Spring launch, two system choices

The same launch, with two ways to account for energy.

SystemMass only

Choose the system

Compression 0.30 m Speed 0.00 m/s Ready to release

The spring force is external to the mass. Its work increases the mass’s kinetic energy.

Frictionless track · ideal massless spring · fixed support · mass not attached

Energy accounts at the same instant

Kinetic Spring Total

Mass only

Spring force is external

Net external work: W_net = W_spring+0.0 J

Kinetic energy: K_mass0.0 J

ΔK_mass = W_spring

Work is energy transferred to the mass from the spring.

Mass + spring

Spring force is internal

Net external work: W_net = 00.0 J

K 0.0 J U_spring 4.50 J Total 4.50 J

ΔK + ΔU_spring = 0

U_spring = ½k(Δx)². Its zero is at the relaxed length.
The fixed support exerts a force but does no work.

Mass

Spring constant

Initial compression

Launch progress0%

Released from rest on a frictionless horizontal track. The mass is not attached: contact ends at the spring’s relaxed length, then the mass coasts. The spring’s mass is neglected. Gravity and the track’s normal force do no work; the fixed support does no work. Switching systems pauses without changing the motion or energy values. The drawing is schematic.

Space release/pause/play · R restart · H controls · T theme · F11 full screen · 50% progress: spring relaxed; mass begins coasting.