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Question

A block of mass m sliding on a smooth horizontal surface with a velocity v meets a long horizontal spring fixed at one end and having spring constant k as shown in figure. Find the maximum compression of the spring . Will the velocity of the block be the same as v when it comes back to the original position shown?
1069443_fab068c6de4948ac93d02d1cb6285fad.png

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Solution

The energy stored in the spring exists in the form of the potential energy and it is given as:
PE=12kx2

When the block is left from maximum compression, the potential energy gets converted into kinetic energy of the block.
KE=12mv2

At maximum compression
KE=PE
12kx2=12mv2
x=mkv
The magnitude of velocity will be the same but the direction will be opposite.

971935_1069443_ans_80b528aa7916482797f2c6c1134f66f9.png

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