5-Momentum

Slideshow: Momentum & Impulse Slideshow

Textbook: Chapter 5 & chapter 6.7 in Mastering Physics (get online code for registration on about page of google classroom)

Objectives:

  • Single objects:
    • Use impulse momentum equation (2nd one below) to find F, t, impulse, change in momentum, m or change in speed.
    • Select data from a lab to show or test relationships in impulse momentum equation
    • Include qualitative and graph based analysis (in particular the area under an F v t graph = change in momentum).
  • 2 Object systems: Use conservation of momentum with & without impulse to find change in momentum,
    • calculate changes in momentum of the center of mass due to an impulse from a F v t graph or from given values
    • define open & closed systems
    • Predict the velocity of the center of mass of a closed system (if no external forces, then velocity of center of mass does not change).
  • Collisions
    • Classify collisions as elastic or inelastic and justify that momentum is conserved.
    • Use conservation of momentum to solve for both energy and momentum in elastic and inelastic collisions (solve or calculate for p, Δp, F, t, m, v, or K)
    • Explain partially inelastic collisions in terms of where energy may go & plan to investigate
    • Predict different outcomes for inelastic and elastic collisions
    • Use momentum conservation to find v you use later in energy scenarios
    • Qualitatively explain a collision in 2D (where there is both X and Y momentum -- just solve each axis independently)
  • Design/Analyze experiments
    • Evaluate data to verify that momentum is conserved both with an external force and without.
    • Design a lab for a single object to collect data to investigate the relationship between
      • changes in momentum and average force and time t.
      • the direction of force and the ange in momentum caused by that force.
    • Plan lab to test the conservation of momentum for elastic and inelastic situations.
      • Make predictions using conservation of momentum
      • use analysis of graphs to determine if elastic or inelastic
      • Express uncertainty of measurements numerically
      • evaluate the prediction against your outcome
      • Refine a scientific question to look for interactions not considered if the prediction is not consistent with data.

Equations:

Conservation of momentum equations will not be provided to you. You need to be able to write conservation of momentum equations that are tailored to the scenario you are considering, especially the following:

  • partially inelastic and perfectly elastic collisions
  • perfectly inelastic collisions
  • explosions

Common Misconceptions:

  • Misconception: Momentum is not a vector.
    • Principle: Momentum really is a vector. We can tell because a collision where two objects with the same momentum magnitude by opposite directions will result in a zero speed after colliding. This is only explained by have a sum of zero momentum, which would be true if momentum is a vector. This also explains why a an object of lower mass bounces back off a stationary object of larger mass after a collision.
  • Misconception: Conservation of momentum applies only to collisions.
    • Principle: Momentum is conserved in all closed systems or can be tracked as impulse in an open system. Challenge: Apply conservation of momentum to these non collisions: the explosion of a firecracker or a person in space throwing another object (or even just continuing motion).
  • Misconception: Momentum is the same as force.
    • Principle: Changes in momentum are caused by force (impulse momentum theory). As a result faster moving objects or larger objects are able to deliver a greater force than smaller or slower objects when colliding, but an object can have momentum without interacting with other objects and therefore momentum cannot be the same as force.
  • Misconception: Moving masses in the absence of gravity do not have momentum.
    • Principle: momentum is a property intrinsic to an object with mass and velocity. I really don't get why anyone would think this, but space is an excellent scenario for conservation of momentum because it can so often be considered as a closed system. So, when you see the center of mass has a velocity of v and there is separation of the system, you can know that the center of mass of the system maintains that same velocity v even though the individual objects have different speeds.
  • Misconception: The center of mass of an object must be inside the object.
    • Principle: The center of mass of an object can be found by taking the average position (X, Y, Z coordinate) of all the particles in an object. This is a mathematical value with importance in how things behave, but without physical substance. Consider a donut or a two cart system.
  • Misconception: Center of mass is always the same location as the center of gravity.
    • This detail is not relevant for our course, but I hate to delete things. Center of mass is the average location of the mass of all the particles in an object whereas center of gravity is the average location of force of gravity on all the particles. Really tall objects experience a slightly different g value at the top of their structure than at the bottom, so the particles at the top have a slightly smaller weight than similar particles at the bottom, causing the center of gravity to be slightly lower than the center of mass. This actually matters in some large scale engineering applications, but would not be tested in AP Physics.
  • Misconception: Momentum is not conserved in collisions with "immovable" objects
    • Principle: Newton's 2nd law: the immovable object is simply experiencing a much smaller acceleration (a=F/m) because it is either much more massive or attached to an object more massive that whatever you have colliding with it.
    • 2nd Principle: How you define your system determines if the system is open or closed. If you define your system as the object that is changing momentum you will never have momentum conserved within your system, but if you include all the interacting objects in your system you will have momentum conserved. So, the immovable object is only immovable because it is attached to the earth (like a wall), and if you include the earth in your system then an object that experiences a ∆p in the +x direction will have had the earth experience a ∆p in the -x direction as a result. Of course, given the mass of the earth, there is no noticeable result of this, just like jumping off the earth causes additional force on the earth, but we don't notice any change in motion of the earth from that either.
  • Misconception: Momentum and kinetic energy are the same.
    • Principles: momentum is directly related to velocity; kinetic energy is quadratically related to velocity; mechanical energy is not conserved in any real collisions (only ideal elastic collisions). When collisions happen people want to talk about transferring energy and momentum interchangeably. In isolated collisions, though, mechanical energy is frequently not conserved, which is how we even prove that momentum is a thing. Take the case of a collision where a 1 kg object going 1 m/s runs into, and sticks to a 1 kg stationary object. Together they now have a mass of 2 kg, conservation of momentum predicts that 1(1) + 0 = (1+1)v, the final speed will be 0.5 m/s. If you consider energy, you have 1/2 (1)(12)+ 0 = 0.5 J before the collision and 1/2 (2) (0.52) = 0.25 J after, so kinetic energy was not conserved (some was converted to non-mechanical forms of energy). Yes energy was transferred and momentum was transferred, but they were not transferred in the same way and are not the same thing.