Kinetic and Potential Energy

Kinetic energy

Kinetic energy ($E_k$) is the energy an object has because it is moving.

$$E_k=\frac{1}{2}m{v}^2$$

• $m$ = mass (kg)
• $v$ = speed (m/s)
• $E_k$ = kinetic energy (J)

Gravitational potential energy

Gravitational potential energy ($E_p$ or GPE) is energy stored because an object is raised up against gravity.

$$E_p=mgh$$

• $m$ = mass (kg)
• $g$ = gravitational field strength (9.8 N/kg on Earth)
• $h$ = height raised (m)

Swapping between kinetic and potential

When something falls (ignoring air resistance), all the GPE it loses becomes kinetic energy:

$$mgh=\frac{1}{2}m{v}^2$$

The mass cancels! So the speed at the bottom is:

$$v=\sqrt{2gh}$$

A swinging pendulum

• At the highest points: most GPE, zero kinetic energy (it stops for an instant).
• At the lowest point: least GPE, most kinetic energy (fastest).
• Over time, air resistance turns some energy into heat, so each swing gets a bit lower.

Quick summary

• Kinetic energy: $E_k=\frac{1}{2}m{v}^2$. Double the speed gives four times the energy.
• Gravitational potential energy: $E_p=mgh$.
• Falling objects turn $E_p$ into $E_k$. Rising objects do the reverse.
• With no friction, $mgh=\frac{1}{2}m{v}^2$, so $v=\sqrt{2gh}$, whatever the mass.
• In real life, friction and air resistance turn some energy into heat.

Quiz