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

Option 1)

8.5 cm

Option 2)

5.5 cm

Option 3)

2.5 cm

Option 4)

11.0 cm

Answers (1)

As we learnt in

Negative Work -

\frac{\pi }{2}< \Theta \leq \pi

- wherein

\Theta is the angle between force vector and displacement vector

 

 Change in Kinetic energy = Work done by all forces.

Here  \Delta K=W_{s}+W_{f}

Wf = Work done by spring 

Wf = Work done by friction

    \frac{1}{2}.2\times 2\times 4^{2}=15x+\frac{1}{2}\times 10,000\ x^{2}

\Rightarrow\ 16=5000x^{2}+15x

\Rightarrow\ 5000x^{2}+15x-16=0

On solving it x = 5.5 cm

Correct answer is 2


Option 1)

8.5 cm

This is an incorrect option.

Option 2)

5.5 cm

This is the correct option.

Option 3)

2.5 cm

This is an incorrect option.

Option 4)

11.0 cm

This is an incorrect option.

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