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FORCES AND
MOTION
By
Pn Aminah bt Ab Rahman
SM Sains Tengku Muhammad Faris Petra,
16100 Pengkalan Chepa, Kelantan
MOTION IN A STRAIGHT LINE
( LINEAR MOTION )
Movement in a direction
ANALYSING LINEAR MOTION
Analysing motion involving in
distance, displacement,
speed, velocity,
and
acceleration.
Physical quantities consist of
scalar quantities and vector quantities
North
DISTANCE AND DISPLACEMENT
East
Distance, d
Distance is a base quantity. It has a magnitude only.
Displacement is a vector quantity. It has a magnitude and
direction.
Example :
distance, d
=
20.0 m
displacement, s
=
20.0 m due east
SPEED AND VELOCITY
Distance, d
Speed is a base quantity. It has a magnitude only.
Speed = distance / time taken
Velocity is a vector quantity. It has a magnitude and direction.
Velocity = displacement / time taken
QUESTION 1
Ani is jogging in Taman Tengku Anis. She jogs 400 m due east
and 100 m due north and finally turns to jog 300 m due west. It
takes her 10 minutes.
North
a. Find the total distance travelled.
East
b. Find average speed in ms-1.
a.
Total distance =
400 + 100 + 300
=
300 m
b.
800 m
Average speed =
=
100 m
400 m
800 / 10(60)
1.33 ms-1
QUESTION 2
20 m
5m
A ball moves at a distance of 20 m before it hits a wall. A ball then,
bounces back and moves 5 m before it stops.
a. Find the total distance travelled.
b. Find displacement.
c. If a ball takes 30 s to stop, find the average speed and velocity.
a.
Total distance =
20 + 5 =
25 m
b.
Displacement =
20 - 5
15 m
c.
Average speed =
25 / 30 =
0.83 ms-1
Velocity
15 / 30 =
0.5 ms-1
=
=
KINEMATICS : Movement in a direction
RULES OF DIRECTION
POSITIVE
NEGATIVE
ANALYSING LINEAR MOTION
The average speed
=
Total distance / time taken
=
5 / 0.20
=
25 miles/hour
On the average, the car was moving with a speed of 25 miles per hour.
During a trip, there may have been times that it was stopped and other times that
it’s speedometer was reading 50 miles per hour; yet on the average the car was
moving with a speed of 25 miles per hour.
ANALYSING LINEAR MOTION
TICKER-TIMER
An instrument to analyse motion
Increasing speed
ANALYSING TICKER TAPES – Determine time taken for 1 tick
1 tick
The power supply used in our lab has a frequency 50 Hz.
Thus, a ticker timer will ticks with a frequency 50 Hz also
A frequency of 50 Hz means,
in 1 s, the ticker timer ticks 50 dots
So, the time taken for 1 tick ( or 1 dot ) is t = 1/50 s.
ANALYSING TICKER TAPES
–
Determine time taken for 10 ticks
0
1
2
3
4
5
6
7
8
9
10 ticks
If
1 tick
=
1/50 s =
10 ticks
=
( 1/50 ) x 10
=
1/5
=
0.2 s
0.02 s
10
ANALYSING TICKER TAPES
–
Determine distance for 10 ticks
s
0
1
2
3
4
5
6
8
7
9
10
10 ticks
Distance of 10 ticks
=
length of ticker tapes of 10 ticks
=
displacement, s ( in a certain
direction)
ANALYSING TICKER TAPES
–
Determine velocity for 10 ticks
s
0
1
2
3
4
6
5
7
8
9
10 ticks
velocity for 10 ticks
=
displacement, s / time taken for 10 ticks
=
s / (10 x (1/50))
=
s / (1/5)
=
s / 0.2
10
ANALYSING TICKER TAPES
–
Initial velocity and final velocity
10 dots
10 dots
x1
x2
…….. …….. ……………………………….
n dots
Initial velocity, u
Final velocity, v
=
velocity during the first (10) ticks
=
x1 / time taken for 10 ticks
=
velocity during the last (10) ticks
=
x2 / time taken for 10 ticks
ANALYSING TICKER TAPES
–
Determine motion
Direction of motion
Motion with a constant velocity
Initial velocity = final velocity
Direction of motion
Motion with a decreasing velocity
Initial velocity > final velocity
Direction of motion
Motion with a increasing velocity
Initial velocity < final velocity
The red car moves with a constant speed, covering the
same distance in each second
The green and blue cars are speeding up, thus covering
an increasing distance in each second
The blue car changing its velocity at a more drastic rate
The blue car has a greater acceleration
ACCELERATION, a
Rate of change of velocity
Change in velocity / change in time
=
( Final velocity – Initial velocity ) / change in time
If final velocity > initial velocity , ( increasing velocity )
motion with acceleration
If final velocity < initial velocity , ( decreasing velocity )
motion with deceleration
ANALYSING LINEAR MOTION
ANALYSING TICKER TAPES – to find acceleration
10 dots
10 dots
x1
x2
…….. …….. ……………………………….
n dots
Initial Velocity, u
=
displacement, x1 / time taken for 10 dots
Final Velocity, v
=
displacement, x2 / time taken for 10 dots
Acceleration, a
=
( v – u ) / time taken for n dots, t
ANALYSING TICKER TAPES
Uniform Velocity
The distance of the dots is
equally distributed.
All lengths of tape in the chart
are of equal length.
The object is moving at a
uniform / constant velocity
ANALYSING TICKER TAPES
Increasing velocity
The distance between the
dots increases uniformly.
The length of the strips of
tape in the chart increase
uniformly.
The velocity of the object is
increasing uniformly
The object is moving at a
constant acceleration.
ANALYSING TICKER TAPES
Decreasing velocity
The distance between the dots
decreases uniformly.
The length of the strips of tape
in the chart decreases
uniformly.
The velocity of the object is
decreasing uniformly,
The object is decelerating
uniformly.
ANALYSING TICKER TAPES – a ticker tapes chart
Displacement / 10 ticks
Acceleration
nonuniformly
Time
INCREASING WITH A
NONUNIFORM VELOCITY
ANALYSING TICKER TAPES – a ticker tapes chart
Displacement / 10 ticks
Non uniform
Deceleration
Time
DECREASING WITH A NON
UNIFORM VELOCITY
Analysing Displacement - Time Graph
the gradient of the graph is
equal to the velocity of motion.
Gradient = 0
Hence, velocity = 0
The object is at rest
(not moving).
Analysing Displacement - Time Graph
Gradient is constant,
hence, velocity is uniform / constant
Gradient is negative and constant,
hence velocity is uniform
and in opposite direction
Analysing Displacement - Time Graph
Gradient is increasing,
hence velocity is increasing.
Gradient is decreasing,
hence velocity is decreasing.
Analysing Velocity - Time Graph
The gradient gives a value of
the changing rate in velocity
Gradient
= (change in velocity ) / (change in time)
which is the acceleration of the object
Analysing Velocity - Time Graph
Uniform velocity
Uniform acceleration
Analysing Velocity - Time Graph
Increasing acceleration
Uniform deceleration
Analysing Velocity - Time Graph
Decreasing acceleration
CONSTANT POSITIVE VELOCITY
Velocity = gradient of Position Vs Time graphs
Acceleration = gradient of Velocity Vs Time graphs
CONSTANT NEGATIVE VELOCITY
Velocity = gradient of Position Vs Time graphs
Acceleration = gradient of Velocity Vs Time graphs
INCREASING VELOCITY - ACCELERATION
Velocity = gradient of Position Vs Time graphs
Acceleration = gradient of Velocity Vs Time graphs
DECREASING VELOCITY - DECELERATION
Velocity = gradient of Position Vs Time graphs
Acceleration = gradient of Velocity Vs Time graphs
EXERCISE 1
Describe the characteristics of the motion below.
Decelerates from high speed to low speed. It stop and remain at rest
for a while. The accelerates until the trace ends.
Travels at a constant speed during the first time interval, then
accelerates until the trace ends
Travels at a constant speed during the first time interval, then
decelerates to a stop and remain at rest for some time. Then moves
with a constant speed which is slower than the first speed
ANALYSING MOTION GRAPHS
position,s
The body is not moving at all ! At
anytime, its position remain the
same.
The body is at rest.
velocity, v = 0
time,t
What can you say about its motion?
From graph,
What can you say about its velocity?
velocity, v = gradient
=0
ANALYSING MOTION GRAPHS
position,s
The body moves with a constant
velocity
velocity, v is contant
From graph,
velocity, v = gradient
time,t
What can you say about its motion?
What can you say about its velocity?
What can you say about its acceleration?
ANALYSING MOTION GRAPHS
position,s
velocity,v
velocity, v is contant
time,t
What can you say about its acceleration?
From graph,
acceleration, a = gradient = 0
What can you say about its displacement?
time,t
ANALYSING MOTION GRAPHS
From,
velocity,v
v = displacement,s / time,t
s=vt
v
displacement, s =
Area below graph v-t
t
time,t
What can you say about its acceleration?
From graph,
acceleration, a = gradient = 0
What can you say about its displacement?
EXERCISE 2
Describe the motion.
velocity, v
(ms-1)
10
0
2
8
20
time,t (s)
A body moves with an increasing velocity uniformly for 2 s until its velocity is
10 ms-1. Then it continues with a constant velocity for 6 s. The body then
moves with a decreasing velocity uniformly for 12 s.
EXERCISE 2
Find acceleration and deceleration.
velocity, v
(ms-1)
10
0
2
20
8
time,t (s)
A body moves with an increasing velocity uniformly for 2 s until its velocity is
10 ms-1. Then it continues with a constant velocity for 6 s. The body then
moves with a decreasing velocity uniformly for 12 s.
Acceleration, a = ( v - u ) / t
= ( 10 – 0 ) / 2
= 5 ms-2
EXERCISE 2
Find total displacement.
velocity, v
(ms-1)
10
A
0
C
B
2
Total displacement, s
20
8
time,t (s)
=
Total area below graph
=
area A + area B + area C
=
( ½ ( 10)(2)) + (10 x (8-2)) + ( ½ (10)(20-8))
=
10 + 60 + 60
=
130 m
EXERCISE 2
Find total displacement.
velocity, v
(ms-1)
10
0
2
20
8
22
time,t (s)
-5
Total displacement, s
=
Total area below graph
=
area A + area B + area C + area D
=
130 + ( ½ ( -5)(22-20)
=
130 + ( -5 )
=
125 m
ANALYSING MOTION - EQUATIONS
From,
a
=
(v–u)/t
v
=
u + at
Average velocity =
(1)
½(v+u)
So, from s = vt
s
=
½(v+u)t
From (1), v = u + at,
s
s
=
½ ((u + at) + u ) t
=
½ ut + ½ut + ½ at2
=
ut + ½at2
(2)
ANALYSING MOTION - EQUATIONS
From (1), v = u + at,
t
=
(v–u)/a
Substitute into s
=
½(v+u)t
s
=
½(v+u)(v–u)/a
2as
=
(v+u)(v–u)
v2
=
u2 + 2as
(3)
UNDERSTANDING
INERTIA
DYNAMICS :
WAYS IN WHICH MOTION CAN BE
EXPLAINED
The tendency of an object to remain at rest, or keep on moving
at a constant speed in a straight line.
The behavior of all objects can be
described by saying that objects tend
to "keep on doing what they're doing“
and resist changes in their state of
motion
What can you say about the ladder state of motion when a
truck moves down the road ?
As the truck moves down the road, the ladder moves with it
What will happen to the ladder when the truck abruptly stop
and the straps were no longer functioning ? Why ?
The ladder would slide off the top of the truck and be
hurled into the air because the ladder in motion would
continue in motion
NEWTON’S FIRST LAW OF MOTION
An object at rest tends to stay at rest and an object in motion tends
to stay in motion with the same speed and in the same direction
unless acted upon by an unbalanced force.
There is no unbalanced
force acting upon the book
and
thus
the
book
maintains its state of
motion.
There is no unbalanced force
acting upon the person and
thus the person maintains
his/her state of motion.
The force of gravity pulling downwards and the force of the table
pushing upwards on the book are of equal magnitude and in
opposite directions. These two forces balance each other.
However, there is no force present to balance the force of friction.
As the book moves to the right, friction acts to the left to slow the
book down. This is an unbalanced force; and as such, the book
changes its state of motion
It is the natural tendency of objects to keep on doing what they're
doing. All objects resist changes in their state of motion. In the
absence of an unbalanced force, an object in motion will maintain this
state of motion. This is often called the law of inertia.
Experiencing inertia in an automobile while it is braking to a
stop
The force of the road on the locked
wheels provides the unbalanced force to
change the car's state of motion, yet
there is no unbalanced force to change
the state of motion.
Thus, an object will continue in motion, sliding forward along the seat.
A person in motion tends to stay in motion with the same speed and in the
same direction ...
unless acted upon by the unbalanced force of a seat belt.
Seat belts are used to provide safety for passengers whose motion is
governed by Newton's laws. The seat belt provides the unbalanced force
which brings the object from a state of motion to a state of rest.
What motion would the passengers undergo if they failed to use
their seat belts and the car were brought to a sudden and abrupt
halt by a collision with a wall?
The passengers in motion would continue in motion. The
passengers would likely be propelled from the car and be
hurled into the air
If the motorcycle were to abruptly stop, then the rider in motion
would continue in motion. The rider would likely be propelled from
the motorcycle and be hurled into the air.
APPLICATIONS
The head of a hammer can be tightened onto
the wooden handle by banging the bottom of
the handle against a hard surface.
To dislodge ketchup from
the bottom of a ketchup
bottle, the bottle is often
turned upside down, thrust
downward at a high speed
and then abruptly halted.
MASS AND INERTIA
Inertia is the resistance an object
has to a change in its state of
motion.
The tendency of an object to resist changes in
its state of motion is dependent upon its mass
MASS AND INERTIA
The figure shows a child and
his mother sitting on two
identical swings.
They are pushed with the
same amount of forces.
Which is more difficult to be moved ?
The swing which the mother sits on is more difficult
to be moved because she has more mass.
The tendency of an object to resist changes in its
state of motion is higher
MASS AND INERTIA
The swing which the mother sits on is more difficult to be
moved because the tendency of her to resist changes in her
state of motion ( which is at rest ) is higher
HIGHER MASS SHOWS A HIGHER RESISTANCE TO CHANGE
HIGHER MASS HAS A HIGHER INERTIA
Quiz
Truck X carries petrol in one big tank while truck Y carries
petrol in 3 small tanks. Which is safer ? Explain
Y, because Y has a smaller inertia.
Big tank has a large mass. A large mass has a large
inertia. The heavy tank will continue to move if the truck
stops suddenly. It will collide with the driver’s cabin.
ANALYSING
MOMENTUM
By
Pn. Aminah bt. Ab. Rahman
Physics’s Teacher
SM Sains Tengku Muhammad Faris Petra,
16100 Pengkalan Chepa, Kelantan.
MOMENTUM
Tendency of an object to keep on moving with the
same speed in the same direction
Momentum, p = m v
m = mass
v = velocity
Vector Quantity
Same direction of the velocity
Unit : Kgms-1
MOMENTUM
A mass of an object which traveling with a certain velocity has momentum
Momentum, p = m v
The momentum of an object will increase if
•
the mass of the object increase
•
the velocity of the object increase
MOMENTUM
Which has more momentum ? Why ?
The Principle of Conservation of Momentum
In any collision or interaction between two or
more objects in an isolated system,
the total momentum of the system will remain constant;
that is,
the total initial momentum will
equal the total final momentum
A 15-kg medicine ball is thrown at a velocity of 20 km/hr to a 60-kg person
who is at rest on ice. The person catches the ball and subsequently slides
with the ball across the ice
Before the collision, the ball has momentum and the person does not
The collision causes the ball to lose momentum and the person to gain
momentum. After the collision, the ball and the person travel with the same
velocity ("v") across the ice
What is the total initial momentum ?
Initial momentum of the ball
Initial momentum of the girl
=
mv
=
( 15 ) ( 20 )
=
300 kgkmh-1
=
mv
=
( 60 ) ( 0 )
=
0 kgkmh-1
What is the total final momentum ?
Total final momentum
Find final velocity, v.
=
m1 v + m2 v
=
15 v + 60 v
=
( 15 + 60 ) v
Find final velocity, v.
total initial momentum = total final momentum
(60 + 15 ) v
75v
v
=
=
=
300
300
4 km/hr
Granny (m1=80 kg) whizzes around the rink with a velocity of 6 m/s. She
suddenly collides with Ambrose (m2=40 kg) who is at rest directly in her path.
Rather than knock him over, she picks him up and continues in motion without
"braking."
Determine the final common velocity of Granny and Ambrose
COLLISION
Three types of collisions :
i.
Elastic collision
ii. Inelastic collision
iii. Explosion
Elastic
collision
Characteristics of Elastic Collision
•
The objects will separate and move off with
different velocities after they do collide
•
The total system kinetic energy before the
collision equals the total system kinetic energy after
the collision
m1
u1
BEFORE
m2
u2
m1
v1
AFTER
m2
v2
Elastic Collision
m1
u1
m2
u2
m1
m1u1 + m2u2
m2
AFTER
BEFORE
total initial momentum
v1
=
total final momentum
=
m1v1 + m2v2
v2
Inelastic
collision
Characteristics of Inelastic Collision
•
The objects will move together with the same
velocity after they do collide
•
The total kinetic energy before the collision is not
equal to the total kinetic energy after the
collision. A
portion of the kinetic energy is
converted to other forms
of energy such as sound energy and thermal energy
m1
u1
BEFORE
m2
u2
m1
m2
v
AFTER
Inelastic Collision
m1
u1
m2
u2
m1
m1u1 + m2u2
m1u1 + m2u2
v
AFTER
BEFORE
total initial momentum
m2
=
total final momentum
=
=
m1v + m2v
(m1 + m2 ) v
Explosion
The separation of objects which are initially at rest
BANG !
m1
m2
At rest ; u = 0
After collision, each moves in different direction and velocities
Balloon moves
upwards
air
balloon
Air moves
downwards
Momentum of the air downwards, is moving the balloon upwards.
Initial velocity of bullet and gun = 0
Gun moves
backwards
Momentum of gun backwards
Bullet
moves
forwards
= Momentum of bullet forwards
canon
Man steps forward out of a boat and onto the nearby river bank
Momentum of man forwards moves boat
backwards
Man moves
forwards
Boat moves
backwards
Rocket propulsion
•
A mixture of
hydrogen gas and
oxygen is burnt in a
combustion
chamber.
•
Liquid
hydrogen
•
Liquid oxygen
•
The exhaust gases
are discharged
downwards at a high
velocity
The jet of exhaust
gases have a large
momentum
downwards.
exhaust gases push
the rocket upward
Combustion
chamber
exhaust
ROCKET
How an airplane moves forwards ?
Atmospheric air is drawn into the engine and compressed by a
compressor
The compressed air is fed into the combustion chamber and produce
gases with a high temperature.
Kerosene fuel is injected and the mixture is ignited.