Question

Two identical 0.200-kg masses are pressed against opposite ends of a light spring of force constant 1.75 N/cm, compressing the spring by 39.0 cm from its normal length.

Find the speed of each mass when it has moved free of the spring on a frictionless, horizontal table.

Answer 1

Energy stored due to compression of spring is given by:

E = (1/2)*k*x^2

k = spring constant = 1.75 N/cm = 175 N/m

x = compression = 39.0 cm = 0.39 m

So,

E = (1/2)*175*0.39^2 = 13.31 J

Now when both mass will be released free, then total energy will be converted into kinetic energy, Since at this moment there will be no potential energy, Also since both mass are identical, So speed of both mass will be same.

E = KE1 + KE2

E = (1/2)*m*V^2 + (1/2)*m*V^2

E = m*V^2

V = sqrt (E/m)

V = sqrt (13.31/0.200)

V = 8.16 m/sec = Speed of each block

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