If neutrons aren't affected by electromagnetic force, what causes it to bounce off matter? Say a neutron is heading for a mountain, what would cause it to bounce off said amalgamation of matter? Electromagnetism is ruled out, gravity is too weak, (if I'm not mistaken) nuclear strong force is a glue, not a repulsion, and [although I admittedly don't understand this force at all] from what lve read,  electro weak force should not play a part.. I'm assuming I just have a misunderstanding of electro weak force so it would be greatly appreciated if you could describe how the weak force causes the neutrons to bounce off matter or an explanation of what is really at work here. Thanks in advance.
 A: Actually, neutrons are affected by electromagnetic forces. Specifically, by the 
"magnetic" part- they are electrically neutral, but have a significant magnetic dipole moment. So they are scattered by the magnetic fields inside a material and especially from nuclei. This is used as a tool to understand materials in neutron scattering experiments (1).
That said, it is also possible for neutrons to scatter off nuclei due to the (residual) strong force. It is not obvious at first which of these processes is going to dominate, since the nuclear force is inherently much stronger than magnetic scattering but only sets in at very short length scales. It turns out  that at relatively low energies, both are comparable sources of scattering from most atoms (2), so at least if you are imagining a relatively slow beam of neutrons it will be scattered both by residual strong interactions and magnetic interactions.
A: Remember that Neutron is not a fundamental particle but rather made of gluons and quarks. This means that it won't interact with other (fundamental) particles elastically. This is especially more pronounced in low energies or large scales. In other words, as it is approaching charged (anti)leptons (electron, muon, tau) and gauge bosons (W and Z) on one hand or uncharged leptons (neutrinos) and photons on the other hand, it will be seen by the incident fundamental particle as a packet of constituent particles. Amongst the charged incident particles, you still have EM interaction while amongst the uncharged incident particles, you will have Weak interaction. The other scenario would be when you are colliding neutrons with other non-fundamental particles namely (hadrons and mesons) in which case you will have strong interactions between constituents particles among the colliding parties. So, in summary, you will have only inelastic collisions between neutrons and any other particle (fundamental or not) and interactions amongst them doesn't have to be always EM as mentioned above. 
A: Strong interaction with other atomic nuclei, especially 'heavy' ones like lead, uranium.
If energy and momentum are conserved 'elastic' scattering.
If they disrupt nuclear structure - remember nucleus is quantized and has energy levels - energy and momentum transfer occurs, therefore 'inelastic' scattering.
The study and control of Nuclear Fission was an early triumph - The Fermi Project - U238 was an unstable nucleus, split by energetic neutrons, control was done by raising or lowering graphite (C12) rods, which reduced neutron energy to below the fissile threshold.
