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(III) Billiard balls A and B, of equal mass, move at right

Physics: Principles with Applications | 6th Edition | ISBN: 9780130606204 | Authors: Douglas C. Giancoli ISBN: 9780130606204 3

Solution for problem 44P Chapter 7

Physics: Principles with Applications | 6th Edition

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Physics: Principles with Applications | 6th Edition | ISBN: 9780130606204 | Authors: Douglas C. Giancoli

Physics: Principles with Applications | 6th Edition

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Problem 44P

(III) Billiard balls A and B, of equal mass, move at right angles and meet at the origin of an xy coordinate system as shown in Fig. 7-36. Initially ball A is moving along the y axis at +2.0 m/s, and ball B is moving to the right along the x axis with speed +3.7 m/s. After the collision (assumed elastic), ball B is moving along the positive y axis (Fig. 7-36) with velocity v'B. What is the final direction of ball A, and what are the speeds of the two balls?

FIGURE 7;36 Problem 46. (Ball A after the collision is not shown.)

Step-by-Step Solution:

Solution 44P:

Whenever two bodies collide, their speed and direction of motion changes. In this problem, we have to determine speed of ball A and ball B, and the final direction of ball A after collision.

Step 1 of 5</p>

Concept:

        Law of conservation of linear momentum: When no external force acts on the system, then the final momentum of the system is equal to their initial momentum.

        Law of conservation of Energy: Energy can neither be created nor be destroyed. It can only be converted from one form into other. The total amount of energy in an isolated system remains constant.

Step 2 of 5</p>

Let the mass of balls be

The initial speed of balls A and B are  and   respectively.

The final speed of ball B is along positive y-axis.

Let the final speed of ball A be  making an angle  with the positive x-axis as shown in figure below.

 

Step 3 of 5</p>

As no external force acts on the system, therefore momentum has to conserved.

Applying law of conservation of momentum along x-axis, we get,

        

                                 

                                …(1)

Similarly, applying law of conservation of momentum along y-axis, we get,

        

                                 

                                

                         …(2)

Squaring and adding equations (1) and (2), we get,

            

                            …(3)

Step 4 of 5

Chapter 7, Problem 44P is Solved
Step 5 of 5

Textbook: Physics: Principles with Applications
Edition: 6
Author: Douglas C. Giancoli
ISBN: 9780130606204

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(III) Billiard balls A and B, of equal mass, move at right

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