Energy can't be created or destroyed, only transformed! Specifically, kinetic energy (KE) and gravitational potential energy (GPE) can swap places in a process known as energy transfer, but the total energy, called mechanical energy, stays the same. In an ideal, frictionless world, the energy exchange between KE and GPE is perfect - the energy loss from one is the exact gain for the other.

Imagine a satellite whizzing around a planet in the vacuum of space. The satellite's speed isn't constant - it speeds up and slows down, changing its kinetic energy. But the mechanical energy of the satellite stays the same, because as it gains kinetic energy, it loses gravitational potential energy, and vice versa.

Imagine a snowboarder at the top of a 50m hill (start from rest, so initial KE = 0). As they go down the slope, they trade GPE for KE. We can't use kinematic equations (suvat) here because the acceleration isn't constant. Using energy conservation, we can find the snowboarder's speed at the bottom: v = √(2 × 9.8 × 50) = 31 m/s (that's roughly 110 km/hr!). However, this doesn't account for air resistance and friction.

Fun Fact: Regardless of the snowboarder's mass, the speed at the bottom remains the same, as the mass cancels out in the equations.

• A ball thrown upwards: The ball's initial KE is converted into GPE at the highest point of its trajectory. Using KE = 0.5mv² and GPE = mgh, we can calculate the maximum height the ball will reach.
• A pendulum bob: If the bob is released from a certain height, we can calculate its speed as it passes through the lowest point using conservation of energy principles (KE at the lowest point = GPE at the highest point).
• Ski jumping: A ski jumper loses some GPE as they descend down the ramp, which is transferred into KE, but not all of it because of resistive forces (like air resistance).