One has to think broader in order to answer those questions. Sure you can imagine a magical 'spring' being attached to a baseball, but there is no way to attach it to the light ray. There is simply not enough magic in this world.
Instead, let's focus on what forces could be actually applied to light. Currently, we are aware of four different types of interactions: electromagnetism, strong and weak nuclear forces, and finally, gravity.
Classical electromagnetism does not influence light because of the linearity of its equations of motion (the Maxwell equations). In classical electrodynamics, light is just an electromagnetic wave propagating in space-time. This wave is a solution of the linear homogeneous Maxwell equations, which is a specific realization of the general principle:
Any solution of a linear inhomogeneous differential equation can be expanded as a sum of some particular solution (vanishing at infinity and corresponding to the physical electromagnetic-interaction part of electromagnetism) and any solution of the corresponding homogeneous differential equation. Moreover, all solutions of the homogeneous Maxwell equations are plane waves (identified by momenta and polarization) which we experience as light.
Therefore, classical electromagnetic fields can not in any way influence the motion of light.
In quantum electrodynamics, which is a much more fundamental theory of nature, however, everything is much more complicated. Light is actually made of tiny quanta called photons which have electromagnetic charge zero (and therefore aren't influenced by E/M fields just like in classical theory). However, the overall equations of motion are no longer linear because of other charged quantum fields (for example, the electron/positron field).
This makes photons behave very much differently. They can spontaneously transform into pairs of electrons and positrons (this was actually experimentally observed millions of times and is called pair production). They can even interact with each-other by means of exchanging virtual electrons. Light can also be emitted or absorbed by electrons, which is how we experience its presence after all.
But these effects can only be observed with photons of much greater frequency than those visible to us, humans. Photons from visible spectrum would still travel through weak electromagnetic fields relatively untouched.
Now comes the most interesting part: gravity. The current widely-accepted theory of gravity is Einstein's General Relativity. One of the basic ideas of General Relativity is that gravity is not a physical field in the usual sense, but is described by the geometry of spacetime itself. This immediately implies that even the propagation of light is influenced by gravity (since light propagates in spacetime). So yes, light rays get bent by gravity. This was actually observed experimentally several times during the 20-th century by looking at how the light from stars is bent by the gravitational field of the Sun (these experiments are quite famous, because the only time one can observe the Sun and stars simultaneously is at the time of a total solar eclipse).
Note that the gravitational bending of the light can only be explained by General Relativity. Therefore you can not use special relativistic formulas (like you do in your question).