Forces cause a change in momentum because of the fundamental relationship between force and momentum known as Newton's second law of motion. According to this law, the net force acting on an object is directly proportional to the rate of change of its momentum.
Mathematically, Newton's second law can be expressed as F = ma, where F represents the net force applied to an object, m is its mass, and a is the resulting acceleration. However, momentum (p) is defined as the product of an object's mass and velocity (p = mv).
By rearranging the equation for momentum, we get p = ma × v. Substituting the value of acceleration (a) from Newton's second law into this equation, we get p = m(F/m) × v. Simplifying further, we find p = F × (mv/m), which can be reduced to p = F × v.
From this equation, it is evident that force (F) directly affects the change in momentum (Δp), as a greater force will produce a greater change in momentum. In other words, when a force is applied to an object, it causes its momentum to change in the direction of the force.
This relationship can be intuitively understood by considering that a force applied to an object imparts an acceleration to it. This acceleration causes a change in the object's velocity, and since momentum depends on both mass and velocity, any change in velocity will lead to a change in momentum.
Therefore, forces are responsible for changing an object's momentum because they cause acceleration, which in turn alters the object's velocity and consequently its momentum.