# Chapter 06:Linear Momentum¶

## Ex6.1:pg-189¶

In [2]:
  import math  #Example 6_1

#To calculate how large is the average force retarding its motion
m=1500    #units in Kg
vf=15.0     #units in meters/sec
v0=20     #units in meters/sec
t=3    #units in sec
f=((m*vf)-(m*v0))/t     #Units in Newtons
print "The average retarding force is F=",round(f)," Newtons"

The average retarding force is F= -2500.0  Newtons


## Ex6.2:pg-190¶

In [3]:
  import math  #Example 6_2

#To estimate the average stopping force the tree exerts on the car
m=1200    #units in Kg
vf=0     #units in meters/sec
v0=20     #units in meters/sec
v=0.5*(vf+v0)     #units in meters/sec
s=1.5     #units in meters
t=s/v     #units in sec
f=((m*vf)-(m*v0))/t     #Units in Newtons
print "The average stopping force the tree exerts on the car is F="
print f,"Newtons"

The average stopping force the tree exerts on the car is F=
-160000.0 Newtons


## Ex6.3:pg-191¶

In [4]:
  import math  #Example 6_3

#To find out how fast and the direction car moving
m1=30000     #units in Kg
m2=1200      #units in Kg
v10=10     #units in meters/sec
v20=-25     #units in meters/sec
vf=((m1*v10)+(m2*v20))/(m1+m2)    #unis in meters/sec
print "The car is moving at vf=",round(vf,2)," Meters/sec\n"
print "The positive sign of vf Indicate the car is moving in the direction the truck was moving"

The car is moving at vf= 8.0  Meters/sec

The positive sign of vf Indicate the car is moving in the direction the truck was moving


## Ex6.5:pg-193¶

In [5]:
  import math  #Example 6_5

#To find the velocity of each ball after collision
m1=0.04     #units in kg
m2=0.08     #units in kg
v1=0.3     #units in meters/sec
v2f=(2*m1*v1)/(m1+m2)        #units in meters/sec
v2f1=v2f*100     #units in cm/sec
print "The velocity V2f=",round(v2f,1)," meters/sec or ",round(v2f1)," cm/sec\n"
v1f=((m1*v1)-(m2*v2f))/m1    #units in meters/sec
v1f1=-v1f*100     #units in cm/sec
print "The velocity V1f=",round(v1f,1)," meters/sec or ",round(v1f1)," cm/sec\n"

The velocity V2f= 0.2  meters/sec or  20.0  cm/sec

The velocity V1f= -0.1  meters/sec or  10.0  cm/sec



## Ex6.6:pg-196¶

In [6]:
  import math  #Example 6_6

#To calculate the speed of the pellet before collision
h=0.30        #units in meters
g=9.8         #units in meters/sec**2
v=math.sqrt(2*g*h)       #units in meters/sec
m1=2     #units in Kgs
m2=0.010     #units in kgs
v10=((m1+m2)*v)/m2      #units in meters/sec
print "The speed of the pelet before collision is V10=",round(v10)," meters/sec"
#In textbook the answer is printed wrong as V10=486 meters/sec the correct answer is V10=487 meters/sec

The speed of the pelet before collision is V10= 487.0  meters/sec


## Ex6.7:pg-196¶

In [7]:
   import math  #Example 6_7

#To calculate how large a forward push given to the rocket
m=1300     #units in Kgs
vf=50000     #units in meters/sec
v0=0        #units in meters/sec
F=((m*vf)-(m*v0))          #units in Newtons
print "The Thrust is F=",round(F)," Newtons"

The Thrust is F= 65000000.0  Newtons


## Ex6.8:pg-197¶

In [8]:
  import math  #Example 6_8

#To determine the velocity of the third peice
momentumbefore=0     #units in kg meter/s
m=0.33      #units in Kgs
vz=momentumbefore/m
print "The Z component of velocity is Vz=",round(vz)," meters/sec\n"
m=0.33      #units in Kgs
v0=0.6      #units in meters/sec
vy=-(m*v0)/m      #interms of v0 and meters/sec
print "The Y component of velocity is Vy=",round(vy,1),"*V0\n"
v01=1     #units in meters/sec
v02=0.8       #units in meters/sec
vx=-((v01+v02)*m)/m      #interms of v0 and units in meters/sec
print "The X component of velocity is Vx=",round(vx,1),"*V0"

The Z component of velocity is Vz= 0.0  meters/sec

The Y component of velocity is Vy= -0.6 *V0

The X component of velocity is Vx= -1.8 *V0


## Ex6.9:pg-198¶

In [9]:
  import math  #Example 6_9

#To find out the velocity of second ball after collision
v1=5     #units in meters/sec
theta=50.0     #units in degrees
v2=2     #units in meters/sec
vx=v1/(v2*math.cos(theta*math.pi/180))    #units in meters/sec
vy=-(v2*math.cos(theta*math.pi/180))      #units in meters/sec
v=math.sqrt(vx**2+vy**2)      #units in meters/sec
print "After the collision the second ball moves at a speed of v=",round(v,2)," Meters/sec"
#in textbook the answer is printed wrong as 4.01 meters/sec the correct answer is 4.1 meters/sec

After the collision the second ball moves at a speed of v= 4.1  Meters/sec


## Ex6.10:pg-199¶

In [11]:
  import math  #Example 6_10

#To find the average speed of the nitrogen molecule in air
ap=1.01*10**5     #units in Newton/meter**2
nofmol=2.69*10**25     #Number of molecules
nitmass=4.65*10**-26     #units in Kg
v=math.sqrt((ap*3)/(nofmol*nitmass))     #units in meters/sec
print "The average speed of the nitrogen molecule in air is V=",round(v)," meters/sec"

The average speed of the nitrogen molecule in air is V= 492.0  meters/sec