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A proton moving with speed $v_{A 1}$ in the $+x$ -direction makes an elastic, off-center collision with an identical proton originally at rest. After impact, the first proton moves with speed $v_{A 2}$ in the firstquadrant at an angle $\alpha$ with the $x$ -axis, and the second moves with speed $v_{B 2}$ in the fourth quadrant at an angle $\beta$ with the $x$ -axis $(\text { Fig. } 8.13)$ . (a) Write the equations expressing conservation of linear momentum in the $x$ - and $y$ -directions. (b) Square the equationsfrom part $(a)$ and add them. (c) Now introduce the fact that the collision is elastic. (d) Prove that $\alpha+\beta=\pi / 2 .$ (You have shown that this equation is obeyed in any elastic, off-center collision between objects of equal mass when one object is initially at rest.)

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$\alpha+\beta=90^{\circ}=\frac{\pi}{2} \mathrm{rad}$

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Moment, Impulse, and Collisions

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

Lectures

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

03:30

In physics, impulse is the integral of a force, F, over the time interval, t, for which it acts. Given a force, F, applied for a time, t, the resulting change in momentum, p, is equal to the impulse, I. Impulse applied to a mass, m, is also equal to the change in the object's kinetic energy, T, as a result of the force acting on it.

02:01

Problem2: A proton; moving…

01:37

A proton, moving with a ve…

01:55

00:49

11:54

Two protons (each with res…

06:31

04:18

Consider the reaction $p+p…

Consider the reaction $\ma…

03:21

Two protons approach each …

05:00

In some proton accelerator…

Yeah in discussion based on the given information we draw figures. Oh The 4th on no comes through part E. So here we have to find out the X component and by component of momentum. So was we are going to find out the X component of moving well X I'm your name of momentum is mm We a one yes zero it was you am multiplied by. We do what was al far less we we do was better. So from elbow we get we ate too was out of our yes me we do cause beta equals we a one. Now we consider this as equation one similarly why component of momentum? Yes 00 equal to I'm multiplying we mm you will signed alpha love minus we video fine vita. So from abu we get we ate too sign alpha minus me. Really you fine vita Equals to zero. Now we consider this as exploration. Oh now comes to party. So here on adding and the scrapping equation one and no we get now We square and their equations one and 2. Therefore we get me a two the square less me b to the square less. No me even very deeply about we Or if we need to multiply by VV two force L a far less better equals you me even the square or we can write this as me a two square plus we? Re to square minus. We even the square plus to humanity blah blah. We a two quality flour. We video well alpha less beta equals zero. Now we consider this as equation see no comes to our see. So yeah we use the low conservation of frenetic energy. So according to the law of conservation of the kinetic energy We get one divided by two. I am very deeply whereby we a one square Plus one divided by two Animal people are B one square. It will do one divided by two M. My popular but we ate two square Plus one divided by two M. I T B. B. To the square. No I'm simplifying the bubble equation. We get The A two Squares plus we B two square minus me. A one square X squared zero. Now we use this in equation see so we get two me A two multiplayer Barbie legal post and populous vita equals you. Zero nonsense the eight when we we do is not equal to zero. Therefore laws alpha plus B equals two zero. So yeah Cause L four plus Vita it was zero. Is the sex or it lasted or Liza now comes to part the So here since of course alpha plus better equals two zero. So we can write this as all of us. Alpha. Less made equal to close. Why you? I did. Why? No? So from a bow we get L fabulous vita equals two. Why divided by 2? Which we have? Right

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