whats the difference between kinetic energy and momemtum

Question

I was just trying to get an explanation of the difference between momentum and kinetic energy. I know the formulas for each but i cant grasp how they are different.

Answer 1

It's difficult to get an intuitive understanding of what momentum is because the unit of mass is weird in the 

mks system.  (meter, kilogram, second)  Here's one way to look at it.

 

The short answer:

We know that energy is equivalent to force times the distance over which it is applied.

    How far we pushed an object with some force.

    E = n*m     (newton-meters: force times distance)

Momentum is equivalent to the product of force and the time that force is applied to an object.

    How long did we pushed an object with some force.

 

How do we get to that conclusion?

You can use the units only from the kinetic energy formula to find the equivalent units for mass.

KE = kg * velocity^2             (This is equivalent to the units of energy: n*m)

velocity is m/s                       (meters per second)

kg * m^2 / s^2 = n*m         (Equate the result to the know units for energy.)

kg = n * m * s^2  / m^2

kg = n * s^2 / m

 

Substitute this unit into the units for the momentum formula:

P = kg * m / s

P = (n * s^2 / m) * ( m / s)

P = n * s                                 (force times time)

 

Hope this gives you a little insight into what the difference is.

 

 

Answer 2

Linear momentum:

 

p = mv

 

It is a measure of the amount of motion a body of mass m has when moving at speed v.

 

Kinetic energy:

 

K = (1/2)mv²

 

It is the amount of energy due to motion that a body of mass m has when moving at speed v (as opposed to potential energy, which is the amount of energy a body has due to its position in a force field).

 

Linear momentum and kinetic energy are related by

 

K = p² / 2m

 

Note the formulas are very different.