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Momentum and Force

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Introduction
Problems
Answers

      
Introduction

Linear Momentum The symbol for linear momentum is p.  p = mv   Since velocity is a vector, momentum is also a vector.  The reference frame must be specified.  Normally, momentum with no qualifier is linear momentum.

Momentum can only be changed by applying a force.  The momentum can be increased or decreased by changing the magnitude of the velocity.  It can also be changed by changing direction even if the magnitude of the velocity remains constant.

Newton's Second Law of Motion     The rate of change of momentum of a body is proportional to the net force applied to it.

           /\p
F = ----                ( both mass and velocity can change ) 
           /\t
   

F = ma               ( special case when mass does not change )    

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Problems

1.     How much momentum does a 100. kg fullback have running at 9.50 m/s.
    
2. What is the change in momentum if a 40.0 g superball hits a wall at 25.0 km/h and rebounds at 180o with a speed of 20.0 km/h?
   
3. Water coming out of a hose at 2.0 kg/s and 30. m/s strikes a wall and falls straight down without splashing back.  What is the force exerted by the water on the wall?
   
4. A 4.00 N force is applied for 5.00 s in the same direction a 300. g baseball is all ready moving at 50.0 m/s.  What is the acceleration and new velocity of the baseball?

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Answers

1.     How much momentum does a 100. kg fullback have running at 9.50 m/s.
    
   
p = mv = 100. kg x 9.50 m s -1 = 950. kg m s -1 
   
   

   

2. What is the change in momentum if a 40.0 g superball hits a wall at 25.0 km/h and rebounds at 180o with a speed of 20.0 km/h?
   
   
25.0 km      1000 m         1 h                                                   20.0 km      1000 m         1 h        
------------ x ----------- x ----------- = 6.94 m/s                            ------------ x ----------- x ----------- = 5.56 m/s
   1 h              1 km        3600 s                                                   1 h              1 km        3600 s
   

/\v = v2  -  v1 = -5.56 m/s  -  6.94 m/s =  -12.50 m/s

/\p = /\mv = 0.0400 kg x ( -12.50 m/s ) =   -0.500 kg m s -1 
   

   

   

3. Water coming out of a hose at 2.0 kg/s and 30. m/s strikes a wall and falls straight down without splashing back.  What is the force exerted by the water on the wall?
   
   
Every second 2.0 kg of water hit the wall and comes to a rest.

     
           /\p       2.0 kg x ( 0. m/s  - 30. m/s )
F = ----- = -------------------------------------- =   -60. N       
This is the force on the water
           /\t                      1.0 s
    

60. N is the force of the water on the wall.
     

   

   

4. A 4.00 N force is applied for 5.00 s in the same direction a 300. g baseball is all ready moving at 50.0 m/s.  What is the acceleration and new velocity of the baseball?
   
    
                                 F          4.00 N
F = ma    =>  a = -------  =  ------------- = 13.3 m s -2  
                                   m          0.300 kg
    

v = v1 + at = 50.0 m s -1  +  13.3 m s -2 x 5.00 s = 116.5 m/s
    

 

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