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Grade 11Mechanics

A block of mass 50kg is projected horizontally on a rough horizontal floor.The coefficient of friction between the block and floor is 0.1The block strike a light spring of stiffness k =100N/m with a velocity 2m/s.Find the maximum compression of spring.

Profile image of Pragati Ranjan
8 Years agoGrade 11
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2 Answers

Profile image of Aditya
8 Years ago
Ans is 1 mApply work energy theorem by equating work done by frictional force and spring force to change in kinetic energy. Take distance covered=compression in spring=x . You will get a quadratic eqn in x i.e x²+x-2=0 and thus you will get your ans i.e 1mAditya GuptaJEE aspirantAll the Best
Profile image of Apurv Kumar Jha
7 Years ago
By applying Work Energy Theorem on the block we get
 Work by frictional force + Work by Spring force=kinetic energy final-initial
It comes out as 50x+1/2*100x^2 = 1/2*50*2^2-0
Now it comes out as x^2+x-2=0
Therefore x=1 m
,where x is the compression in spring. 
Apurv Kumar Jha 
JEE Advanced Aspirant