Conservation of Energy

As an object moves, its energy can shift back and forth between motion (kinetic energy) and position (potential energy), but the total mechanical energy stays the same as long as friction and air resistance aren't stealing any away. A falling object trades height for speed, and a rising object trades speed for height — the sum never changes.

E = ½ · m · v² + m · g · h

• E — total mechanical energy (J): the combined energy of motion and position, constant without friction
• m — mass (kg): how much matter the object has
• v — speed (m/s): how fast the object is moving at that moment
• g — gravitational acceleration (m/s²): the strength of gravity's pull, about 9.8 m/s² near Earth's surface
• h — height (m): how far above a reference level the object is

A 2 kg ball swings through its path at a height of 5 m above the ground, moving at 4 m/s. Using g = 10 meters per second squared, what is its total mechanical energy?

• m = 2 kg
• v = 4 m/s
• h = 5 m

1. E = ½ · m · v² + m · g · h
2. E = ½ · 2 kg · (4 m/s)² + 2 kg · 10 m/s² · 5 m

E = 116 J

The same 2 kg ball now reaches a height of 10 m, still moving at 4 m/s at that point. What is its total mechanical energy?

• 232 J
• 216 J
• 116 J

A ball rolls down a frictionless hill, losing height as it goes. What happens to its speed and its total mechanical energy?

• Speed increases, total energy stays the same
• Speed decreases, total energy stays the same
• Speed increases, total energy increases