# Basic question on the newton and acceleration

1. May 11, 2009

### esvion

I am a chemistry student and don't know much about physics. I am trying to understand the definition of the coulomb. Correct me if I am wrong please...

A newton is the amount of work it takes to push one kilogram 1 meter per second... Two newtons would accelerate the object from 0 m/s to 2 m/s..

Would an object traveling at 5 m/s require an additional 1 N to accelerate it to 6 m/s? I thought it would require more and more energy (or Newtons) to push an already moving object even faster - more than just 1 N. I can't quite understand the difference between a joule and a newton. I can see how the mass is square in the formula for a joule, but can't understand why. Can anyone help me with this?

Thanks.

2. May 11, 2009

### Dr.D

A Newton is a unit of force. One newton will impart an acceleration of 1 m/s^2 to a mass of 1 kg according to Newton's second law, F = m*a.

A Joule is a unit of work, the product of force and the distance through which the force acts. Thus a force of 1 N acting through a distance of 1 m produces a 1 J of work.

None of this gets you the definition of a coulomb, but these are the basics.

3. May 11, 2009

### Staff: Mentor

Lotta jumbled thoughts in there:

-A Newton is a unit of force, not energy (work)
-A Joule is a unit of work: applying 1 N throught a distance of 1 m requires 1 J of work (w=f*d)
-An object traveling at 5m/s can use any force to get to 6m/s depending on the time (s=a*t and a=f/m)
-Kinetic energy (work) does increase as a square function of force applied (constant acceleration).
-Mass isn't squared in an energy (work) equation.

4. May 11, 2009

### esvion

Ah, the coulomb is one ampere second and the ampere is the "constant current which will produce an attractive force of 2 × 10–7 newton per metre of length between two straight, parallel conductors of infinite length ."

5. May 11, 2009

### diazona

Maybe I'm a little late for this, but in the interest of not wasting the ~10 minutes I spent typing this up:
As the previous replies have pointed out, a Newton is a certain amount of force (not work). Force in physics is the thing you apply to an object to increase its velocity. (Actually to increase its momentum, but that's another story) One Newton of force will push a kilogram 1 meter per second faster than it was going before for every second the force is applied. If you push on a 1-kilogram mass with a force of 1 Newton for 1 second, it will be going 1 m/s faster. If you push on 1 kg with 1 N for 2 seconds, it will be going 2 m/s faster. Or if you push on 1 kg with 2 N for 1 second, it will also be going 2 m/s faster. The stronger the force, the more the velocity increases; but also, the longer you apply the force, the more the velocity increases. The equation for this is
$$F \Delta t = m \Delta v$$
You can see that the change in velocity $$\Delta v$$ is proportional to the force, but also to the change in time. Incidentally, if you rearrange that a little you get
$$F = m \frac{\Delta v}{\Delta t}$$
But $$\Delta v/\Delta t$$ is just the rate of change in velocity, a.k.a. the acceleration a. So F = ma - guess what, you just derived Newton's second law of motion :-)

Again, as the previous answers have pointed out, an object traveling at 5 m/s would only require 1 N (for 1 second) to accelerate it to 6 m/s. It takes the same amount of force, for the same amount of time, to change the velocity by 1 m/s, regardless of whether the object is moving already or not. However, it does take more and more energy (which is measured in Joules) to accelerate something the faster it moves. Energy is something the object has, whereas force is something you apply to the object. Think about it this way: when you push on something, you can feel the force you're applying to it (actually you feel the force it's applying to you, but again, that's another story). But how much energy it takes depends on whether the thing is moving or not, and how fast. You could lean against a solid wall all day and not even get tired - in that case, you can feel that there's a force, but you're not losing any energy because you're not moving. On the other hand, if you go for a jog you're basically pushing yourself along the ground; you might be applying the same force that you did to the wall, but it makes you pretty tired because now you have to get yourself moving. And once you get moving, it becomes increasingly more tiring to run faster and faster.

The mathematical reason it takes more energy, but not more force, to accelerate something that's already moving faster, lies in the formula
$$E = \frac{1}{2}mv^2$$
E is the energy and v is the velocity. If a 1-kilogram mass is moving at 1 m/s, it has an energy of 1 Joule. If it's moving at 2 m/s, it has 4 Joules; 3 m/s gives it 9 Joules, and so on (4 ->16, 5 ->25). So to accelerate it from 4 m/s to 5 m/s takes 9 Joules, whereas to accelerate it from 1 m/s to 2 m/s only takes 3 Joules. At higher speeds, it takes more energy to apply the same amount of force.

6. May 11, 2009

### esvion

Lets say we are in space and push a 1kg object with the force of 1N. That object will travel on forever and produce an infinite amount of joules, correct? 1 J for each m it traveled for infinity.

EDIT: After reading your last part, I guess not.... I keep thinking that the joule is the amount of energy that the 1kg object produced as it moved 1 m.

I see.

Last edited: May 11, 2009
7. May 12, 2009

### Staff: Mentor

Absorb, not produce, but yes.
Nope - doesn't depend on mass. However, since a=f/m, you need mass to know how fast you are applying that amount of energy to it. Ie, power.

8. May 12, 2009

### esvion

So the energy required to apply 1 N to a 5 m/s object is different than the amount of energy required to apply 1 N to a 7 m/s object?

Thanks, you have been a great help.

9. May 12, 2009

### Dr.D

Power is the rate of doing work,
P = F*v
where
P = Power
F = Force
v = velocity
Thus the power of a 1 N force applied at 5 m/s is 5 J/s = 5 W
The power of a 1 N force applied at 7 m/s is 7 J/s = 7 W

10. May 12, 2009

### f95toli

Unfortunately yes, but it is an awkward definition to say the least. It is important to understand that this is how the STANDARDS used to calibrate instruments are in turn calibrated; i.e. this definition was chosen for practical reasons and not because it has any deeper physical significance (and it reality this definition is not even in use anymore, today current meters are calibrated by applying a known voltage across a known resistor, or by using calculable capacitors).

It is better to think of the current as charges/second which is also how (hopefully) the Ampere will be re-defined at some point in the future (it is an area of active research).