Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

In Fig. 9-80, block 1 of mass $m_{1} = 6.6 k g$ is at rest on a long frictionless table that is up against a wall. Block 2 of mass $m_{2}$ is placed between block 1 and the wall and sent sliding to the left, toward block 1, with constant speed $v_{2 i}$ . Find the value of $m_{2}$ for which both blocks move with the same velocity after block 2 has collided once with block 1 and once with the wall. Assume all collisions are elastic (the collision with the wall does not change the speed of block 2).

The value of mass $m_{2}$ is 2.2 kg .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Understanding the given information

i) Mass of block 1, $m_{1} i s 6.6 k g$ .

ii) The speed of block 2 is $v_{2 i}$ .

Step 2: Concept and formula used in the given question

You use the concept of conservation of momentum to find the mass. You use the equations given in the book 9-75 and 9-76 and can solve for the mass of block 2.

$V_{1 f} = \frac{2 m_{2}}{m_{1} + m_{2}} v_{2 i} V_{2 f} = \frac{(m_{2} - m_{1})}{m_{1} + m_{2}} v_{2 i}$

Step 3: Calculation for the value of m2 for which both blocks move with the same velocity after block 2 has collided once with block 1 and once with the wall

We can use the below equations to find mass as,

$V_{1 f} = \frac{2 m_{2}}{m_{1} + m_{2}} v_{2 i} V_{2 f} = \frac{(m_{2} - m_{1})}{m_{1} + m_{2}} v_{2 i}$

Here, $v_{2 i}$ is the initial velocity of block -2.

The velocity of block 2, after bouncing off the wall, will be the same as before but with a negative sign; we can write it as,

$V_{1 f} = - V_{2 f}$

Substitute the values in the above expression, and we get,

$\frac{2 m_{2}}{m_{1} + m_{2}} v_{2 i} = \frac{(m_{2} - m_{1})}{m_{1} + m_{2}} v_{2 i} 2 m_{2} = - m_{2} - m_{1} 3 m_{2} = m_{1} m_{2} = \frac{m_{1}}{3}$

Substitute the values in the above expression, and we get,

$m_{2} = \frac{6.6}{3} = 2.2 k g$

Thus, the mass of block 2 is $m_{2} = 2.2 k g$ .

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Understanding the given information

Step 2: Concept and formula used in the given question

Step 3: Calculation for the value of m2 for which both blocks move with the same velocity after block 2 has collided once with block 1 and once with the wall

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Fundamentals Of Physics

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Step by Step Solution

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