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Q.

A 2kg block slides on a horizontal floor with a speed 4 m/s. It strikes an uncompressed spring and-compresses it till the block is motionless. The kinetic friction is 15 N and spring constant is 10,000 N/m. The spring compresses by :

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a

8.5 cm

b

5.5 cm

c

2.5 cm

d

11.0 cm

answer is B.

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Detailed Solution

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$\begin{array}{l} W = ΔKE \Rightarrow W_{spring} + W_{friction} = \frac{1}{2} {mv}_{2}^{2} - \frac{1}{2} {mv}_{1}^{2} \end{array}$
$\Rightarrow - \frac{1}{2} (10000) x^{2} - (15) x = 0 - \frac{1}{2} (2) (4)^{2}$
$\Rightarrow 10000 x^{2} + 30 x = 16$
x = 5.5cm

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