A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 
. The block is pushed such that the length of the spring becomes 1 m and then released. At distance 
from the wall, the speed of the block will be
Text Solution
Verified by ExpertsA
Natural length of the spring: 2 meters
Initial compression of the spring 
: 1 meter
Final compression of the spring when the block is at distance 
meters
Solution:
To find the block's speed, we'll use energy conservation. Initially, the spring's potential energy is fully converted to kinetic energy and spring potential energy at the new position 
.
Conservation of Energy:
Initial kinetic energy ( 
) is 0 since the block starts from rest.
Initial potential energy ( 
) due to spring compression is 
.
At a distance 
, the kinetic energy ( 
) is 
and the potential energy ( 
) is 
.
Rearrange to find 
:
Substitute known values:
Simplify and solve for 
:
Finally, take the square root to find 
:
Therefore, the speed of the block at distance 
from the wall is given by the expression above.
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