   Chapter 6, Problem 72AP

Chapter
Section
Textbook Problem

Two objects of masses m and 3m are moving toward each other along the x-axis with the same initial speed v0. The object with mass m is traveling to the left, and the object with mass 3m is traveling to the right. They undergo an elastic glancing collision such that m is moving downward after the collision at right angles from its initial direction, (a) Find the final speeds of the two objects, (b) What is the angle θ at which the object with mass 3m is scattered?

(a)

To determine
The final speed of the two objects.

Explanation

Object 1 has a mass m and object 2 has mass 3m.

Conservation of the x-component of the momentum gives,

(3m)v2x+0=mv0+(3m)v0v2x=23v0 (I)

• m is the mass of the particle

Conservation of the y-component of the momentum gives,

mv1y+(3m)v2y=0v1y=3v2y (II)

As the collision is elastic,

KEf=KEi12mv1y2+12(3m)(v2x2+v2y2)=12mv02+12(3m)v02v1y2+3(v2x2<

(b)

To determine
The angle θ at which the object with mass 3m is scattered.

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