DISPLACEMENT and DISTANCE

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DISPLACEMENT and DISTANCE
FISIKA 1
18 SEPTEMBER 2013
Fakultas Teknologi Pertanian
UGM
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•
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20% : HOMEWORK / QUIZ
10% : CLASS ACTIVITY
35% : MIDTERM
35% : FINAL EXAM
MOTION!
Motion defined
• Any change in position with respect
to a frame of reference.
• Frame of reference – any physical
entity which could serve as basis in
telling that an object is moving.
Mechanics
the branch of Physics that is concerned with
the analysis of the action of forces on matter
or material systems.
• Dynamics is the
branch of
mechanics that is
concerned with the
effects of forces on
the motion of a
body or system of
bodies, especially
of forces that do
not originate within
the system itself.
• Kinematics
branch of
mechanics that
studies the
motion of a body
or a system of
bodies without
consideration
given to its mass
or the forces
acting on it
Unlocking of Difficulties
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Distance
Displacement
Speed
Velocity
Acceleration
Deceleration
Instantaneous Speed
Instantaneous Velocity
WHAT IS DIFFERENCE
BETWEEN….
DISPLACEMENT
and
DISTANCE
????????
Displacement and distance
To go to school from home...
l2
your
school
your
home
l1
l3
Distance = length of path
you travelled = l1 + l2 + l3
Displacement and distance
To go to school from home...
your
home
Size = length
of this arrow
your
school
displacement from
home to school
A displacement has size & direction.
Displacement and distance
Displacement requires :
– Length of a straight line going from the
old to the new positions
i.e. size/magnitude
– Direction of the movement
Distance vs. Displacement
Distance is the extent
of space between two
objects or places; an
intervening space. It is
also the total length
traversed by a moving
object. It is a scalar
quantity.
Displacement is
the shortest
length between
two points. It is a
vector quantity.
Displacement along a straight
line
• Set an initial point,
• Use positive (+) and negative (−)
signs to represent the direction.
* Remember assign a direction as positive!
Displacement along a straight
line
Take the direction to the right as positive.
Displacement along a straight line
Displacement in a plane
What is the total displacement of the car?
Displacement in a plane
Graphical method
From O to A and then to B.
3 km
4 km
37 5 km
N
total displacement
= 3 km to the east
Algebraic method
It is easy to add displacements if they are
perpendicular to each other.
e.g.
N
3 km
5 2 = 42 + d
2
 d = 3 km
4 km 37 5 km
Speed vs. Velocity
• Speed is the ratio of • Velocity is the ratio
distance traveled to
of change in
time interval. It is a
position to time
scalar quantity.
interval over which
change takes
place. It is a vector
quantity.
the two terms can just be interchanged in an
ordinary conversation, but they should have
a distinction in Physics.
WHAT IS DIFFERENCE
BETWEEN….
VECTOR
and
SCALAR
????????
Vectors
• A scalar quantity is one that is represented by a
single number
– mass; length; time; temperature; volume;
energy; charge; etc.
• A vector is a quantity which has both magnitude
and direction.
– Velocity, Displacement, Momentum, Force, …
• In physics we need vectors because the real
world is (at least) 3 dimensional.
Location in Space
• To locate an object in space we need to establish a
coordinate system with an origin and axes.
• Points are located by giving their x and y (and z)
coordinates.
A vector describes a displacement or
from one point to another
y
The components of the vector describe
the displacement in the x and y
direction.
7
A
(1,5)
6
5
4
3
2
1
C
VAB=(4,-2)
B
Two vectors are parallel if they describe
(5,3)
the same displacement even if that
displacement begins at different points.
(3,2)
x
origin
1
2 3
4
5
6
7
Vector Addition
A+B=C
Geometrically: Parallel transport the tail of B to the head
of A. The sum goes from the tail of A to the head of B.
Note: This construction only works if head of A is at the tail of
B. Otherwise you need to move B to make that true
Algebraically: Add the components
C(3,5)
B(-2,4)
A (5,1)
A 5
B -2
C 3
1
4
5
Vector addition is commutative and associative
Problem
Given that q = +12 mC and d = 16 cm,
(a) find the direction and magnitude of the net
electrostatic force exerted on the point charge q2 in
Figure below.
(b) (b) How would your answers to part (a) change if
the distance d were tripled?
Solution
Draw free body for JUST q2

F21 
k
(12mC ) 24mC 
(0.16m) 2
in direction from 1 to 2
  101N xˆ

F23

k
(24mC ) 36mC 
(0.16m) 2
in direction from 3 to 2
  303N xˆ
Solution, cont’d

F2  (101N  303N ) xˆ  202N in  x - direction
B) Tripling the separations decreases all
forces by a factor of 32=9
F2 = 22.4 N, +x direction
Distance and Displacement
• A physics teacher
walks 4 meters
East, 2 meters
South, 4 meters
West, and finally 2
meters North.
• 1. What is the
distance?
• 2. What is the
displacement?
Distance and Displacement
1. What is the distance?
2. What is the displacement?
Speed and Velocity
• The skier has an
average speed of
• (420 m) / (3 min) =
140 m/min and an
average velocity of
• (140 m, right) / (3
min) = 46.7 m/min,
right
Velocity along a straight line
Take direction towards right as positive

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