Which branch of science studies forces and energy?

Forces are introduced in Newtonian mechanics and are a fundamental idea of classical physics. In classical physics, that is the physics that describes human dimension phenomena (like the motion of a car, the flowing of water in ducts, the gravitational attraction on the earth surface and so on) , the study of force laws is one of the key elements and this is an important point also in biophysics, macroscopic chemistry and several other science branches based on classical mechanics.

Energy was originally introduced in classical physics too, but only the quantum and relativistic physics have clarified completely its deep meaning so that in modern physics energy has substituted the concept of force as the key physical quantity in the study of physical systems evolution. Naturally, chemistry at atomic level, astrophysics and so on share completely this characteristics.