A 0.500 kg wood block is firmly attached to a very light horizontal spring with

Question

A 0.500 kg wood block is firmly attached to a very light horizontal spring with a spring constant k of 180 N/m. The block is first moved to the left so that it compresses the spring by 5.0 cm, and then released with v0 = 0. The block moves to the right and has stretched the spring by 2.5 cm when it comes to rest.
Find the coefficient of kinetic friction between the block and the table & speed of the block as it passes the point where the spring is neither stretched nor
compressed on the way from – 5.0 cm to + 2.5 cm.

Explanation / Answer

energy stored in the spring gets converted to the workdont by the friction and the again the energy stored due to stretched string:

=> (1/2)kx2 = f.s + (1/2)kx21

and f = mg , s = 7.5cm = 0.075m

and hence by solving we get :

= 0.45

when the spring isnt stretched, compressed , the speed is :

(1/2)k0.052 = f.(5) + (1/2)mv2

and hence we have :

v = 0.67 m/s

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