Question

A block whose mass is 5.7kg slides on horizontal frictionless table top with a constant speed of 5m/s .It is brought momentarily to rest by compressing a spring in its path.By what maximum distance is the spring compressed? (spring constant of spring K=1282.5N/m)​

Answer 1

Please refer to the enclosure...

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Answer 2

Given:

The mass of the block = 5.7 kg

The horizontal constant speed of the block = 5 m/s

The spring constant of the spring = 1282.5 N/m

To find:

The maximum distance by which the spring is compressed.

Solution:

The kinetic energy of the block will go away in compressing the spring. Hence by energy conservation we get:

1/2 mv² = 1/2 kx²

mv² = kx²

5.7 × 5² = 1282.5 × x²

x² = 0.11

x = 0.33 m

Thus, the maximum distance by which the spring is considered is 0.33 m.