A system composed of just a single object can only ever have kinetic energy — there's no second object for it to interact with, so potential energy simply isn't possible. The moment a system contains objects that interact through conservative forces (or that can reversibly change shape, like an ideal spring), it can have both kinetic and potential energy.
A system's mechanical energy is simply the sum of its kinetic and potential energies:
You get to choose your system so that its total energy is constant — and if that total ever does change, the change is always exactly equal to whatever energy crossed the system's boundary. Nothing more, nothing less.
Try the classic energy bar chart representation below — a direct visualization of energy shifting between kinetic, potential, and (if friction is present) lost forms.
A 4 kg block starts at some height, possibly against a compressed spring, then is released. Build the initial and final energy bar charts — watch the total bar height stay constant unless friction is switched on.
With no friction, the final kinetic energy bar exactly matches the initial total height — mechanical energy is fully conserved.
Energy is conserved in all interactions — full stop, no exceptions. But mechanical energy specifically stays constant only under a more specific condition:
This directly echoes Lesson 2.1's lesson about choosing systems wisely. Include friction inside your system boundary, and you'll need to track energy dissipating as heat and sound. Draw your system boundary to exclude the friction interaction entirely, and mechanical energy conservation becomes a clean, simple tool again.
Putting it all together gives the full conservation of energy equation — exactly matching this unit's header art:
Explore the whole idea live below, using the roller coaster from this unit's header.
The roller coaster from this unit's header art. A 300 kg car drops from 20 m, then climbs a second, shorter hill. Scrub through the ride and toggle friction to see mechanical energy behave differently.
Without friction, Ug + K stays exactly constant throughout the ride — watch the car reach the same speed at the bottom no matter how winding the track is, as long as it starts from the same height.
A 2 kg ball is released from rest at the top of a frictionless 5 m tall ramp, sliding down onto a horizontal surface. Find the ball's speed at the bottom.
The same 2 kg ball now slides down the same 5 m ramp, but the horizontal surface at the bottom has friction, exerting a 4 N force over the 3 m the ball travels before stopping. Verify this is consistent with conservation of energy.