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)
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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.
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