Q. 475.0( 1 Vote )

# A block of mass sliding on a smooth horizontal surface with a velocity meets a long horizontal spring fixed at one end and having spring constant k as shown in figure (8-E10). Find the maximum compression of the spring. Will the velocity of the block be the same as when it comes back to the original position shown?

The compression distance of the spring is given as

Given

The sliding velocity of the block is given as with spring constant k.

Formula Used

Using the conversation of energy, we equate the energies of spring compression and potential energy of the mass of the block, the formula of the energy stored in spring compression is

And the energy stored in the block is formulated as

where

The value of spring constant is denoted as “k”, the compression distance is “x”, the mass of the block is given as “m”, v is the velocity of the block.

Explanation

The kinetic energy of the block is given as

The energy stored in the compressed spring is given as

Equating the energies together we get the compression distance as

The compression distance of the spring is given as

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