Physics Momentum John G. Cramer Professor of Physics B451 PAB cramer@phys.washington.edu

Momentum and the 2nd Law Momentum Units: kg m/s or N s. Momentum is a vector quantity. Force changes momentum. Momentum Units: kg m/s or N s. October 27, 2006

Solving Momentum Problems Drawing a before-and-after pictorial representation Sketch the situation. Use two drawings, labeled “Before” and “After,” to show the objects before they interact and again after they interact. Establish a coordinate system. Select your axes to match the motion. Define symbols. Define symbols for the masses and for the velocities before and after the interaction. Position and time are not needed. List known information. Give the values of quantities known from the problem statement or that can be found quickly with simple geometry or unit conversions. Before-and-after pictures are usually simpler than the pictures you used for dynamics problems, so listing known information on the sketch is adequate. Identify the desired unknowns. What quantity or quantities will allow you to answer the question? These should have been defined as symbols in Step 3 above. October 27, 2006

Colliding Train Cars Car 2 at rest m1=m2=m Cars couple October 27, 2006

A System of N Particles The N=3 Case: For every pair of particles, the action/reaction pairs Fj on k and Fk on j are equal and opposite force vectors. In addition, each particle may be subjected to possible external forces Fext on k from agents outside the system. Defining “The System”: In considering the conservation of momentum, we will normally define “the system” as a group of interacting particles NOT subject to external forces. October 27, 2006

The Law of Conservation of Momentum Law of Conservation of Momentum: The total momentum P of an isolated system is a constant. Interactions within the system do not change the system’s total momentum. October 27, 2006

Example: Two Balls Shot from a Tube A 10 g ball and a 30 g ball are placed in a tube with a massless spring between them. When the spring is released, the 10 gm ball flies out of the tube at a speed of 6.0 m/s. With what speed does the 30 g ball emerge from the other end? October 27, 2006

Strategy: Conservation of Momentum MODEL: Clearly define the system If possible, choose a system that is isolated or within which the interactions are sufficiently short and intense that you can ignore external forces for the duration of the interaction (the impulse approximation). Momentum is conserved. If it’s not possible to choose an isolated system, try to divide the problem into parts such that momentum is conserved during one segment of the motion. Other segments of the motion can be analyzed using Newton’s laws or, as you’ll learn in Chapters 10 and 11, conservation of energy. VISUALIZE: Draw a before-and-after pictorial representation. Define symbols that will be used in the problem, list known values, and identify what you’re trying to find. SOLVE: The mathematical representation is based on the law of conservation of momentum: In component form, this is: ASSESS: Check that your result has the correct units, is reasonable, and answers the question. October 27, 2006

Example: Rolling Away Bob sees a stationary cart 8.0 m in front of him. He decides to run to the cart as fast as he can, jump on, and roll down the street. Bob has a mass of 75 kg and the cart’s mass is 25 kg. If Bob accelerates at a steady 1.0 m/s2 before jumping on, what is the cart’s speed just after Bob jumps on? October 27, 2006

It Depends on the System Is momentum conserved in the system? No! (external force) Yes! (mostly, neglect Sun’s force?) Goal: To chose a system in which momentum IS conserved. October 27, 2006