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Question

Consider a block of mass 10 kg collides with a spring of spring constant 10 N/m. The speed of block is 5 m/s, when the compression in spring is 2 m. Calculate the speed of the block, when compression is 5 m?

A
1 m/s
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B
2 m/s
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C
0.5 m/s
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D
2.2 m/s
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Solution

The correct option is B 2 m/s
Given initial velocity vi=5 m/s when compression in spring is xi=2 m,
let vf be velocity of block when compression in spring is xf=5 m

According to law of conservation of energy
Ui+Ki=Uf+Kf [Sum of potential energy stored in spring and kinetic energy of block will be constant]
12Kx2i+12mv2i=12Kx2f+12mv2f
12×10×(2)2+12×10×52=12×10×52+12×10×v2f
10(52v2f)=10(5222)
vf=2 m/s

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