Ablock of mass m=1kg sliding along a rough horizontal surface is traveling at a speed v0=2m/s when it strikes a massless spring head-on and compresses the spring a maximum distance x=10cm. if the spring has stiffness constant k=10n/m, determine the coefficient of kinetic friction between block and surface.

The coefficient of kinetic friction between block and surface is :  1.99

Given data :

mass of block ( m ) = 1 kg

Speed of block ( ) = 2 m/s

spring compression ( x ) = 10 cm = 0.1 m

stiffness constant ( k ) = 10 N/m

Applying the work energy theorem

Wf + Ws = Kf - Ki  ------ ( 1 )

where : Kf = 0,  Ki = = 2J ,  

Back to equation ( 1 )

Work done by frictional force ( Wf ) becomes

           Wf   = - μmgd

                   =  - μ * 1 * 9.8 * 0.10

                   = -0.98 μ

work done by Ws

Ws =

     = 1/2 * 10 ( 0 - 0.10² )

     = -0.05 J

Insert all values into equation ( 1 )

μ ( coefficient of kinetic friction between block and surface ) = 1.99

Hence we can conclude that The coefficient of kinetic friction between block and surface is :  1.99

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Here we can use the work energy theorem

here we know that

as it come to rest finally

now work done by friction force will be given as

Work done by spring force is given as

so now plug in all data above

so above is the friction coefficient

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