A block of mass m is initially moving to the right on a horizontal frictionless surface...

 

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A block of mass m is initially moving to the right on a horizontal frictionless surface at a speed v. It then compresses a spring of spring constant k. In terms of the three variables m, v, and k, derive a symbolic expression for the distance by which the spring is compressed at the instant when the kinetic energy of the block is equal to the potential energy of the spring. Use that the spring's potential energy is zero when it has its natural length. (3 points) A block of mass m is initially moving to the right on a horizontal frictionless surface at a speed v. It then compresses a spring of spring constant k. In terms of the three variables m, v, and k, derive a symbolic expression for the distance by which the spring is compressed at the instant when the kinetic energy of the block is equal to the potential energy of the spring. Use that the spring's potential energy is zero when it has its natural length. (3 points)

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