The Lemon Fool

E = energy (measured in joules, J)
m = mass (measured in kilograms, kg)
c = the speed of light (measured in metres per second, ms ), but this needs to be "squared".

panamagold wrote:E = energy (measured in joules, J)
m = mass (measured in kilograms, kg)
c = the speed of light (measured in metres per second, ms ), but this needs to be "squared".

So why do I feel I have less energy since I have put on some extra mass?

jfgw wrote:

panamagold wrote:E = energy (measured in joules, J)
m = mass (measured in kilograms, kg)
c = the speed of light (measured in metres per second, ms ), but this needs to be "squared".

So why do I feel I have less energy since I have put on some extra mass?

I think it is all relative.

John

panamagold wrote:
c = the speed of light (measured in metres per second, ms ), but this needs to be "squared".

That bit has always 'bothered' me
What is a velocity squared?
It's definitely not a velocity.
10km/s = 6 miles/s approx
100km/s is not 36 miles/s

in the equation E = mc^2
it is equating the dimensions of Energy (Joules) to mass (kg) x speed (m / s) x speed (m / s)

so the units of 'c^2' are m^2 / s^2 (not just m/s)

so, in your example 100km^2 / s^2 is analogous to 36 miles^2 / s^2

-Dom

OK so what is a second squared

It's always bothered me why it isn't E = (mc2)/2 like the equation for kinetic energy E= (mv2)/2

When I asked my physics teacher as a child I was fobbed off with because c is so large it doesn't matter about the 1/2.

Regards,

Percol

try this

http://www.vendian.org/mncharity/dir3/knowing_joule/

Percol351 wrote:It's always bothered me why it isn't E = (mc2)/2 like the equation for kinetic energy E= (mv2)/2

When I asked my physics teacher as a child I was fobbed off with because c is so large it doesn't matter about the 1/2.

Regards,

Percol

E=mc^2 and the Newtonian Kinetic Energy equation are showing two different things.

The Newtonian equation for Kinetic Energy is E(k) = (m/v^2) / 2
The Relativistic equation for Kinetic Energy is E(k) = E(total energy) - E(rest energy)
E(k) = mc^2 / sqrt(1 - (v^2 / c^2) ) - mc^2

At low speeds (ie v << c) we can approximate this using the first two terms of a Taylor expansion for a reciprocal square root

E(k) ~ mc^2 (1 + v^2 / 2c^2) - mc^2 ~ (mv^2)/2
which is the Newtonian equation, i.e. at low speeds, relative to the speed of light, the Newtonian equation is a good approximation of the Relativistic equation.

-Dom

psychodom wrote:
E=mc^2 and the Newtonian Kinetic Energy equation are showing two different things.

The Newtonian equation for Kinetic Energy is E(k) = (m/v^2) / 2
The Relativistic equation for Kinetic Energy is E(k) = E(total energy) - E(rest energy)
E(k) = mc^2 / sqrt(1 - (v^2 / c^2) ) - mc^2

At low speeds (ie v << c) we can approximate this using the first two terms of a Taylor expansion for a reciprocal square root

E(k) ~ mc^2 (1 + v^2 / 2c^2) - mc^2 ~ (mv^2)/2
which is the Newtonian equation, i.e. at low speeds, relative to the speed of light, the Newtonian equation is a good approximation of the Relativistic equation.

-Dom

Wow....I am not worthy!