# Chapter 1 Motion¶

## Example 1.1 Page no 17¶

In [3]:
#given
d=180                              #Distance of satellite above the surface of earth in km
t=90                               #Time taken to complete one revolution of the earth in minutes
r=6400                             #Radius of the earth in kms

#Calculations
R=(r+d)*1000
T=t*60
v=(2*3.14*R)/T
a=(v**2/R)

#Output
print"Orbital speed is ",round(v,0),"m/s"
print"Centripetal acceleration is ",round(a,1),"m/s**2"

Orbital speed is  7652.0 m/s
Centripetal acceleration is  8.9 m/s**2


## Example 1.2 Page no 17¶

In [7]:
#given
m=0.05                           #Mass of the stone in kg
r=0.4                            #Radius of the string in m

#Calculations
import math
vh=math.sqrt(9.8*r)
vl=math.sqrt((2/m)*(((1/2.0)*m*vh**2)+(m*9.8*2*r)))

#Output
print"Minimum speed when the stone is at the top of the circle is ",round(vh,2),"m/s"
print"Minimum speed when the stone is at the bottom of the circle is ",round(vl,2),"m/s"

Minimum speed when the stone is at the top of the circle is  1.98 m/s
Minimum speed when the stone is at the bottom of the circle is  4.43 m/s


## Example 1.3 Page no 17¶

In [14]:
#given
m=0.2                             #Mass of the ball in kg
r=1.5                             #Radius of vertical circle in m
q=35                              #Angle made by the ball in degrees
v=6                               #Velocity of the ball in m/s

#Calculations
import math
T=(m*((v**2/r)+(9.8*math.cos(q*3.14/180.0))))
at=9.8*math.sin(q*3.14/180.0)
ar=(v**2/r)
a=math.sqrt(at**2+ar**2)

#Output
print"Tension in the string is ",round(T,1),"N"
print"Tangential acceleration is ",round(at,2),"m/s**2"
print"Radial acceleration is ",ar,"m/s**2"

Tension in the string is  6.4 N
Tangential acceleration is  5.62 m/s**2
Radial acceleration is  24.0 m/s**2


## Example 1.4 Page no 17¶

In [18]:
#given
#A small ball is released from height of 4r measured from the bottom of the loop, where r is the radius of the loop

#Calculations
import math
ar=(6*9.8)
at=(9.8*math.sin(90*3.14/180.0))

#Output
print"Radial acceleration is ",ar,"m/s**2"
print"Tangential acceleration is ",round(at,1),"m/s**2"

Radial acceleration is  58.8 m/s**2
Tangential acceleration is  9.8 m/s**2


## Example 1.5 Page no 18¶

In [21]:
#given
l=0.95                                  #Length of the strring in m
m=0.15                                  #Mass of the bob in kg
r=0.25                                  #Radius of the circle in m

#Calculations
import math
h=math.sqrt(l**2-r**2)
t=2*3.14*math.sqrt(h/9.8)

#Output
print"The period of rotation is ",round(t,2),"s"

The period of rotation is  1.92 s


## Example 1.6 Page no 18¶

In [3]:
#given
N=40.0                                  #Minimum speed of rotor in rpm
r=2.5                                   #Radius of rotor in m

#Calculations
t=60/N
u=(9.8*t**2)/(4.0*3.14**2*r)

#Output
print"The coefficient of limiting friction between the object and the wall of the rotor is ",round(u,3)

The coefficient of limiting friction between the object and the wall of the rotor is  0.224


## Example 1.7 Page no 18¶

In [27]:
#given
a=30                                  #Angle of inclination in degrees
t=3                                   #Time in s

#Calculations
import math
a=(9.8*math.sin(a*3.14/180.0))
v=(0+a*t)

#Output
print"Speed of the block after ",t,"s is ",round(v,1),"m/s"

Speed of the block after  3 s is  14.7 m/s


## Example 1.8 Page no 19¶

In [6]:
#given
m=10.0                            #Mass of the block in kg
F1=40                            #Horizontal force to start moving in N
F2=32                            #Horizontal force to move with constant velocity in N

#Calculations
u1=(F1/(m*9.8))
u2=(F2/(m*9.8))

#Output
print"Coefficient of static friction is ",round(u1,3)
print"Coefficient of kinetic friction is ",round(u2,4)

Coefficient of static friction is  0.408
Coefficient of kinetic friction is  0.3265


## Example 1.9 Page no 19¶

In [54]:
#given
m=(3,12)                               #Masses of the blocks in kg
q=50                                   #Angle made by the string in degrees
a=3                                    #Acceleration of 12kg block in m/s^2

#Calculations
import math
T=m[0]*(9.8+a)
u=(m[1]*(9.8*math.sin(q*3.14/180.0)-a)-T)/(m[1]*9.8*math.cos(q*3.14/180.0))

#Output
print"Tension in the string is ",T,"N"
print"The coefficient of kinetic friction is ",round(u,3)

Tension in the string is  38.4 N
The coefficient of kinetic friction is  0.207


## Example 1.e.1 Page no 9¶

In [10]:
#given
w=50                                           #Weight in N
a=(40,50)                                      #Angles made by two cables in degrees

#Calculations
#Solving two equations obtained from fig. 1.10 on page no.10
#-T1cos40+T2cos50=0
#T1sin40+T2sin50=50
import math
A = array([[math.cos(a[1]*3.14/180.0),-math.cos(a[0]*3.14/180.0)],
[math.sin(a[0]*3.14/180.0),math.sin(a[1]*3.14/180.0)]])
b = array([0,50])
X = solve(A, b)
T2=X[1]
print "T2=",round(T2,1),"N"
T1=(math.cos(a[1]*3.14/180.0)/math.cos(a[0]*3.14/180.0))*T2
print "T1",round(T1,1),"N"

T2= 32.7 N
T1 27.4 N


## Example 1.e.5 Page no 13¶

In [56]:
#given
m=100.0                                    #Mass of block in kg
F=500                                      #Force in N
q=30                                       #Angle made with the horizontal in degrees
u=0.4                                      #Coefficient of sliding friction

#Calculations
R=m*9.8
f=(u*R)
a=(F*math.cos(q*3.14/180.0)-f)/m

#Output
print"The acceleration of the block is ",round(a,2),"m/s**2"

The acceleration of the block is  0.41 m/s**2


## Example 1.e.6 Page no 14¶

In [1]:
#given
m=(20.0,80.0)                               #Masses of blocks in kg
F=1000                                  #Force with which 20kg block is pulled in N

#Calculations
a=F/(m[0]+m[1])
T=F-(m[0]*a)

#Output
print"The acceleration produced is ",a,"m/s^2"
print"The tension in the string connecting the blocks is ",T,"N"

The acceleration produced is  10.0 m/s^2
The tension in the string connecting the blocks is  800.0 N


## Example 1.e.8 Page no 15¶

In [1]:
#given
w=588                                 #Weight of the person in N
a=3                                   #Acceleration in m/s^2
b=180

#Calculations
m=(w/9.8)
P=(w+(m*a))
p=w-b

#Output
print"Weight of the person when the elevator is accelerated upwards is ",P,"N"
print"Weight of the person when the elevator is accelerated upwards is ",p,"N"

Weight of the person when the elevator is accelerated upwards is  768.0 N
Weight of the person when the elevator is accelerated upwards is  408 N