# Potential and kinetic energy

If a ball stays on the ground, it has no height and no velocity. So what energy does it have kinetic or potential?

• Can you explain what kinetic energy is? – lemon Apr 12 '15 at 11:35
• energy that a body possess when it has movement. The formula is Ek= 1/2 mv squared. – Vase Dodevski Apr 12 '15 at 11:38
• Right, so would the ball in your example have kinetic energy? – lemon Apr 12 '15 at 11:39
• no it wont. It doesn't have any velocity – Vase Dodevski Apr 12 '15 at 11:39
• Indeed. And what does it mean to have potential energy? – lemon Apr 12 '15 at 11:43

As you've worked out, since $v=0$ then the kinetic energy must also be zero.
Potential energy is a little more dubious. At school you are usually taught that the gravitational potential energy is $E=mgh$ but that's not quite right; this equation is the work that you must do to lift an object of mass $m$ a height $h$ or, equivalently, the work done by gravity in accelerating that object downwards by a height $h$.
$E^2=m^2c^4+(pc)^2$
Here $m$ is the rest mass of the body. So when velocity is zero so is momentum by the formula $p=mv$. Hence the above energy-momentum relation reduces to $E=mc^2$ which is the energy the body would posses at rest. Hope this clarifies.