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Standard XII

Physics

Thermal Expansion

A 2kg block...

Question

A $2 k g$ block slides on a horizontal floor with a speed of $4 m / s$ . It strikes an 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:

5.5 c m

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2.5 c m

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11.0 c m

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8.5 c m

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Solution

The correct option is A $5.5 c m$
The total kinetic energy possessed by the block goes into the potential energy of the spring and the work done against friction.

Let $x$ be the compression of the spring.

Thus $\frac{1}{2} m v^{2} = f_{r} x + \frac{1}{2} k x^{2}$

$⟹ 5000 x^{2} + 15 x - 16 = 0$

$⟹ x = 0.055 m = 5.5 c m$

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A 2kg block slides on a horizontal floor with a speed of 4m/s. It strikes an 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:

The correct option is A 5.5cmThe total kinetic energy possessed by the block goes into the potential energy of the spring and the work done against friction.Let x be the compression of the spring.Thus 12mv2=frx+12kx2⟹5000x2+15x−16=0⟹x=0.055m=5.5cm

A $2 k g$ block slides on a horizontal floor with a speed of $4 m / s$ . It strikes an 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: