Joule to newton?

Question

A joule is "equal to the energy expended in applying a force of one newton through a distance of one metre."

Yet a newton is "the amount needed to accelerate 1 kilogram of mass at the rate of 1 meter per second squared".

I now understand the newton with the increase in velocity per second, but that the joule is defined as the newton through a distance of one meter seems confusing as this adds an additional meter onto the overall definition.

Is it simply worded wrong or how is this explained?

Answer 1

Think of the work function work energy = force over some distance; Q = FS in math talk.



You know F = MA, which is kg.m/s^2 in mks units.

So Q = FS = MAS, which is (kg.m/s)^2 in the same mks units.



By arcane definition Newton ~ kg.m/s^2 and

Joule ~ kg.(m/s)^2



And there you are Joule ~ kg.m.m/s^2 ~ Newton.m



The issue is in using those arcane units Joule and Newton, which carry no useful information, when the standard mks units suffice and tell us some physics as well.

Answer 2

Joules and Newtons are different types of units. A Joule is a measure of energy, while a Newton is a measure of force.



Think of it like this: Newtons measure the same things pounds do. If you have a weight that weighs 1 Newton on earth, this would be the equivalent of 0.2248 pounds. It would have a mass of around 102 grams - or 0.102 kilograms. That is to say, the force of gravity is pulling the weight down to the earth with a force of 1 Newton. Using the formula F = m * a, 1 N = 0.102 kg * a, you would find that the acceleration of the weight is around 9.8 m/s^2 (read it as 9.8 meters per second, each second).



If this weight is on the ground and you lift it up 1 meter high, you are exerting a force over a certain distance; you have spent 1 Joule of energy (or rather, you have increased the potential energy of the weight by one Joule).



So in summary, those definitions are correct, but a bit difficult at times to visualize.

Answer 3

It is correct.



You can think in terms of energy (work) or acceleration - they are equivalent and give the same answer.

________________________



Imagine you exert 1N force on a 1kg mass, pushing it through a distance of 1m.



The work done on the object is W = Fd = 1N x 1m = 1Nm = 1J.



If there is no friction, this means the kinetic energy given to the object = 1J



KE = ½mv²

1 = ½ x 1 x v²

v = √2 = 1.414m/s

___________________



The acceleration is a = F/m = 1N/1kg = 1m/s²



The velocity after 1m is given by:

v² = u² + 2as

= 0² + 2x1x1

= 2

v = √2 = 1.414m/s



So whether we do the calculation in term of energy or acceleration we get exactly the same result.

Answer 4

A Joule is a unit of energy. A Newton is a unit of force.