Read Inelastic Collisions
Read about inelastic collisions on page 483 of your physics textbook.  Continue by studying "Example 9.10" on pages 484 and 485 of the textbook. After complete Self-Check 1.


Read Unit Introduction
Study "Example 9.11" on page 485 of your textbook.

 

Answer "Practice Problem 1" on page 484 of your textbook.

Given:                  
           
             Â«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»m«/mi»«mi»p«/mi»«/msub»«mo»=«/mo»«mn»1«/mn»«mo».«/mo»«mn»00«/mn»«moȤ#160;«/mo»«mi»k«/mi»«mi»g«/mi»«/math»

Required: The velocity of the bullet just before impact,   .

Analysis and Solution:

Choose the system of bullet and pendulum as an isolated system. Since the pendulum is stationary before the bullet hits, its initial velocity is zero; thus, its initial momentum   . After the collision, the bullet and pendulum move together as a unit. The kinetic energy of the pendulum-bullet system is converted into gravitational potential energy:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»E«/mi»«mi»k«/mi»«/msub»«mo»=«/mo»«msub»«mi»E«/mi»«mi»p«/mi»«/msub»«/math»

 

Apply the law of conservation of energy to find the speed of the pendulum-bullet system just after impact:

 

 

Apply the law of conservation of momentum to find the initial velocity of the bullet:

 

Paraphrase:

The initial velocity of the bullet immediately before impact was 391 m/s [forward].


Answer "Practice Problem 1" on page 485 of your textbook.

Given:

mass of dart md=0.012 kg 
mass of block-glider  mb  = 0.200 kg
final velocity of system  
initial velocity of dart  

Required:  The amount of kinetic energy lost immediately after the interaction.

Analysis and Solution:

The initial energy of the system comes from the kinetic energy of the dart:

The final kinetic energy comes from the dart-block-glider system.

 

The difference between the initial and final kinetic energies is the kinetic energy lost.


Paraphrase: There was 1.1 J lost immediately after the interaction of the dart and the block-glider system. 



Try This
Answer "Practice Problem 2" on page 484 and "Practice Problem 2" on page 485 of the textbook.