Forces vs Energy We have conservation of momentum and conservation of energy. Both are similar in some respects but different in others. It is quite amazing that the momentum in a system of two particles is always conserved, but kinetic energy is not conserved. This indicates to me that Energy and work are two completely different things.
But at the same time, the definition of work is given by The product of the force and the displacement in the direction of the force. 
This is what I get stuck on. I imagine a given quantity of energy being lost as heat and applying the equation above to solve for displacement in the direction of the force or for the net force. Clearly this is hard to visualize for work done due to electrical, heat, or light energy.
It get's even weirder when I think about the relationships between energy and waves and quantum mechanical phenomena. I struggle to observe the connection between these phenomena and the idea of a force.
And the last thing I want to say is to mention how Chemistry has a lot of rigorous theory on things like energy levels, bond energies, ionization energies and a lot more stuff related to energy.
I want to know if we can talk about the same phenomena in terms of forces just as effectively, and I want to be informed of any advantages and disadvantages one gets from talking about phenomena in terms of forces instead of energy.  (Chemistry related phenomena like bond breaking energies and quantum energy levels) 
Thanks everyone
 A: The general answer to your question is that all forms of energy are equivalent and can be interconverted into each other. If you can think of mechanical work as force times displacement, then all you have to do is convert the other forms into mechanical work to see their relation to forces and distances.
Answering in the order you gave in the comments:


*

*It's obvious that mechanical work can be converted into heat - just rub your hands together for a while. What's not so obvious is that heat can be converted into work. To do this, we use a thermodynamic concept called a heat engine, which uses a temperature difference between two objects to repeatedly expand and contract a volume of gas, which moves a piston. (This concept is actually the basis for modern combustion engines.) So the amount of work done heating an object is equivalent to the amount of work the heat engine (specifically, an ideal Carnot engine) could do under ideal conditions (specifically, when your Carnot engine is connected to your heated object on one side and a large reservoir at absolute zero on the other side), until your object returns to its original temperature.

*Light is a form of electromagnetic radiation, consisting of oscillating electric and magnetic fields that propagate through space. These fields are oriented perpendicular to each other; you can use Maxwell's equations and basic facts of calculus to determine that because of their particular configuration, they store momentum (the particular magnitude and direction of the momentum is, specifically, $\frac{1}{c^2}(\vec{E}\times\vec{B})$. This derivation is done elsewhere, in particular Feynman's famous lectures, if you need more depth. In any case, the fact that these fields store momentum means that when they are absorbed or reflected, they transfer that momentum - and thus you feel a force. Specifically, the force per unit area you feel from the absorption of light is called radiation pressure, and takes the form $P_{rad}=\frac{\epsilon_0}{2c}E^2$. For reflected light, due to the extra change in momentum, you feel twice as much radiation pressure. So the energy contained in light is equivalent to the amount of mechanical work that the light can do by exerting force on an ideal absorber via radiation pressure.

*The amount of electrical energy stored in a certain configuration of charges is equivalent to the amount of mechanical work an ideal motor could do if it used that charge configuration as a battery until the charges had been completely neutralized.

*A wave carries an energy $E=kA^2$, where $A$ is the wave's amplitude and $k$ is a constant that depends on the specific medium in which the wave travels. Mechanical waves also carry momentum, though the reasoning is much more subtle. Essentially, every mechanical wave on a string, even a transverse one, will generate complementary longitudinal waves that push the string forwards and backwards slightly. The momentum density $g$ of a wave $f(x,t)$ on a string of mass per unit length $\mu$ is $g=-\mu\frac{\partial f}{\partial x}\frac{\partial f}{\partial t}$. For mechanical waves not on a string, you get something similar. So the energy of a mechanical wave is equivalent to the amount of work that it will do pushing on a wall, reflecting back and forth until it is exhausted.

*Any quantum-mechanical object has a wavefunction $\psi(p)$ in momentum-space. The value of the momentum wavefunction at a particular momentum $p$ roughly corresponds to the probability that you will measure the object's momentum to be $p$. As the object interacts with its environment, $\psi(p)$ changes in such a way that the change over time in the average value you would measure for momentum is equivalent to the average force on the object (and, by symmetry, the negative of the force exerted by the object). The energy of the object is equivalent to the amount of work you can extract from the object through various means (e.g. pushing something around via electrical repulsion) until its momentum wavefunction is $\psi(p)=\delta(p)$, i.e. until you will always measure its momentum to be zero, and until its internal energy (i.e. electric potential from separated charges, mass-energy, etc.) falls to zero.
And finally, using energy rather than using forces has multiple advantages. For one thing, energy is a scalar, while force is a vector, so it reduces the number of equations you have to consider in the first place (as the force must be broken down into components). In addition, energy has another very, very useful property: it's conserved in any isolated system. This symmetry simplifies calculations greatly.
