Speed of compression

Classical Mechanics Level pending

A box of 2 kg is sliding along a floor with speed \(v_{1} = 5 m/s\). It then runs into and compresses a spring until the box momentarily stops. Its path to the initially relaxed spring is frictionless, but as it compresses the spring, a kinetic frictional force from the floor acts on the box. The kinetic frictional coefficient is \(μ_{k} = 0.5\). The maximum of the static frictional coefficient is\(μ_{s} = 0.7\). The spring constant is k = 160 N/m. Ignore the size of the box.

calculate the speed of the box when it re-enters the frictionless floor

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