Energy with Springs

Part of the Mechanics section of Coddy's Physics journey. Lesson 63 of 97.

Without friction, kinetic energy, gravitational PE and elastic PE add up to the same total:

$\tfrac{1}{2} m v^2 + m g h + \tfrac{1}{2} k x^2 = \text{constant}$

A block starts at rest at the top of a smooth ramp at height h, slides down onto a level floor and runs into a spring with constant k fixed to a wall

A smooth ramp, a level floor and a spring at the wall.

Write the total at two moments and set them equal. Where the object stops for an instant, its KE is 0.

Energy bars for the 2 kilogram block: 9.8 joules of potential energy at the start, 9.8 joules of kinetic energy at the bottom, 9.8 joules of elastic energy in the spring when it has stopped the block

Energy bars for the $2\ \mathrm{kg}$ block: PE becomes KE, then spring energy.

Challenge

A toy launcher points straight up. Its spring, with $k = 490\ \mathrm{N/m}$ , is squeezed $0.2\ \mathrm{m}$ under a $0.5\ \mathrm{kg}$ ball, and air resistance is too small to count. The picture shows the ball twice: on the spring and at its highest point. Draw the forces on it at its highest point, then find the height $h$ it reaches above its starting point.