The block shown in figure is released from rest. Find out the speed of the block when the spring is compressed by 1 m

Explanation

In the above problem only one conservative force (spring force) is working on the block so from mechanical energy conservation
`K_(f) + u_(f) = K_(i) + u_(i) ` ….(i)
at A block is at rest so ` K_(i)` = 0
`u_(i) = (1)/(2) kx_(1)^(2) = (1)/(2) k(2)^(2)` = 2k joule
At position B if speed of the block is v then
`K_(f) = (1)/(2) mv^(2) = (1)/(2) xx 2 xx v^(2) = v^(2)`
`u_(f) = (1)/(2) kx_(2)^(2) = (1)/(2) xx k xx 1 = (k)/(2)`
Putting the above values in equation (i),we get
`rArr " " v^(2) (k)/(2) = 2k " " rArr " " v^(2) = (3k)/(2)`
`rArr " " v = sqrt((3k)/(2))` m/sec