Momentum Review

Hello readers,

Momentum-
  1. a property of a moving body that the body has by virtue of its mass and motion and that is equal to the product of the body's mass and velocity; broadly :  a property of a moving body that determines the length of time required to bring it to rest when under the action of a constant force or moment
--Webster definition

Momentum=mass (kg)*velocity(m/s)
                 p =m*v
Whenever we write momentum, we must remember that it is on a vector, meaning we are required to indicate the direction, in both a sketch, which will say which way is positive and negative, and in our equations through the use of - to indicate going down or backwards on the x and y scale.

Any object in motion has momentum, however if it is at rest, it has none. This is clear on a free body diagram, where despite an object having a force due to gravity, and a normal force, if it is stationary, there is none due to momentum. The unit of momentum is kg per m/s.

Sample problem:
A bowling ball weighing 8 Kg is rolling along at 2 m/s, what is its momentum?
      p=m*v
      p=8*2
      p=16kg/(m/s)
Momentum = 16Kg/(m/s)
The next step in momentum is impulse. Impulse is derived from Newton's second law, which states that:
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
--Physics classroom 
Mass is always measured in Kg.
Acceleration is: (Δv/ΔT)
 Forcenet=mass*acceleration
 wherein force and acceleration are directly proportional, and mass and acceleration are inversely proportional.
 This means that if acceleration increases, so does force directly. And if the force stays the same, but the mass increases, acceleration decreases in a direct manner.

 The unit of impulse (J) is newtons, and it is the force times the time. Impulse=change in momentum.
 Thus we have the formula:
Impulse=(forcenet*change in time=(mass*acceleration))*change in time.)
Thus, j=p
which means fnet*Δt=m*(a=(Δv/Δt)).
 So our final impulse formula is:
j=fnet*Δt

 Sample problem:
What is the impulse of a 1800 kg car that collides with a fencepost weighing 20 Kg for 3 seconds?
First, to find fnet I multiply 1800*10 which is 18000
-----------> j=fnet*Δt
                  j= 18000*3
                  j=54000N

Now that we know what momentum and impulse are, we can learn the new formula's which take advantage of this understanding in collision. However there is a mathematical model that we base these formula's on.
This is p(total before)=p(total after) as energy must be accounted for throughout.
There are 2 types of collisions:
Unstuck--> unstuck  =  mava+mbvb=mava+mbvb
 Unstuck-->stuck      =  mava+mbvb=(ma+mb)*(Va*b)

We must remember that the force in which two objects hit each other is always equal due to newton's third law, however the repercussions on each other in terms of momentum can be different.

Sample problem:
Unstuck to stuck
If a 150 kg skateboarder travelling at 15 m/s hits a 275 kg marble ball at rest, what is the final velocity of the two travelling forward after they collide?
mava+mbvb=(ma+mb)*(Va*b)
150*15+275*0=(150+275)*(vab)
2250= 475*Vab
2250/475= (475*Vab)/475
Vab=4.7 m/s.

Unstuck to Unstuck 
A 2500 kg blue car is travelling forward at 40m/s, and collides with another 1500 kg red car traveling 16 m/s, what is the red car's speed after rebounding off each other if the blue car slows down to 8 m/s?
Formula: mava+mbvb=mava+mbvb
 (2500*40)+(1500*16)=(2500*8)+(1500*vb)
                         124000=20000+1500VB
              124000-20000=20000+1500VB-20000
                         104000=1500Vb
                104000/1500=1500Vb/1500
                     69.33 m/s=vb
The red car speeds up to 69.33 m/s.