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. At the instant when the kinetic energy
of the block is equal to the potential energy of the spring, the spring is compressed a distance of:

The distance that the spring compresses is:

Explanation:

Kinetic and Elastic Potential Energy

The kinetic energy of an object of mass m traveling at a speed v is:

The elastic potential energy of a spring of constant k that compresses a distance x is:

The block of mass m is moving at a speed v when compresses a spring of constant k. The kinetic energy will eventually transform into elastic energy, but before that, both energies will be equal. It happens when:

Simplifying:

Dividing by k:

Taking square root:

The distance that the spring compresses is

that is probably false!

the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."