#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"
#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"
#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"
#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"
#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"
#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)
#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"
#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)
#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)
#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"
#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"
#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"
#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"