A 2kg block slides on a horizontal floor with a speed of 4m/s.
A 2kg block slides on a horizontal floor with a speed of 4m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15N and spring constant is 10,000N/m. The spring compresses by
(a) 8.5cm
(b) 5.5cm
(c) 2.5cm
(d) 11.0cm
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b) : Let the spring be compressed by x
Initial kinetic energy of the mass = potential energy of the spring + work done due to friction
1/2 x 2 x 42 = 1/2 x 10000 x x2 + 15x
or 5000x2 + 15x – 16 = 0
or x = 0.055m = 5.5cm.
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