Final answer:
Conservative forces are path-independent and conserve mechanical energy, while non-conservative forces are path-dependent and can change the system's mechanical energy. The law of conservation of linear momentum states that the total momentum of a closed system remains constant if no external forces are acting.
Step-by-step explanation:
The difference between conservative and non-conservative forces is fundamental in mechanics. Conservative forces, such as gravity and spring forces, are path-independent and have potential energies associated with them. This means that the work done by a conservative force on an object moving between two points is the same, regardless of the path taken. Moreover, when only conservative forces are doing work, the total mechanical energy (the sum of kinetic and potential energy) of a system is conserved.
In contrast, non-conservative forces like friction and air resistance depend on the path taken and do not have potential energies associated with them. Work done by non-conservative forces adds or removes energy from the system, often in forms such as heat, which cannot be completely converted back into mechanical energy. As a result, these forces can lead to a change in the total mechanical energy of a system.
The law of conservation of linear momentum states that the total linear momentum of a closed system remains constant provided no external forces are acting on it. This principle is crucial in analyzing collisions and interactions at both macroscopic and subatomic levels. To prove this law, one can use Newton's second law in terms of momentum (the rate of change of momentum is equal to the net force applied) and consider Newton's third law (for every action, there is an equal and opposite reaction) in systems where the internal forces are the only forces acting. In a closed system, the sum of forces is zero, so the total momentum before and after any interaction must be the same.