# Difference between force and energy.

1. Mar 11, 2012

### suchal

I guess my tittle is self explanatory, but I see energy's concept of relativity not of "ability to do anything".
if electromagnetism a force, then why some people say it is energy?

2. Mar 11, 2012

### jambaugh

Electromagnetism is a phenomenon. It involves momentum, force, energy, space and time. Energy and force have very specific meanings.

In most general terms when a system can move or change (translate through space, rotate, deform, etc.) A force relates the amount of energy expended (or gained) when one moves the system a given (small) distance. If you push on an object with a certain force $F$ over a certain distance $\Delta x$ the object gains Kinetic energy by the amount $F\cdot \Delta x$. Note direction and +/- signs matter here. Throw a rock up (positive direction) and the downward (negative) force is opposite the upward motion so it gains negative kinetic energy (looses kinetic energy) and slows.

If you can move an object in many directions it is easier to express the components of force in each direction as a single vector force with direction and magnitude. This vector will point in the direction in which the object gains the most energy for a given amount of motion and the magnitude corresponds to the energy per distance in that direction.

Note that while force can have a direction, energy does not. Energy is a scalar while force is a vector quantity.

Another important quantity is momentum. Momentum relates a (small) change in kinetic energy to a small change in velocity when considering a system changing position over time. Now momentum itself depends on velocity so you'll see a factor of 1/2 in formulas for kinetic energy.
$KE = \frac{1}{2} m v^2=\frac{1}{2}pv$, where $p = mv$
$\Delta KE = \frac{1}{2}\Delta p \cdot v + \frac{1}{2}p\cdot \Delta v = \frac{1}{2}(2 m v \Delta v) = p\Delta v$
(here the $\Delta$ symbol means "change in").

Note that again momentum is a vector quantity as is velocity.

This gives another interpretation of a force as the rate of change of momentum of an object. When momentum is velocity times (a constant) mass you get Newton's F = ma where a is the acceleration (rate of change of velocity).

We can generalize these to rotary motion and speak of rotary force (torque) as the amount of work done per angle we turn an object and the rotary momentum (angular momentum) as the rate of change in kinetic energy as we change speed of rotation.

3. Mar 12, 2012

### suchal

thank you very much. I got it. Just one confusion is there, when p=mv2 then why a photon for which m=0 has p>0 and it's E==KE but depends on it's wavelength and frequency?

4. Mar 12, 2012

### Staff: Mentor

The photon's energy and momentum are not determined by it's mass. Instead see here for how to determine the photons energy and momentum: http://en.wikipedia.org/wiki/Photon#Physical_properties
As for the why, I believe it is because it is an electromagnetic wave, not a particle with mass.