PreClass Notes: Chapter 9, Sections 9.3-9.6 From Essential University Physics 3 rd Edition by Richard Wolfson, Middlebury College 2016 by Pearson Education, Inc. Narration and extra little notes by Jason Harlow, University of Toronto This video is meant for University of Toronto students taking PHY131. Outline 9.3,9.4 Impulse and Momentum Energy in Collisions 9.5 Totally Inelastic Collisions 9.6 Elastic Collisions [Animated gif from http://giphy.com/gifs/fail-bump-chest-e95jhtb4kpm2c] A collision is a brief, intense interaction between objects External forces are negligible so the total momentum of the colliding objects remains essentially unchanged. R.Wolfson 1
Impulse The impulse upon a particle is defined as Impulse has units of N s, but you should be able to show that N s are equivalent to kg m/s. The impulse-momentum theorem states that the change in a particle s momentum is equal to the impulse on it. Impulse Changes Momentum Example: When a car is out of control, it is better to hit a haystack than a concrete wall. Physics reason: Same impulse either way, but extension of hitting time reduces the force. 2
Collisions: vocabulary Every collision or explosion involves a short, intense interaction in which external forces are usually negligible: that means collisions and explosions conserve momentum. The kinetic energy of the system before and after is not generally conserved. There are four categories: If the final kinetic energy is less than the initial kinetic energy, this is an inelastic collision (K f < K i ). Heat or bending of materials has absorbed energy. If the final kinetic energy is more than the initial kinetic energy, this is an explosive collision, or an explosion (K f > K i ). Some internal chemical or elastic energy must have been released. If the final kinetic energy equals the initial kinetic energy, this is an elastic collision (K f = K i ). Collisions: vocabulary A sub-category of inelastic collisions is: If the two objects stick together in the end, this is a totally inelastic collision. (K f < K i ), ( v 1f = v 2f ) Maybe there was Velcro or glue or they just got melded together in the collision. 3
Got it? Classify the following collisions based on the four categories of the previous slides: A. Two magnets approach, their north poles facing; they repel and reverse direction without touching. B. A truck strikes a parked car and the two slide off together, crumpled metal hopelessly entwined. C. A basketball is dropped from 1.5 m above the floor, and bounces up to a maximum height of 1.2 m above the floor. D. A toy containing a compresses spring is dropped from 1.5 m above the floor, when it hits the floor the spring is released, causing it to jump to a maximum height of 2.2 m above the floor. Totally Inelastic Collisions Totally inelastic collisions are governed entirely by conservation of momentum. Since the colliding objects join to form a single composite object, there s only one final velocity: Before collision After collision Therefore conservation of momentum reads m v m v m m v 1 1 2 2 1 2 f 4
Inelastic collision occurs when colliding objects result in deformation and/or the generation of heat. Single car moving at 10 m/s collides with another car of the same mass, m, at rest. From the conservation of momentum, (net mv) before = (net mv) after (m 10) before = (2m V) after V = 5 m/s Elastic Collisions Elastic collisions conserve both momentum and kinetic energy: Before collision After collision Therefore the conservation laws read m v m v m v m v 1 1i 2 2i 1 1f 2 2f m v m v m v m v 1 2 1 2 1 2 1 2 2 1 1i 2 2 2i 2 1 1f 2 2 2f 5
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Special Cases: 1-D Elastic Collisions; m 2 Initially at Rest 1) m 1 << m 2 : Incident object rebounds with essentially its incident velocity 7
Special Cases: 1-D Elastic Collisions; m 2 Initially at Rest 2) m 1 = m 2 : Incident object stops; struck object moves away with initial speed of incident object Special Cases: 1-D Elastic Collisions; m 2 Initially at Rest 3) m 1 >> m 2 : Incident object continues with essentially its initial velocity; struck object moves away with twice that velocity 8
Elastic Collisions in 2-D 2015-07-31 Got it? Ball A is at rest on a level floor. Ball B collides elastically with Ball A, and the two move off separately, but in the same direction. What can you conclude about the masses of the two balls? A. Ball A and Ball B have the same mass. B. Ball B has a greater mass than Ball A. C. Ball A has a greater mass than Ball B. D. You cannot conclude anything without more information. 9
Elastic Collisions in 2-Dimensions 10