1. OBJECTIVES:
In this chapter we will learn :
Some important kinds of Forces such as ; NORMAL &
FRICTION Forces
The Laws of Motion
How to solve dynamics problems by the Laws of Motion

2. DYNAMICS 1. NORMAL Force:
is the relation between FORCE & is REACTION Force, perpendicular to
MOTION the surface that the action force is
applied
FORCE: is the Effect that can destroy,
stop or move the objects.
Since it shows a DIRECTION. Then it
is a VECTOR Quantity.
THE KINDS OF FORCES

3. FRICTIONAL FORCE
• Frictional force: It is an important force which only acts when two objects are
touching and are applying force to one another.
• It is a force that slows down moving objects and brings them to rest.
• It always acts in a direction opposite to the direction of the force applied to the
object.
• Walking is possible only on a frictional surface.
• Water also applies a frictional force to the objects moving in it.
• Frictional force does not depend on the area of the rubbing surfaces. The
frictional force between the object and the table depends on two factors;
a. The weight of the object.
b. The roughness of the surfaces rubbing together.

4. 2. FRICTION Force: Ex: Find the friction F F N
force in both case.
is REACTION Force, formed N
in opposite direction to the
action force applied. F f max   .N 
W  mg W  mg
N W  F N W  F
Re ady to Move F f max  .W  F  F f max  .W  F 
No Motion
F ext
F f F f max
Ff FNET  Fext  F f max F f max
Between two
F f max
surface, there is
Static Kinetic a maximum value
Friction of Friction Force.
Friction Fext
Let us write an equation about this maximum
friction force between two surface.
F f max
F f max  N  const
N
We call this constant as the coefficient of
friction, µ between two surface
F f max   .N

5. 3. TENSION Force: Planet Field Strength Mass Weight
is ACTION-REACTION Force, Mercury 3,78 N/kg X 40 kg = 151 N
formed along stretch Force Venus 8,94 N/kg X 40 kg = 358 N
applied. Earth 10 N/kg X 40 kg = 400 N
Moon 1,7 N/kg X 40 kg = 67 N
Mars 3,79 N/kg X 40 kg = 152 N
Jupiter 25,4 N/kg X 40 kg = 1067N
Saturn 10,7 N/kg X 40 kg = 428 N
Uranus 9,2 N/kg X 40 kg = 368 N
Neptune 12 N/kg X 40 kg = 480 N
Pluto 0,3 N/kg X 40 kg = 12 N
Ex: What is the weight of an object on the Moon
which has the weight on Earth as 100N ?
W  mg  100 N  10m  m  10kg
4. GRAVITATIONAL Force: W  mg  10.1,7  17 N
is Natural Attractive Field Force, between
two bodies that appears as the WEIGHT.
5. MAGNETIC Force:
6. ELECTROSTATIC Force:
FG FG FG FG
7. NUCLEAR Force:
We define the Gravitational Field as; .
FG .
g FG  W  W  m.g
m .

6. LAWS OF MOTION II-) ACTION PRINCIPLE:
I-) INERTIA PRINCIPLE: If the NET FORCE is not ZERO on an object ;
Either the object will be accelerated or decelerated
INERTIA: is the tendency to keep the initial
position F NET  a
FNET
m a
m 2 FNET
2a
3FNET
m 3a
FNET
 const  mass(m)
a
PRINCIPLE: If the NET FORCE is ZERO on
an object ; Either the object stops or FNET  m.a
moves steadily (with constant velocity)
III-) ACTION-REACTION PRINCIPLE:
If an object applies a Force on
another object. The Other One
replies with the same Force in
opposite direction

7. INCLINED PLANE: Along x-axis, There is motion. W . sin   F R
Fnet  ma
y N
Ff Fnet  FR  Ff  W . sin   Ff  ma
mg sin   .mg cos   ma
W . sin  W . cos 

a  g.sin    cos  
x
W If there is no FRICTION, then take;  0
a  g. sin 

Object is sliding down.
Along y-axis, There is no motion.
Fnet  0
F f   .N
N  W . cos   0
F f   .mg cos 
N  mg cos 

8. LIFT PROBLEMS: B- The Lift accelerated downward or decelerated
upward ;
Let us look at the cases by both the observers
inside the Lift and outside the Lift
FNet  0
A- The Lift accelerated upward or decelerated
downward ; T  W  F fic.  0
FNet  0
T  W  F fic. F fic
T  W  F fic.  0 T  mg  ma T
a
T  W  F fic. T  m g  a 
T  mg  ma W  mg
T  m g  a 
T
FNet  ma FNet  ma
 
a
T  W  m.a F fic T  W  m.  a
W  mg
T  mg  ma T  mg  ma
T  m g  a  T  m g  a 

9. Apparent Weight
W = mg W = m(g+a) W = m(g-a) Weightless

10. Ex.:What is the acceleration of the object, a=? Ex.:A force of 10N is applied on the mass of
  the 2kg with and angle of 370. If the coefficient
N a
of friction between mass and surface is 0.1, what
 is the acceleration of the mass in m/s2 ?
 m=10 kg
F  100 N
Ff    
a
  0,5
N FY F  10 N
  
W
m=2 kg 37 0
Ff FX
Along y-axis; There is no MOTION, ay=0  
         0,1
FNet  0  N  W  0  N  W  mg N  100 N  FX  F.cos37 0  10 N .0,8  8 N
 
W FY  F.sin370  10 N .0,6  6 N
Along x-axis; There is MOTION, a=ax
    Along y-axis; There is no MOTION, ay=0
FNet  ma F f  N       
   FNet  0  N  FY  W  0  N  W  FY
F  F f  ma  0,5.100 N 
N  20 N  6 N  14 N
100 N  50 N  10kg.a  50 N Along x-axis; There is MOTION, a=ax
   
a  5m / s 2
FNet  ma
  F f  N

FX  F f  ma  0,1.14 N
8 N  1,4 N  2kg.a  1,4 N
a  3,3m / s 2

11. Ex.: Two masses which are contact with each other Ex.: Three masses are connected with ropes. A
are pushed by a force of 20 N. What force does the force of 280 N acted on the masses as shown
mass A apply to the mass B when coefficient of in the figure. Find the tensions in the rope T1
friction between the masses and the surface; µ=0 ,T2 . 
and µ=0.1?   N1 
 N3 N2 a
N1 a   m3  20kg  m  20kg  m1  30kg 
N2 T2 2 T1 F  280N
 
F  20 N m1=3kg R   
m2=2kg Ff 3  Ff 2  Ff 1   0,2
  W3 W2 
Ff 1  Ff 2    W1
W1
W2 F f 1  N1  0,2.300 N  60 N
 
Along y-axis; There is no MOTION, ay=0 Ff 2  N 2  0,2.200 N  40 N
  
FNet  0 F f 3  N 3  0,2.200 N  40 N
     
 N1  W1  30 N F f 1  N1  0,1.30 N  3N For all system; FNet  mT a
   
 
    
 N 2  W2  20 N F f 2  N 2  0,1.20 N  2 N F  Ff 1  Ff 2  Ff 3  m1  m2  m3 .a
Along x-axis; There is MOTION, a=ax 280 N  (60 N  40 N  40 N )  (30  20  20)kg .a
   
FNet  mT a FNet  mT a a  2m / s 2

 
   
F  m1  m2 a

F  F f 1  F f 2  m1  m2 a For m3 ; For m 2 ;
20 N  5kg .a 20 N  5 N  5kg.a    
FNet  m3a FNet  m2a
 
a  4m / s 2 a  3m / s 2       
T2  Ff 3  m3.a T1  T2  Ff 2  m2 .a
 
For Reaction Force, For Reaction Force, T2  40 N  20kg.2m / s 2 T1  80 N  40 N   20kg .2m / s 2
R; Choose one of the  
R; Choose one of the
T2  80 N T2  200 N
masses, ex; m2 masses, ex; m2
      
FNet  R  m2 a FNet  R  F f 2  m2 a
 
R  2kg.4m / s 2  8 N R  2 N  2kg.3m / s 2  8 N

12. 
Ex.: Two masses are F ? Ex. ( Atwood Machine) :
connected to each other When the system is
as shown in figure are released , find the tension
pulled up by force F. If in the rope in N, T= ? 
the tension in the cord m1  5kg a
For all system;
is 42N what is the 
 
force F? W1 FNet  mT a
    
For m 2 ; FNet  m2a
 T  42N 
a W1  W2  m1  m2 .a  
  T
T  W2  m2 .a
 150 N  50 N  (15kg  5kg ).a T
m2  3kg
42 N  30 N  3kg.a a  5m / s 2
  m2  5kg m1  15kg
a  4m / s 2 
W2 For m1 ; FNet  m1a
      
For all system; FNet  mT a W1  T  m1.a W2 W1
 
    
F  W1  W2  m1  m2 .a 150 N  T  15kg .5m / s 2
 
F  50 N  30 N   5kg  3kg .4m / s 2 T  75N

F  112 N

13. Ex.: Find acceleration of the system and T1 & T2 Ex.: When the system is released, what is the
When the coefficient of friction between 10kg of Acceleration of the system. The coefficient
mass and the surface,µ=0 and µ=0.1? of friction is µ=0,1.

 m3  10kg   a 
T2 T1 a N
 m1  2kg
T 
   W1sin 370 2.10.0,6  12 N
.
T2 T1 m2  2kg  F f  N  0,1.16 N  1,6 N
W1. cos 370

m1  6kg W1 370
m2  4kg 
W2  20 N N  W1. cos 37  2.10.0,8  16 N
0
 
 W1 
W2 For all system; FNet  mT a
   
  W2  W1. sin 37  Ff  m1  m2 .a
0
For all system; FNet  mT a
   20 N  12 N  1,6 N  (2kg  2kg ).a
W1  W2  m1  m2  m3 .a
a  1,6m / s 2
60 N  40 N  (6kg  4kg  10kg ).a
a  1m / s 2
For m1 ; For m 2 ;
   
FNet  m1a FNet  m2a
     
W1  T1  m1.a T2  W2  m2 .a
 
60 N  T  6kg .1m / s 2 T2  40  4kg.1m / s 2
 
T1  54 N T2  44 N

14. Ex.: Find the velocities of the objects K and L Ex.: In the figure the coefficient of kinetic friction is
shown in figure .3 seconds later, after they are
 µ for all interacting surfaces. Find the accelerations
released.   N of the blocks a.
a1 m1  4kg  N1  W1  m1g
T1 N1
N 2 N 2  W1  W2  m1  m2 g
     
a2  2a1 T1 Ff T
a
   
  T1   0,1 W1  Ff 1 
m1 F 
T2  2T1 T
f1 a 
F f  N W1 m F

T2  0,1.40 N
  2
 Ff 2 W2
a2 m2  8kg  4N  
F f 1  N1  10m1 Ff 2  N 2  10m1  m2 

W2
For m1 ; For m 2 ;
For m1 ; For m 2 ;    
    FNet  m1a FNet  m2a
FNet  m1a1 FNet  m2a2        
      T  Ff 1  m1.a F  T  Ff 2  Ff 1  m2 .a
T1  Ff  m1.a1 W2  T2  m2 .a2
 F  Ff 1  m1a  Ff 2  Ff 1  m2 .a
T1  4  4a1 80  T2  8.a2
F  m1g  m1a  m1  m2 g  m1g  m2 .a
 40  T1  8.a1 80  2T1  8.2a1
12a1  36 F  m1g  m1a  m1g  m2 g  m1g  m2 .a
a1  3m / s 2 a2  6m / s 2 F  3m1g  m1a  m2 g  m2 .a
v1  a1.t v2  a2 .t F  3m1  m2 g  m1  m2 .a
 3m / s 2 .3s  6m / s 2 .3s F  3m1  m2 
 18m / s a g
 9m / s m1  m2 

15. Ex.: The objects K and L are released in a
frictionless system as shown in figure. Find the
tension T on the rope which joins the objects K and
L . mK=mL=1kg 
T

 a 
NK NL
K 
 WK . sin 530 L 
WK . cos 530
 0
WL . cos 370
 WL . sin 37
WK 0 
0W
53 37 L
 
For all system; FNet  mT a
  
WK sin 530  WL sin 370  mK  mL .a
10.0,8  10.0,6  (1kg  1kg ).a
a  1m / s 2

16. CHECKING OF UNDERSTANDING (HOMEWORK)
The Answers of them should be placed just after this Chapter before the Next Chapter.
1. What is Force? How many kinds of Forces are there?
2. Why do we need to use the kind of ``NORMAL FORCE``?
3. What are the factors that the force of friction depends on?
2. What is the difference between uniform motion and uniformly
accelerated motion?
3. Driving on an icy high way is particularly dangerous. Why?
4. What is INERTIA and its Principle? Give some examples
5. You hit a ball with your foot. Since the forces are F and –F
can you say the total force is zero? Then why does the ball
start to move?
6. The x-component of the projected objects is always constant
, why?
7. Mostly which Law of Motion is used to solve Dynamics
Problems?
8. What is Atwood Machine? And how do we find the
acceleration of it?
9. Can we feel ``Weightlessness`` on Earth? How?

17.  0
0
F ext
F ext