In [1]:

```
import math #Example 4_1
#To calculate the force required
vf=12 #units in meters/sec
v0=0 #units in meters/sec
t=8 #units in sec
a=(vf-v0)/t #units in meters/sec**2
m=900 #units in Kg
F=m*a #units in Newtons
print "The force required is F=",round(F)," N"
```

In [2]:

```
import math #Example 4_2
#To find the friction force that opposes the motion
F1=500 #units in Newtons
F2=800 #units in Newtons
theta=30 #units in degrees
Fn=F1+(F2*math.sin(theta*math.pi/180)) #units in Newtons
u=0.6
f=u*Fn #units in Newtons
print "The Frictional force that is required is f=",round(f)," N"
```

In [4]:

```
import math #Example 4_3
#To find out at what rate the wagon accelerate and how large a force the ground pushing up on wagon
F1=90 #units in Newtons
F2=60 #units in Newtons
P=F1-F2 #units in Newtons
F3=100 #units in Newtons
F4=math.sqrt(F3**2-F2**2) #units in Newtons
a=9.8 #units in meters/sec**2
ax=(F4*a)/F1 #units in Meters/sec**2
print "The wagon accelerates at ax=",round(ax,1)," meters/sec**2\n"
print "Force by which the ground pushing is P=",round(P)," N"
```

In [5]:

```
import math #Example 4_4
# To calculate How far does the car goes
w1=3300 #units in lb
F1=4.45 #units in Newtons
w2=1 #units in lb
weight=w1*(F1/w2) #units in Newtons
g=9.8 #units in meters/sec**2
Mass=weight/g #units in Kg
speed=38 #units in mi/h
speed=speed*(1.61)*(1/3600) #units in Km/sec
stoppingforce=0.7*(weight) #units in Newtons
a=stoppingforce/-(Mass) #units in meters/sec**2
vf=0
v0=17 #units in meters/sec
x=(vf**2-v0**2)/(2*a)
print "The car goes by x=",round(x,1)," meters"
#In text book the answer is printed wrong as x=20.9 meters the correct answer is x=21.1 meters
```

In [6]:

```
import math #Example 4_5
#To find the acceleration of the masses
w1=10 #units in Kg
w2=5 #units in Kg
f1=98 #units in Newtons
f2=49 #units in Newtons
w=w1/w2
T=round((f1+(w*f2))/(w+1)) #units in Newtons
a=(f1-T)/w1 #units in meters/sec**2
print "Acceleration is a=",round(a,1)," meters/sec**2"
```

In [7]:

```
import math #Example 4_6
#To find the acceleration of the objects
w1=0.4 #units in Kg
w2=0.2 #units in Kg
w=w1/w2
a=9.8 #units in meters/sec**2
f=0.098 #units in Newtons
c=w2*a #units in Newtons
T=((w*c)+f)/(1+w) #units in Newtons
a=(T-f)/w1 #units in meters/sec**2
print "Acceleration a=",round(a,1)," meters/sec**2"
```

In [8]:

```
import math #Example 4_7
#To estimate the lower limit for the speed
#In a practical situation u should be atleast 0.5
u=0.5
g=9.8 #units in meter/sec**2
x=7 #units in meters
v0=math.sqrt(2*u*g*x) #units in meters/sec
print "The lower limit of the speed v0=",round(v0,1)," meter/sec"
```

In [9]:

```
import math #Example 4_9
#To calculate how large a force must push on car to accelerate
m=1200 #units in Kg
g=9.8 #units in meters/sec**2
d1=4 #units in meters
d2=40 #units in meters
a=0.5 #units in meters/sec**2
P=((m*g)*(d1/d2))+(m*a) #units in Newtons
print "The force required is P=",round(P)," N"
#In text book the answer is printed wrong as P=1780 N but the correct answer is P=1776 N
```

In [10]:

```
import math #Example 4_10
#To calculate the tension in the rope
u=0.7
sintheta=(6.0/10)
w1=50 #units in Kg
g=9.8 #units in meter/sec**2
costheta=(8.0/10)
Fn=w1*g*costheta #units in Newtons
f=u*Fn #units in Newtons
T=f+(w1*g*sintheta)
print "The tension in the rope is T=",round(T)," N"
```

In [11]:

```
import math #Example 4_11
#To find the acceleration of the system
w1=7.0 #units in Kg
a=9.8 #units in meters/sec**2
w2=5 #units in Kg
w=w1/w2
F1=29.4 #units in Newtons
F2=20 #units in Newtons
f=(F1+F2) #units in Newtons
T1=w1*a #units in Newtons
T=(T1+(w*f))/(1+w) #units in Newtons
a=((w1*a)-T)/w1 #units in meters/sec**2
print "Acceleration a=",round(a,2)," meters/sec**2"
```