Momentum


Momentum Notes


  • Momentum is the product of a body's mass and velocity
    p=mv (p = momentum)
  • Units --> kg m/s = Ns
  • Momentum is always conserved in a closed system (Law of Conservation of Momentum)
  • Momentum is a vector (has direction and magnitude/size)
  • Momentum is directly proportional to mass and velocity (because of the equation p=mv)

Elastic Collisions
  • Things collide and then separate
  • Kinetic Energy IS conserved
  • Momentum IS conserved
Inelastic Collisions
  • Things collide and stick together
  • Kinetic Energy IS NOT conserved (a lot of energy goes into heat and making the cars stick together)
  • Momentum IS conserved
Momentum in Relation to Force
  • momentum is connected to force and time
  • deriving the equation:
    • ΔF=m*Δv/Δt
    • FΔt=mΔv
    • FΔt=Δp
      • or impulse=change in momentum
Impulse and it's relation to momentum is especially important for sports. For example, when catching a softball, one gives with it so it doesn't hurt your hands. You are decreasing the force on your hand by making the time greater while the momentum remains the same. As shown in the equation as time goes up, force decreases and the change in momentum remains the same.

Momentum is always conserved, on this link you can find videos in slow motion demonstrating the conservation of momentum in daily life. Favorites include the Jello bouncing momentum video clips



    • EXPLOSIONS
      • Kinetic Energy IS conserved
      • Momentum IS conserved
      • *After collision, objects travel in different directions
external image cannon.gif

Law of Conservation of Momentum



    • Since momentum can never be lost, it gets transfered from one object to another when they come in contact.
    • Situation with pool balls: When the cue strikes a ball, that ball moves and hits another ball. The momentum from the striked ball gets transfered to the new ball when they come in contact. The first ball stops moving because its momentum has been transfered to the second ball, which is now in motion because of the momentum it has received.
    • Situation with alloy balls: The first ball that's initiated strikes the ball next to it, transfering its momentum as the two objects come in contact with each other. The momentum from the second ball gets transfered to the third, fourth, and so on, ball. Finally, when the momentum reaches the last ball, the ball swings upwards because of the momentum it just received. When the ball swings back, it strikes the ball next to it, and the process continues.
    • Momentum depends on mass (and velocity). For example, the pool cue strikes the pool ball and it travels x meters. Using the same cue, with the same amount of force*, to strike a bowling ball (an object with much more mass compared to a pool ball) will cause it to travel a distance less than x because of its large mass.
    • *Force: Force also affects momentum because force is mass x acceleration (Newton's 2nd Law, F=ma). Force causes acceleration; and acceleration is the change in velocity. Momentum also depends on velocity (p=ma); therefore, if the force changes, the velocity changes--this means that the momentum will also change due to the velocity's adjustments.

More Equations for momentum


p=mv
-the basic equation of momentum
-momentum (p) is equal to mass (m) times velocity (v)

∆p= m∆v
-change in momentum is equal to mass times change in velocity
-If mass is the same and the change in momentum increases, then the change in velocity must increase
-If mass is the same and the change in momentum decreases, then the change in velocity must decrease also

∑ pi = ∑ pf
-Sum of initial momentum is equal to the sum of final momentum
- pi = initial momentum
-pf = final momentum

p1i + p2i = p1f + p2f
-replacing the sum's of the momentum in the previous equation with two different object's momentum
-initial momentum of object 1 plus initial momentum of object 2 equals final momentum of object 1 plus final momentum of object 2
-p1i = initial momentum of object 1
-p2i = initial momentum of object 2
-p1f = final momentum of object 1
-p2f = final momentum of object 2

-used in conservation of energy problems
m1v1i + m2v2i = m1v1f + m2v2f
-replacing the two different object's momentum with their mass and velocity
-mass of object 1 times initial velocity of object 1 plus mass of object 2 times initial velocity of object two is equal to mass of object 1 times final velocity of object 1 plus mass of object 2 times final velocity of object 2
-used in conservation of energy problems
- m1 =mass of object 1
- v1i =initial velocity of object 1
- m2 =mass of object 2
- v2i =initial velocity of object 2
- v1f =final velocity of object 1
- v2f =final velocity of object 2

Practice Problems - Momentum


Calculate the momentum of a 1200 kg automobile with a velocity of 25 m/s.
What is the momentum of a toy dart gun of mass 35 grams and a velocity of 4 m/s.
What is the momentum of a Boeing 737 at take off velocity (65 m/s) with a mass of 145000 kg.
A 12000 kg railroad car is traveling at 2 m/s when it strikes another railroad car at rest with a mass of 10000 kg. If the cars lock together, what is the final speed of the railroad cars?
A 9300 kg railroad car traveling at a speed of 15 m/s strikes a second boxcar at rest. The two cars stick together and move off with a speed of 6.0 m/s. What is the mass of the second car?
Pendulums
- the amount of time it takes for the bob (mass) to make one full swing
-- the only thing that affects the period is the string length
- pendulums have amplitude, or the distance that the bob is pulled back before it is released
-

external image pend.gif
external image Pendulum_animation.gif

Galileo's Work with Pendulums

More Videos for the Conservation of Momentum:

Video about the transfer or momentum:

-This is a short little video that shows how momentum is transferred from one object to the next. It shows in slow motion with text describing it how two ball's momentum transfers/changes when they come in contact with each other. Furthermore, the video explains how the smaller ball will travel for a longer distance after the collision than the much larger and heavier ball.

Here is an video about momentum and collisions. Hope you like the man's funny accent.

First, the man describes the equation that momentum is P=mv. Later he shows the viewers a soccer ball and a plastic ball. The soccer wall is heavier to it will take more time to stop because if the mass is more than the momentum is more which means that it will take more time to stop. Then, the viewer sees a pool table that shows when two balls hit each other at the same time at the same speed, then the momentum before collision is equal to the momentum after the collision.


http://www.nytimes.com/interactive/sports/olympics/olympics-interactives.html#tab1
In this New York Times video, reporter Henry Fountain and United States Olympic ski jumper Ryan St. Onge break down the physics of Onge's "double full full full," which is a triple backflip with four body flips. By raising his arms, he moves his weight away from his center of rotation (near the hips) and, therefore, his rotational momentum becomes greater. He pushes off of the ramp and twists his hips in a "hula move." To tilt, he lowers his left arm while raising the right. Some of the rotational momentum that is on an axis through the hips is transferred to an axis that runs from his head to his toes, resulting in a spin. Bringing his arms in decreases his rotational inertia on the axis that runs from head to toe. Because his rotational momentum remains the same, but his rotational inertia is decreased, his velocity increases and he spins faster. Before landing, he raises his arms above his head to slow himself down. Isn't nice to know that Olympians use physics, too?