Consider a block attached to horizontal spring that moves along a horizontal, frictionless surface. the system is the block and the spring. if the block is released from rest when the spring is stretched by a displacement of 4.50cm from its unstrained length, determine the displacement of the spring from its unstrained length when its translational speed is 2.00m/s. the mass of the block is 0.200kg and the spring constant of the spring is k=545n/m.

x = 0.023m

and:

x = -0.023m

Explanation:

Using the conservation of energy:

so:

where K is the constant of the spring, Xi is the initial displacement, Xf the displacement when the speed is 2m/s, M the mass of the block and V the velocity of the system.

So, replacing values, we get:

solving for Xf, we get:

Xf = 0.023m

and:

Xf = -0.023m

So, the displacement of the spring from its unstrained length when the speed is 2m/s is 0.023m

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