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A 5.7 kg block slides along a horizontal surface toward a horizontally mounted spring with a spring constant of 150 N/m. At one instant, the block is 5.0 m from the end of the spring and has a speed of 12.0 m/s. If the surface is frictionless, what is the maximum compression of the spring

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leena

Hi there!

We can use the conservation of energy:

Ei = Ef

The initial energy involves kinetic energy while the final energy involves maximum elastic potential energy, so:

1/2mv² = 1/2kx²

We can cancel out the 1/2s for ease of solving:

mv² = kx²

Plug in given values to solve for x:

√(mv²/k) = x

√(5.7)(12²)/(150)) = x

x = 2.339 m

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