Question

What is the relation between force and momentum and how are each of them calculated?

Answer 1

They are related by the fact that force is the rate at which momentum changes with respect to time (F = dp/dt). Note that if p = mv and m is constant, then F = dp/dt = m*dv/dt = ma
Momentum measures the 'motion content' of an object, and is based on the product of an object's mass and velocity. Momentum doubles, for example, when velocity doubles. Similarly, if two objects are moving with the same velocity, one with twice the mass of the other also has twice the momentum.

Force, on the other hand, is the push or pull that is applied to an object to CHANGE its momentum. Newton's second law of motion defines force as the product of mass times ACCELERATION (vs. velocity). Since acceleration is the change in velocity divided by time, you can connect the two concepts with the following relationship:

force = mass x (velocity / time) = (mass x velocity) / time = momentum / time

Multiplying both sides of this equation by time:

force x time = momentum

To answer your original question, then, the difference between force and momentum is time. Knowing the amount of force and the length of time that force is applied to an object will tell you the resulting change in its momentum.