Why is potential energy negative?

[Big L]

If a particle is moving with kinetic energy T(x) in a potential field of energy V(x), why is the total energy E(x) = T(x) - V(x), i.e. why is potential energy negative?

The way I have seen it explained is that the potential energy is less than if the particle was an infinite distance from the source of the potential energy (e.g. an electron experiencing an attractive force to its nucleus).

This does not make sense to me. If you throw a ball, the total energy of the ball is its kinetic energy plus its potential energy due to gravity.

 

[jtbell]

If a particle is moving with kinetic energy T(x) in a potential field of energy V(x), why is the total energy E(x) = T(x) - V(x)

It's not, at least not with the usual definition of potential energy. Can you point us to where you saw this, so we can see what it's actually saying, instead of trying to guess?

 

[sophiecentaur]

The sign of the Potential Energy depends upon whether work is done on or 'by' the object when it was taken to that position from infinity (or another suitable reference). With an attractive force, the work is negative (you get work out). For a repulsive force, the sign of the potential is different and you have to put positive work into bringing the object in from infinity.

The common use of Potential Energy is when considering objects near the Earth's surface. In that case, it is common to use height relative to the ground as a positive quantity so work is put in as the x value increases. This gives a positive value for increasing height. But this positive value is actually the difference between two values of absolute (negative) Potential, relative to infinity. This can be confusing until you actually do some calculations, when it will start to make sense.