/2(m_1_m_2)v^2=` `1/2(m_1+m_2)gsinthetaxx(3/k)(m_1+m_2)gsintheta `rarr `v=sqrt({3/k(m_1+m_2)})gsintheta`

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