Kinetic Energy is NOT Momentum


Beginning students often confuse kinetic energy and momentum. Kinetic energy and momentum are NOT THE SAME!

Scalar Versus Vector:

An important difference is that momentum is a vector quantity - it has a direction in space, and momenta combine like forces do. Kinetic energy is a scalar quantity - it has no direction in space, and kinetic energies combine like "regular numbers."

Dependence on Velocity:

The momentum of an object is proportional to the object's velocity - if you double its velocity, you double its momentum. The kinetic energy of an object is proportional to the square of the object's velocity - if you double its velocity, you quadruple its kinetic energy. This has important consequences...

A Thought Experiment:

Suppose that you were captured by an evil physicist who gave you the following choice:

Truck and Meatball DiagramYou must either:

What's your choice?

Hopefully, you picked the truck! It's a big truck, but it is moving rather slowly (about walking speed), so assuming you don't fall down when it hits you (That would be bad...) the truck is just going to bump into you and move you out of the way.

On the other hand, you probably suspect intuitively that the meatball is a very dangerous object. It isn't that massive, but it is moving very fast (about 10 football fields per second) - and when it hits you it would do considerable damage to you, and keep going!

Consider the momentum and kinetic energy of the truck and the meatball:


Truck's momentum = mv = (1000 kg)(1 m/s) = 1000 kg m/s

Truck's kinetic energy = 0.5 mv2 = (0.5)(1000 kg)(1 m/s)2 = 500 Joules


Meatball's momentum = mv = (1 kg)(1000 m/s) = 1000 kg m/s

Meatball's kinetic energy = 0.5 mv2 = (0.5)(1 kg)(1000 m/s)2 = 500 000 Joules

We know intuitively that the meatball is more dangerous than the truck, yet the momenta of the truck and the meatball are the same. On the other hand, the meatball has 1 000 times the kinetic energy of the truck! Clearly, momentum and kinetic energy tell different things about an object!

Last update November 21, 2007 by JL Stanbrough