Motion
Mechanics
- the study of the motion of objects and the
forces that cause them.
Kinematics is a
quantitative description
of motion without
reference to its
physical causes. It
describes how the
objects move.
Dynamics is the
study of the
relationship
between motion
and force. It
explains why
objects move.
What is
motion?
Who is in
motion?
A. The fast moving car
C. The girl riding on a horse
B. The man riding in the fast
moving car
D. The galloping horse
E. A man watching the girl .
Motion is relative. It depends on where
motion is referred to. A body is in
motion if it had change position with respect to the reference point.
Position – location of an object with
respect to some reference point.
Reference frame is a physical entity to which motion or position of an object is being referred .
Translation is the physical term for
straight line motion.
Physical Quantities that Describe Motion
How far?
distance
How fast?
How long?
speed
time
How far and in what direction?
How fast and in what direction?
How fast is the rate of change in
speed and direction?
scalar quantities
displacement
velocity
acceleration
Vector quantities
SCALARS &
VECTORS
Scalars
Scalars – came from the
word “scala” meaning
steps or ladder.
-quantities which are
described by its magnitude
alone.
Examples include distance,
speed, mass, temperature,
time, pressure and density.
VECTORS
Vectors came the word “vehere” meaning
to carry.
These are quantities which are described by
both magnitude and direction. Ex.
Displacement, velocity, acceleration, force
Graphically, a vector is represented by an
arrow.
The length of the arrow describes the
vector's magnitude
head/tip points to the direction.
Tail is the origin.
Drawing direction
Illustrate the directions of Vectors A, B, C, and
D.
A
A is 500 N of E
B
B is N of W
C is 200 S of E
500
450
D is S
200
C
D
Practice exercise
D is
W
200
B is 400 N of E
N of
B
D
400
780
C
E
E is W
200
150
C is 150 S of W
A
A is 780 S of E
Drawing vectors
Magnitude:
1 scale = 1 unit
Example 1: F = 5.0 N, upward
1 scale = 1.0N
Example 2: d = 35 m, East
1 scale = 7.0m
3. F = 12.0 N, 450 NE
1 scale = 3.0N
4. d= 100 km, West
1 scale = 10 km
1. What is the position of the tree with respect to the dog?
The tree is 15 m, East of the dog .
2. What is the position of the tree with respect to the
house?
The tree is 10 m, West of the house.
3. If the dog traveled exactly to the location of the tree, is
the dog in motion?
Yes, because it had change position with respect to
the tree.
4. What is the position of the dog with respect to the
house?
The dog is 25 m west of the house.
5. What is the total distance travelled by the dog the
from its initial position to the house?
6.
The total distance travelled by the dog is 25 m.
B. Drawing direction:
A is
W
300
E is 700E N of E
N of
A
300
D
700
D is East
400
C
C is 400 S of W
B
B is S of E
C. Drawing Vectors
a) d= 100 km, West
1 scale = 10 km
b) d= 20.0 km, 450 South of West
1 scale = 5.0km
C) F = 100.0 N is 250 N of W
1 scale = 20.0N
25 0
D) F = 12.0 N 450 North of East
1 scale = 2.0N
45 0
E) v= 24.0 m/s , 350 South of East
1scale = 4.0 m/s
35 0
Additional Activity
1) va= 15 m, 200 North of West
1scale = 3 m
200
2) vb= 36 N , 300 South of East
1scale = 6N
300
3) vc= 28.0 m, 450 North of East
1scale = 4.0m
450
VECTOR ADDITION
Resultant is
the sum of
two vectors A
and B.
The operation of vector addition as
described here can be written as C =
A+B
Methods of Adding
Vectors
Graphical Method - adding
vectors using graphing devices
such as ruler, pencil and
protractor.
Analytical Method – adding
vectors using mathematical
equations.
Head-to-Tail Method – used
in adding 2 or more vectors.
Draw the first vector
The tail of the next vector is
drawn from the head of the first
vector.
The resultant is drawn from the
tail of the first vector to the
head of the last vector.
Addition of Vectors
Determine the resultant of the following vectors:
1.d1 = 300 m, East
3. d1 = 9.0 m, North
d2 = 400 m, East
d2 = 12.0 m, West
1scale = 100m
1 scale = 3.0 m
2.
d1 = 80.0 m, West
d2 = 40.0 m, East
1 scale = 10.0m
4. d1 = 5.0m, East
d2 = 3.0 m, South
d3 = 4.0 m, West
1 scale = 1.0m
d1 = 300 m, East
100m
1. dR = d1
+
dR =
2. d1 = 80.0 m, West
2. dR =
dR =
d2 = 400 m, East
1scale =
d2
dR
=
= 700 m, East
d2 = 40.0 m, East
1 scale = 10.0m
+
d1
d2
=
dR = 40.0m, W
3. d1 = 25 km, E and d2 =25 km , W
dR =
+
dR =
dR = 0 km
4. dR = d1
+
d1 = 9.0 m, North
d2
d2 = 12.0 m,
West
dR = 15.0 m, 370 NW
5 dR = d1
5. d1 = 5.0m, East
d2 = 3.0 m, South
d3 = 4.0 m, West
1 scale = 1.0m
+
d2 +
dR = 3.2 m, 720 SE
d3
Analytical addition of Vectors
A. For Vectors acting in opposite or the same direction
Add the vectors by getting their algebraic sum.
B. Addition of Vectors acting at an angle
Trigonometric Method – used in
adding 2 vectors (drawn at a
common point) using trigonometric
functions.
Component Method – used in
adding 2 or more vectors by
resolving vectors into their
Addition of Vectors
Determine the resultant of the following vectors:
A. Vectors acting in the same direction
d1 = 300 m, East
d2 = 400 m, East
dR = d1 + d2 = (+300 m) + (+ 400 m )
dR = + 700m = 700 m, East
B. Vectors acting in opposite direction
d1 = 300 m, West
d2 = 400 m, East
dR = d1 + d2
dR = (- 300 m) + (+400 m)
dR = + 100 m = 100 m, East
Determine the resultant of the following vectors
acting in other directions:
3. dy = 9.0 m, North
dx = 12.0 m, West
a) Magnitude of R
R = √ x2 + y2
= √ (-12.0m) 2 + (9.0m)2
R = √ 144m2 + 81m2 = √ 225 m2
R = 15 m
b) Direction : Ɵ = tan-1 /x÷y/
Ɵ = tan-1 /-12.0m ÷ 9.0 m/ = tan-1 /-1.33333333/
Ɵ = 53.130102350
= 530 North of West
dR = 15m, 530 North of West
Determine the resultant of the following vectors
acting in other directions:
3. dy = 4.0 m, North
dx = 3.0 m, East
a) Magnitude of R
R = √ x2 + y2
= √ (3.0m) 2 + ( 4.0m)2
R = √ 9.0m2 + 16 m2 = √ 25 m2
R = 5.0 m
b) Direction : Ɵ = tan-1 /x÷y/
Ɵ = tan-1 / 3.0m ÷ 4.0 m/ = tan-1 /0.75/
Ɵ = 36.869897650
= 370 North of East
dR = 5.0m, 370 North of East
4. The boy walks 75 m East, then 50 m North, then
75 m West and finally 50 m South. What is the
resultant displacement of the boy?
Total displacement :
dtotal = sum of dx + sum of dy
dtotal = ( 75m, E + 75m, W) + ( 50m, N + 50m, S)
Vectors
d1
d2
d3
X axis(East and West)
+ 75m
+50m
-75m
d4
Sum
Y axis ( North
and South
Om
dtotal = 0
-50m
0m
Terms that describe Motion
A
d2 = 4.0m
d1 =6.0m
d3 =3.0m
B
Distance ,d, refers to the actual length
of path taken by an object from its
initial position to its final position. It is
a scalar quantity.
Displacement, d refers to the straight
line distance between its initial and final
position. It is a vector quantity.
It is also known as distance with
direction.
d1 = 6.0m, East
d2 = 4.0 m, South
d3 = 3.0 m, East
Total distance travelled by the boy = 6.0 m + 4.0
m+3.0 m
dtotal = 13.0m
Total displacement
Sum up vectors along x and along y axis:
∑dx = 6.0 m, East + 3.0 m, East = 9.0 m, East
∑ dy = 4.0 m , South
Vectors
d1
d2
d3
Sum
x
y
+6.Om
-4.Om
+3.Om
+9.Om
-4.Om
a) Magnitude of R
R = √ x2 + y2
= √ (+9.0m ) 2 + (-4.0m)2
R = √ 81m2 + 16 m2 = √ 97 m2
R = 9.848857802 m = 9.8 m
b) Direction : Ɵ = tan-1 /x÷y/
Ɵ = tan-1 /9.0m ÷ -4.0 m/ = tan-1 /-2.25/
Ɵ = 66.037511030
=
660 South of East
dR = 9.8 m, 660 South of East
Displacement is a vector whose magnitude is the
shortest distance from initial to the final position.
Example: A child walk 4.0 m, East, then 5.0 m, North,
then 4.0 m West and finally 5.0 m South. What is the
total distance traveled by the child? What is his total
displacement?
Total distance = 4.0m + 5.0 m +4.0m + 5.0m
dtotal = 18.0 m
Total displacement = ∑ x + ∑ y
dtotal = (4.0m, E + 4.0m,W) + (5.0m, N + 5.0m, S)
dtotal = 0 + 0 = 0 km
Example: A car ran 100
meters from point A to point B,
then 50 meters from point B
to point C, and another 100
meters from point C to point D.
What is the total distance
travelled? What is its total
displacement
To solve the total distance travelled you can simply add the
length of path from point A to B, B to C and C to D.
dtotal = length A to B + length B to C + length C to D
dtotal = 100 m + 50 m + 100 m
dtotal = 250 m
Total displacement :
dtotal = sum of dx + sum of dy
dtotal = ( 100m, E + 100m, W) + ( 50m, S)
Vectors
X axis(East and West)
d1
d2
+100m
-100m
d3
Sum
dtotal = 50m, South
Om
Y axis ( North
and South
-50m
-5Om