# What's the difference between energy and force?

1. Oct 22, 2009

### kashiark

Is force just acting energy?

2. Oct 22, 2009

### Nabeshin

Well for one they're completely different.

For two one is a vector the other is a scalar.

3. Oct 22, 2009

### kashiark

How are they completely different?

4. Oct 22, 2009

### Bob S

For one thing, if the energy E is stored energy due to a force Fx in the direction x, then the force is given by the derivative

Fx= dE/dx

For example, if the stored energy E of a mass m is mgy, then the force is

Fy = d(mgy)/dy = mg.

Bob S

5. Oct 23, 2009

### kashiark

So force is just the rate of change of energy?

6. Oct 23, 2009

### A.T.

No, that's power. Force is the rate of change of momentum.

7. Oct 23, 2009

### Nabeshin

Note that "rate of change" by itself doesn't mean anything. You have to specify rate of change with respect to what, which is where the distinction arises:
$$F=\frac{dp}{dt}$$

$$F=\frac{dE}{dx}$$

$$P=\frac{dE}{dt}$$

8. Oct 23, 2009

### A.T.

True. I assumed with respect to time.

9. Oct 23, 2009

### Bob_for_short

Yes, exactly.

If we speak of potential energy U(r) the force F is -dU/dr. dr is the vector indicating in what direction the enegy is acting.

If we speak of kinetic energy in collision T=mv2/2, the force result (work) is ∆T.

Together they can give you the complete solution of a problem.

10. Oct 23, 2009

### kashiark

Ok, I think that I've got it: Force is rate of change of energy with respect to a particular dimension, and it's the rate of change of momentum with respect to time. What is energy measured in? Kg*m²/s²?

11. Oct 23, 2009

### mikelepore

I think this is more like plain English:

A force is a push or a pull applied to something. A force has the ability to overcome the inertia of an object (its tendency to keep the same velocity) and cause it to accelerate (change its velocity). The mass of the object is the constant of proportionality between the force and the resulting acceleration (F=ma). If the force is able to displace an object, the force does work on it, but, if the force is exactly balanced by another force that has the opposite direction, the net force will be zero, and no work will be done on the object. The net work done on an object equals the change in its kinetic energy.

12. Oct 23, 2009

### mikelepore

The equations show that work and energy have the same units:

unit of acceleration
m/s^2

force = (mass)(acceleration)
1 newton = 1 (kg)(m/s^2) = 1 kg m/s^2

work = (force)(displacement)
1 joule = 1 (kg m/s^2)(m) = 1 kg m^2/s^2

... or ...

kinetic energy = (1/2) m v^2
1 joule = 1 (kg)(m/s)^2 = 1 kg m^2/s^2

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