Using the concept of momentum is merely a different way of looking at Newton’s Laws. Newton’s Laws imply that when we apply a net force to an object of mass M, for a time t, it will change the velocity according to

Where v_initial was the velocity when the force was first applied at the beginning of the time interval and v_final is the velocity at the end of the time interval t. Because of this relation we call the quantity mass times velocity

the momentum of the object. Momentum is a vector, it has magnitude and direction, it points in the same direction as the velocity. A 100kg mass with a velocity of 5m/s in the easterly direction has a momentum of 500 kgm/s in the easterly direction.

The momentum of two objects is the vector sum of the individual momenta (plural of momentum). For instance if east is the positive x direction and west is negative, the momentum of a 2kg mass moving west with a speed of 3m/s and a 4kg mass moving east with a speed of 2m/s is

because the 3m/s is westerly, i.e. negative.

The quantity force times time

is called the impulse. An impulse changes momentum. If F is the total or net force, then it is called the total or net impulse. Impulse is a vector also, in the direction of the force.

For example if I apply a 40N force to a 5kg mass for 3s, the impulse is 40Nx3s = 120 Ns. This will equal the change in momentum of the 5kg mass. If the mass was initially at rest, v_initial = 0, then Mv_final = 120 Ns or v_final = 120 Ns/5kg = 24m/s.

If the net impulse is 0, the momentum will not change.

Why do we use foam to cushion us when we fall? It has to do with impulse. If we have a certain momentum, it will take an impulse of equal magnitude and opposite direction to stop us. So F´ t = impulse. If we stop quickly, the time is short, or small, and the force must be large. That hurts, so we usually try to stop ourselves slowly, i.e. longer time, so we can use a smaller force. If I fall onto concrete, the concrete does not deform and I stop quickly. If I fall onto a foam pad, it deforms as I hit it, and the stopping force is applied for a longer time, and is therefore smaller. They often design cars so that they will deform in collisions, so they do not stop too quickly. This reduces the stopping forces on the passengers. This is what we mean by "absorbing the shock".

When two objects collide they exert forces on each other. They are equal and opposite forces (the 3^rd law). If they are the net force acting during the collision, the momentum of the system will not change. For instance, if we have a 2kg mass moving east (+) at 6m/s and it collides with a 4kg block at rest and they stick together after the collision, they will be moving toward the east at 2m/s. The initial momentum was 2kg´ 6m/s = 12 kgm/s. The final momentum will be equal to the initial momentum so

M_total = 2kg + 4kg = 6kg, because they stick together and move as one object.  Then v_final = (12kgm/s)/6kg = 2m/s.

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