Could you please show work ? thanks A spring-loaded mechanism projects a 2kg blo

Question

Could you please show work ?

thanks

A spring-loaded mechanism projects a 2kg block across a surface as shown below. The coefficient of friction between the block and the surface is 0.2 (Consider the spring mechanism to be friction less.) The initial compression of the spring is 0.2m, and the spring constant is 250N/m. The spring returns to its full uncompressed length while accelerating the block. Determine the maximum velocity of the block. Calculate the distance that the block slides before coming to rest

Explanation / Answer

(a) block will have max velocity when system will have no potential energy

1/2kx^2=1/2mv^2 + f*x

friction force,f=0.2mg=3.924 N

v^2=(250*(0.2)^2 -2*3.924*0.2)/2

v=2.053 m/sec

(b) at rest all energy will be used by friction

1/2kx^2=f*s

s=(250*0.2^2)/(2*3.924)=1.274m

  

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