Form 4 -notes [chapter 1 &2 ]

1.1

==what are Physical Quantities==

Physical Quantities

• A physical quantity is a quantity that can be measured.
  

2. A physical quantity can be divided into base quantity and derived quantity.


==what are Base Quantities==

Base Quantities
Base quantities are quantities that cannot be defined in term of other physical quantities.


==state the 5 base quantities and their SI unit==

5 Base Quantites

Quantity	Name of Unit	Symbol of Unit
Length	metre	m
Time	second	s
Temperature	Kelvin	K
Mass	kilogram	kg
Current	Ampere	A

==what is derived quantities?==

Derived QuantitiesA derived quantity
is a Physics quantity that is not a base quantity. It is the quantities
which derived from the base quantities through multiplying and/or
dividing them.



==what is derived unit?==

Derived UnitThe derived unit is a combination of base units through multiplying and/or dividing them.



==what are prefixes?==

PrefixesPrefixes are the preceding factor used to represent very small and very large physical quantities in SI units.

Prefixes	Symbol	Value
Tera	T	1012
Giga	G	109
Mega	M	106
kilo	k	103
desi	d	10-1
centi	c	10-2
mili	m	10-3
micro	µ	10-6
nano	n	10-9
pico	p	10-12
fento	f	10-15

==what are scalar quantities?==

Scalar Quantities

• Scalars are quantities which are fully described by a magnitude alone.
  
• Examples of scalar quantities are distance, speed, mass, volume, temperature, density and energy.
  

==what are vector quantities?==

Vector Quantities

• Vectors are quantities which are fully described by both a magnitude and a direction.
  
• Examples of vector quantities are displacement, velocity, acceleration, force, momentum, and magnetic field.
  

1.2 Error Analysis

==What is error?==

Error
Error is the difference between the actual value of a quantity and the value obtained in measurement.




==What is systematic error?==

Systematic Error
Systematic errors are errors which tend to shift all measurements in a
systematic way so their mean value is displaced. Systematic errors can
be compensated if the errors are known.




==State 3 sources of systematic error.==

Sources of Systematic Error

• zero error, which cause by an incorrect position of the zero point,
  
• an incorrect calibration of the measuring instrument.
  
• consistently improper use of equipment.
  

==State 2 precaution steps to reduce systematic error.==

Steps to reduce Systematic Error

• Conducting the experiment with care.
  
• Repeating the experiment by using different instruments.
  

==What is meant by zero error?==

Zero Error

• A zero error arises when the measuring instrument does not start from exactly zero.
  
• Zero errors are consistently present in every reading of a measurement.
  
• The zero error can be positive or negative.
  

==Define random Error==

Random Error

• Random errors arise from unknown and unpredictable variations in condition.
  
• It changes from one measurement to the next.
  

==State the causes of random error==

Causes of Random Error
Random errors are caused by factors that are beyond the control of the observers. Random error can cause by:

• personal errors such as human limitations of sight and touch.
  
• lack of sensitivity of the instrument: the instrument fail to respond to the small change.
  
• natural errors such as changes in temperature or wind, while the experiment is in progress.
  
• wrong technique of measurement.
  

==How random error can be avoided or reduced?==




How to avoid random error

• Taking repeat readings
  
• Find the average value of the reading.
  

==What is parallax error?==




Parallax ErrorA parallax error is an error in reading an
instrument due to the eye of the observer and pointer are not in a line
perpendicular to the plane of the scale.

1.3 Measurement

==What is meant by precision?==

Precision
Precision is the ability of an instrument in measuring a quantity in a
consistent manner with only a small relative deviation between readings.





==How to measure the precision of a measurement?==

Relative Deviation
The precision of a reading can be indicated by its relative deviation.
The relative deviation is the percentage of mean deviation for a set of measurements and it is defined by the following formula:







==Define accuracy.==

AccuracyThe accuracy of a measurement is the approximation of the measurement to the actual value for a certain quantity of Physics.





==How the accuracy of a measurement can be increased?==
How to Increase Accuracy

• taking a number of repeat readings to calculate the mean value of the reading.
  
• avoiding the end errors or zero errors.
  
• taking into account the zero and parallax errors.
  
• using more sensitive equipment such as a vernier caliper to replace a ruler.
  

==What is meant by sensitivity of a measuring instrument?==
Sensitivity

• The sensitivity of an instrument is its ability to detect small changes in the quantity that is being measured.
  
• Thus, a sensitive instrument can quickly detect a small change in measurement.
  
• Measuring instruments that have smaller scale parts are more sensitive.
  
• Sensitive instruments need not necessarily be accurate.
  

==Describe how a micrometer is used to make a measurement==

Micrometer Screw Gauge

• Turn the thimble until the object is gripped gently between the anvil and spindle.
  
• Turn the ratchet knob until a "click" sound is heard. This is to prevent exerting too much pressure on the object measured.
  
• Take the reading.
  

(This image is licensed under GDFL. The source file can be obtained from wikipedia.org.)
Reading of main scale = 5.5mm
Reading of thimble scale = 0.27mm

Actual Reading = 5.5mm + 0.27mm = 5.77mm

1.4 Scientific Investigation


Scientific ReportA report of the investigation must include:

• Objective of the experiment,
  
• Inference,
  
• Hypothesis,
  
• Three types of variables: manipulated variable, responding variable and fixed variable,
  
• Defined operational variables,
  
• List of apparatus,
  
• Procedure,
  
• Tabulation of data,
  
• Analysis of data,
  
• Conclusion.
  

InferenceInference is a statement to state the relationship between two visible quantities observed in a diagram or picture.






HypothesisHypothesis is a statement to state the relationship between two measurable variables that can be investigated in a lab.





VariablesA variable is a quantity that can vary in value. There are 3 types of variable:

• Manipulated Variables: Manipulated variables are factors which changed for the experiment.
  
• Responding Variables: Responding variables are factors which depend on the manipulated variables.
  
• Constant Variables: Constant variables are factors which are kept the same throughout the experiment.
  

Tabulating DataA proper way of tabulating data should include the following:

• The name or the symbols of the variables must be labelled with respective units.
  
• All measurements must be consistent with the sensitivity of the instruments used.
  
• All the values must be consistent to the same number of decimal places.
  

Drawing GraphGraphs
are used to make a relationship between variables. Gradient value and
extrapolation of a graph are used to analyse a graph.
A well-plotted must contain the following features:

• A title to show the two variables under investigation,
  
• two axes labelled with the correct variables and their respective units,
  
• the graph drawn is greater than 50 % of the graph paper,
  
• appropriate scales (1:1 x 10x, 1:2 x 10x and 1:5 x 10x)
  
• all the points are correctly plotted,
  
• a best fit line is drawn
  

Chapter 2 Force and Motion

2.1 linear motion

Linear Motion
Linear motion is the movement of an object along a straight line.





DistanceThe distance traveled by an object is the total length that is traveled by that object.
Unit: metre (m)
Type of Quantity: Scalar quantity





DisplacementDisplacement of an object from a point of reference, O is the shortest distance of the object from point O in a specific direction.
Unit: metre (m)
Type of Quantity: Vector quantity





Distance vs Displacement

Distance travelled = 200m
Displacement = 120 m, in the direction of Northeast
Distance is a scalar quantity,
Displacement is a vector quantity





SpeedSpeed is the rate of change in distance.
Formula:

Unit: ms-1
Type of quantity: Scalar quantity






VelocityVelocity is the rate of change in displacement.
Formula:


Unit: ms-1
Type of quantity: Vector quantity





AccelerationAcceleration is the rate of velocity change.Acceleration is a vector quantity
Formula:


Unit: ms-2
Type of quantity: Vector quantity





Notes - Acceleration

• An object moves with a constant velocity if the magnitude and direction of the motion is always constant.
  
• An object experiences changes in velocity if
  
  
  
  • the magnitude of velocity changes
    
  • the direction of the motion changes.
    
  </li>
  
• An object that experiences changes in velocity is said to have acceleration.
  
• An object traveling with a constant acceleration, a, if the velocity changes at a constant rate.
  

4 Equations of Uniform Acceleration
The above equation is for solving numerical problems involving uniform acceleration.





Summary

2.2Ticker Tape

Ticker Timer

• A ticker-timer consists of an electrical vibrator which vibrates 50 times per second.
  
• This enables it to make 50 dots per second on a ticker-tape being pulled through it.
  
• The time interval between two adjacent dots on the ticker-tape is called one tick.
  
• One tick is equal to 1/50 s or 0.02 s.
  

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 velocity.
  

Uniform Acceleration

• 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, i.e. the object is moving at a constant acceleration.
  

Uniform Deceleration

• 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, i.e. the object is decelerating uniformly.
  

Finding VelocityVelocity of a motion can be determined by using ticker tape through the following equation:

Caution!:
t is time taken from the first dot to the last dot of the distance measured.








Example 1

Diagram
2.4 shows a strip of ticker tape that was pulled through a ticker tape
timer that vibrated at 50 times a second. What is the

• time taken from the first dot to the last dot?
  
• average velocity of the object that is represented by the ticker tape?
  

Answer:
a.
There are 15 ticks from the first dot to the last dot, hence
Time taken = 15 × 0.02s = 0.3s
b.
Distance travelled = 15cm





Finding AccelerationAcceleration of a motion can be determined by using ticker tape through the following equation:

Caution!:
t is time taken from the initial velocity to the final velocity.




Example 2


The ticker-tape in figure above was produced by a toy car moving down a
tilted runway. If the ticker-tape timer produced 50 dots per second,
find the acceleration of the toy car.
Answer:
In order to find the acceleration, we need to determine the initial
velocity, the final velocity and the time taken for the velocity change.
Initial velocity,
Time taken for the velocity change,
t = (0.5 + 4 + 0.5) ticks = 5 ticks
t = 5 × 0.02s = 0.1s
Acceleration,


Example 3

A
trolley is pushed up a slope. Diagram above shows ticker tape chart
that show the movement of the trolley. Every section of the tape
contains 5 ticks. If the ticker-tape timer produced 50 dots per second,
determine the acceleration of the trolley.

Answer:
In order to find the acceleration, we need to determine the initial
velocity, the final velocity and the time taken for the velocity change.
Initial velocity,
Time taken for the velocity change,
t = (2.5 + 5 + 5 + 5 + 2.5) ticks = 40 ticks
t = 40 × 0.02s = 0.8s
Acceleration,

2.3 Graph of Motion

Displacement - Time Graph

In a Displacement-Time Graph, the gradient of the graph is equal to the velocity of motion.




Analysing Displacement - Time Graph

Gradient = 0 Hence, velocity = 0	Gradient is constant, hence, velocity is Uniform
Gradient is negative and constant, hence velocity is uniform and in opposite direction	Gradient is increasing, hence velocity is increasing.
Gradient is decreasing, hence velocity is decreasing.

Velocity - Time Graph

• The gradient of the velocity-time gradient gives a value of the changing rate in velocity, which is the acceleration of the object.
  
• The area below the velocity-time graph gives a value of the object's displacement.
  

Analysing Velocity - Time Graph

Uniform velocity	Uniform acceleration
Uniform deceleration	Increasing acceleration
Increasing deceleration

Converting a Velocity-Time graph to Acceleration-Time graph
In order to convert a velocity-time graph to acceleration time graph,
we need to find the gradient of the velocity time graph and plot it in
the acceleration-time graph.


Dropping an object from high place

Velocity - Time Graph	Acceleration - Time Graph

Launching Object Upward

Velocity-Time Graph	Acceleration-Time Graph

Object moving upward and fall back to the ground

Velocity-Time Graph	Acceleration-Time Graph

Object falling and bounces back

Velocity-Time Graph	Acceleration-Time Graph

2.4 Inertia Mass
Mass is the amount of matter.
Unit: kilogram (kg)
Type of quantity: Scalar quantity



Inertia
Inertia is the property of a body that tends to maintain its state of motion.





Newton's First Law
In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line).





Jerking a Card
When the cardboard is jerked quickly, the coin will fall into the glass.

Explanation:

• The inertia of the coin resists the change of its initial state, which is stationary.
  
• As a result, the coin does not move with the cardboard and falls into the glass because of gravity.
  

Pulling a Book




When the book is pulled out, the books on top will fall downwards.

Explanation:
Inertia tries to oppose the change to the stationary situation, that
is, when the book is pulled out, the books on top do not follow suit.






Pulling a Thread
Pull slowly - Thread A will snap.


Explanation:

Tension of thread A is higher than string B.
Tension at A = Weight of the load + Pulling Force
Yank quickly - Thread B will snap.


Explanation:


The inertia of the load prevents the force from being transmitted to thread A, hence causing thread B to snap.






Larger Mass - Greater Inertia
Bucket filled with sand is more difficult to be moved. It's also more difficult to be stopped from swinging.

Explanation:

Object with more mass offers a greater resistance to change from its state of motion.
Object with larger mass has larger inertia to resist the attempt to change the state of motion.






Empty cart is easier to be moved
An empty cart is easier to be moved compare with a cart full with load. This is because a cart with larger mass has larger inertia to resist the attempt to change the state of motion.

2.5 Momentum

Momentum
Momentum is defined as the product of mass and velocity.
Formula:


Unit: kgms-1
Type of quantity: Vector



Example 1
A student releases a ball with mass of 2 kg from a height of 5 m from
the ground. What would be the momentum of the ball just before it hits
the ground?

Answer:
In order to find the momentum, we need to know the mass and the velocity of the ball right before it hits the ground.
It's given that the mass, m = 2kg.
The velocity is not given directly. However, we can determine the
velocity, v, by using the linear equation of uniform acceleration.
This is a free falling motion,
The initial velocity, u = 0
The acceleration, a = gravirational acceleration, g = 10ms-2
The dispacement, s = high = 50m.
The final velocity = ?
From the equation
v2 = u2 + 2as
v2 = (0)2 + 2(10)(5)
v = 10ms-1
The momentum,
p = mv =(2)(10) = 20 kgms-1




Principle of Conservation of Momentum
The principle of conservation of momentum states that in a system make out of objects that react (collide or explode), the total momentum is constant if no external force is acted upon the system.

Sum of Momentum Before Reaction
= Sum of Momentum After Reaction





Formula




Example 2: Both objects are in same direction before collision.

A Car A of mass 600 kg moving at 40 ms-1 collides with a car B of mass
800 kg moving at 20 ms-1 in the same direction. If car B moves forwards
at 30 ms-1 by the impact, what is the velocity, v, of the car A
immediately after the crash?

Answer:
m1 = 600kg
m2 = 800kg
u1 = 40 ms-1
u2 = 20 ms-1
v1 = ?
v2 = 30 ms-1
According to the principle of conservation of momentum,
m1u1 + m2u2 = m1v1 + m2v2
(600)(40) + (800)(20) = (600)v1 + (800)(30)
40000 = 600v1 + 24000
600v1 = 16000
v1 = 26.67 ms-1




Example 3: Both objects are in opposite direction before collision.
A 0.50kg ball traveling at 6.0 ms-1 collides head-on with a 1.0 kg ball
moving in the opposite direction at a speed of 12.0 ms-1. The 0.50kg
ball moves backward at 14.0 ms-1 after the collision. Find the velocity
of the second ball after collision. Answer:
m1 = 0.5 kg
m2 = 1.0 kg
u1 = 6.0 ms-1
u2 = -12.0 ms-1
v1 = -14.0 ms-1
v2 = ?

(IMPORTANT: velocity is negative when the object move in opposite siredtion)
According to the principle of conservation of momentum,
m1u1 + m2u2 = m1v1 + m2v2
(0.5)(6) + (1.0)(-12) = (0.5)(-14) + (1.0)v2
-9 = - 7 + 1v2
v2 = -2 ms-1







Elastic Collision

Elastic collision is the collision where the kinetic energy is conserved after the collision.


Total Kinetic Energy before Collision
= Total Kinetic Energy after Collision
Additional notes:
-In an elastic collision, the 2 objects seperated right after the collision, and
-the momentum is conserved after the collision.





Inelastic Collision
Inelastic collision is the collision where the kinetic energy is not conserved after the collision.

Additional notes:

-In a perfectly elastic collision, the 2 objects attach together after the collision, and
-the momentum is also conserved after the collision.





Example 4: Perfectly Inelastic Collision
A lorry of mass 8000kg is moving with a velocity of 30 ms-1. The lorry
is then accidentally collides with a car of mass 1500kg moving in the
same direction with a velocity of 20 ms-1. After the collision, both
the vehicles attach together and move with a speed of velocity v. Find
the value of v.
Answer:
(IMPORTANT: When 2 object attach together, they move with same speed.)
m1 = 8000kg
m2 = 1500kg
u1 = 30 ms-1
u2 = 20 ms-1
v1 = v
v2 = v
According to the principle of conservation of momentum,
m1u1 + m2u2 = m1v1 + m2v2
(8,000)(30) + (1,500)(20) = (8,000)v+ (1,500)v
270,000 = 9500v
v
= 28.42 ms-1





Rocket

• Mixture of hydrogen and oxygen fuels burn in the combustion chamber.
  
• Hot gases are expelled through the exhausts at very high speed .
  
• The high-speed hot gas produce a high momentum backwards.
  
• By conservation of momentum, an equal and opposite momentum is produced and acted on the rocket, pushing the rocket upwards.
  

Jet Engine

• Air is taken in from the front and is compressed by the compressor.
  
• Fuel is injected and burnt with the compressed air in the combustion chamber.
  
• The hot gas is forced through the engine to turn the turbine blade, which turns the compressor.
  
• High-speed hot gases are ejected from the back with high momentum.
  
• This produces an equal and opposite momentum to push the jet plane forward.
  

2.6 Effects of Force

Newton's Second Law
The rate of change of momentum of a body is directly proportional to the resultant force acting on the body and is in the same direction.

Implication:
When there is resultant force acting on an object, the object will accelerate (moving faster, moving slower or change direction).



Force

• A force is push or pull exerted on an object.
  
• Force is a vector quantity that has magnitude and direction.
  
• The unit of force is Newton ( or kgms-2).
  

Formula of ForceFrom Newton's Second Law, we can derived the equation


(IMPORTANT: F Must be the net force)




Summary of Newton's 1st Law and 2nd Law

Newton's First Law:
When there is no net force acting on an object, the object is either stationary or move with constant speed in a straight line.

Newton's Second Law:
When there is a net force acting on an object, the object will accelerate.




Example 1
A box of mass 150kg is placed on a horizontal floor with a smooth
su***ce; find the acceleration of the box when a 300N force is acting
on the box horizontally.

Answer:
F = ma
(300) = (150)a
a = 2 ms-2




Example 2
A object of mass 50kg is placed on a horizontal floor with a smooth
su***ce. If the velocity of the object changes from stationary to 25.0
m/s in 5 seconds when is acted by a force, find the magnitude of the
force that is acting?

Answer:
We know that we can find the magnitude of a force by using the formula
F = ma. The mass m is already given in the question, but the
acceleration is not give directly.
We can determine the acceleration from the formula

From the formula
F = ma = (50)(5) = 250N
The force acting on the box is 250N.





Effects of ForceWhen a force acts on an object, the effect can change the

• size,
  
• shape,
  
• stationary state,
  
• speed and
  
• direction of the object.
  

2.7 Impulse and Impulsive Force

Impulse

Impulse is defined as the product of the force (F) acting on an object and the time of action (t).
Impulse exerted on an object is equal to the momentum change of the object.
Impulse is a vector quantity.



Formula of impulse
Impulse is the product of force and time.


Impulse = F × tImpulse = momentum change

Impulse = mv - mu



Example 1
A car of mass 600kg is moving with velocity of 30m/s. A net force of
200N is applied on the car for 15s. Find the impulse exerted on the car
and hence determine the final velocity of the car.

Answer:
Impulse = F × t = (200) × (15) = 300oNs
Impulse = mv - mu
(3000) = 600v - 600(30)
600v = 3000 + 18000
v = 21000/600 = 35 m/s
[500,000N]




Impulsive Force
Impulsive force is defined as the rate of change of momentum in a reaction.
It is a force which acts on an object for a very short interval during a collision or explosion.




Example 2
A car of mass 1000kg is traveling with a velocity of 25 m/s. The car
hits a street lamp and is stopped in0.05 seconds. What is the impulsive
force acting on the car during the crash? Answer:





Effects of impulse vs Force
A force determines the acceleration (rate of velocity change) of an object. A greater force produces a higher acceleration.
An impulse determines the velocity change of an object. A greater impulse yield a higher velocity change.





Examples Involving Impulsive Force

• Playing football
  
• Playing badminton
  
• Playing tennis
  
• Playing golf
  
• Playing baseball
  

Long Jump

• The long jump pit is filled with sand to increase the reaction time when atlete land on it.
  
• This
  is to reduce the impulsive force acts on the leg of the atlete because
  impulsive force is inversely proportional to the reaction time.
  

2.8 Safety Feature in Vehicles

Crumble Zone

• The crumple zone increases the reaction time of collision during an accident.
  
• This causes the impulsive force to be reduced and hence reduces the risk of injuries.
  

Seat Belt
Prevent the driver and passengers from being flung forward or thrown out of the car during an emergency break.





Airbag
The
inflated airbag during an accident acts as a cushion to lessen the
impact when the driver flings forward hitting the steering wheel or
dashboard.





Head Rest
Reduce neck injury when driver and passengers are thrown backwards when the car is banged from backward.







Windscreen
Shatter-proof glass is used so that it will not break into small pieces when broken. This may reduce injuries caused by scattered glass.





Padded Dashboard
Cover with soft material. This may increases the reaction time and
hence reduce the impulsive force when passenger knocking on it in
accident.





Collapsible Steering
ColumnsThe steering will swing away from driver’s chest during
collision. This may reduce the impulsive force acting on the driver.





Anti-lock Braking System (ABS)Prevent the wheels from
locking when brake applied suddenly by adjusting the pressure of the
brake fluid. This can prevents the car from skidding.






Bumper
Made of elastic material so that it can increases the reaction time and hence reduces the impulsive force caused by collision.





Passanger Safety Cell

• The body of the car is made from strong, rigid stell cage.
  
• This may prevent the car from collapsing on the passengers during a car crash.
  

2.9Understanding Gravity



Gravitational Field
A gravitational field as a region in which an object experiences a force due to gravitational attraction



Gravitational Field Strength
The gravitational field strength at a point in the gravitational field
is the gravitational force acting on a mass of 1 kg placed at that
point.
Unit: N/kg
Symbol: g





Gravitational Field Strength Formula






Gravitational Acceleration
The gravitational acceleration is the acceleration of an object due to the pull of the gravitational force.
Unit: ms-2
Symbol: g

Important notes:

• Gravitational acceleration does not depend on the mass of the moving object.
  
• The magnitude of gravitational acceleration is taken to be 10ms-2.
  

Gravitational Field Strength vs. Gravitational Acceleration

• Both
  the gravitational field strength and gravitational acceleration have
  the symbol, g and the same value (10ms-2) on the su***ce of the earth.
  
• When considering a body falling freely, the g is the gravitational acceleration.
  
• When considering objects at rest, g is the Earth’s gravitational field strength acting on it.
  

Weight
The weight of an object is defined as the gravitational force acting on the object.
Unit: Newton (N)







Differences between Weight and Mass

Weight	Mass
Depends on the gravitational field strength	Independent from the gravitational field strength
Vector quantity	Scalar Quantity
Unit Newton (N)	Unit: Kilogram (kg)

Free Falling
Free falling is a motion under force of gravity as the only force acting on the moving object.
Practically, free falling can only take place in vacuum.





Falling from high place

Acceleration = 10ms-2
Initial velocity = 0
Displacement = high of the location





Launching object upward
Acceleration = -10ms-2
Velocity at maximum height = 0

2.10 Forces in Equilibrium


Addition of 2 Perpendicular Vectors
If
2 vectors (a and b) are perpendicular to each others, the magnitude and
direction of the resultant vector can be determined by the following
equation.




Example 1
Two forces, P and Q
of magnitude 10N and 12N are perpendicular to each others. What is the
magnitude of the resultant force if P and Q are acting on an object?




Example 2

Diagram
above shows that four forces of magnitude 2N, 4N, 5N and 8N are acting
on point O. All the forces are perpendicular to each others. What is
the magnitude of the resulatant force that acts on point O?






Vector Resolution
A vector can be resolve into 2 component which is perpendicular to each others.




Example 3

Diagram above shows a lorry pulling a log with an iron cable. If the
tension of the cable is 3000N and the friction between the log and the
ground is 500N, find the horizontal force that acting on the log.

Answer:
Horizontal component of the tension = 3000 cos30o =2598N
Friction = 500N
Resultant horizontal force = 2598N - 500N =2098N




Example 4

Diagram above shows two forces of magnitude 25N are acting on an object of mass 2kg. Find the acceleration of object P, in ms-2.

Answer:
Horizontal component of the forces = 25cos45o + 25cos45o = 35.36N
Vertical component of the forces = 25sin45o - 25sin45o = 0N
The acceleration of the object can be determined by the equation
F = ma
(35.36) = (2)a
a = 17.68 ms-2





Inclined Plane
Weight component along the plane = Wsinθ.
Weight component perpendicular to the plane = Wcosθ.





Example 5

A
block of mass 2 kg is pulling along a plane by a 20N force as shown in
diagram above. Given that the fiction between block and the plane is
2N, find the magnitude of the resultant force parallel to the plane.

Answer:

First of all, let's examine all the forces or component of forces acting along the plane.
The force pulling the block, F = 20N
The frictional force Ffric = 2N
The weight component along the plane = 20sin30o = 10N
The resultant force along the plane = 20 - 2 - 10 = 8N





Vectors in Equilibrium
When 3 vectors are in equilibrium, the resultant vector = 0. After
joining all the vectors tail to head, the head of the last vector will
join to the tail of the first vector.





Forces in equilibrium
Forces are in equilibrium means the resultant force in all directions are zero.




Example 6


Diagram
above shows a load of mass 500g is hung on a string C, which is tied to
2 other strings A and B. Find the tension of string A.

Answer:

Tension of string C, TC = weight of the load = 5N
All forces in the system are in equilibrium, hence
Vertical component of tension A (TA) = TC
TAcos60o = TC
TA = TC/cos60o
TA = 5
/cos60o = 10

2.11Work and Energy



Work

Work done by a constant force is given by the product of the force and the distance moved in the direction of the force.
Unit: Nm or Joule (J)
Work is a scalar quantity.



Formula of work






Example 1

A
force of 50 N acts on the block at the angle shown in the diagram. The
block moves a horizontal distance of 3.0 m. Calculate the work being
done by the force.

Answer:
Work done,
W = F × s × cos θ
W = 50 × 3.0 × cos30o = 129.9J





Formula of work 2When the direction of force and motion are same, θ = 0o, therefore cosθ = 1
Work done,

W = F × s



Example 2

Diagram
above shows a 10N force is pulling a metal. The friction between the
block and the floor is 5N. If the distance travelled by the metal block
is 2m, find

• the work done by the pulling force
  
• the work done by the frictional force
  
• 
  

Asnwer:
(a) The force is in the same direction of the motion. Work done by the pulling force,
W = F × s = (10)(2) = 20J
(b) The force is not in the same direction of motion, work done by the frictional force
W = F × s × cos180o= (5)(2)(-1) = -10J






Work Done Against the Force of Gravity




Example 3
Ranjit runs up a staircase of 35 steps. Each steps is 15cm in height.
Given that Ranjit's mass is 45kg, find the work done by Ranjit to reach
the top of the staircase.

Answer:
In this case, Ranjit does work to overcome the gravity.
Ranjit's mass = 45kg
Vertical height of the motion, h = 35 × 0.15
Gravitational field strength, g = 10 ms-2
Work done, W = ?
W = mgh = (45)(10)(35 × 0.15) = 2362.5J




Force - Displacement Graph
In a Force-Displacement graph, work done is equal to the area in between the graph and the horizontal axis.




Example 4

The
graph above shows the force acting on a trolley of 5 kg mass over a
distance of 10 m. Find the work done by the force to move the trolley.




Energy
Energy is defined as the capacity to do work.
Work is done when energy is converted from one form to another.
Unit: Nm or Joule(J)





Kinetic Energy
Kinetic energy is the energy of motion.





Example 5
Determine the kinetic energy of a 2000-kg bus that is moving with a speed of 35.0 m/s.



Gravitational Potential Energy
Gravitational potential energy is the energy stored in an object as the result of its vertical position (i.e., height).
Formula:





Example 6
A ball of 1kg mass is droppped from a height of 4m. What is the maximum
kinetic energy possessed by the ball before it reached the ground?

Answer:
According to the principle of conservation of energy, the amount of
potential energy losses is equal to the amount of kinetic energy gain.
Maximum kinetic energy
= Maximum potentila energy losses
= mgh = (1)(10)(4) = 40J




Elastic Potential Energy
Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing.
Formula:






Example 7

Diagram
above shows a spring with a load of mass 0.5kg. The extention of the
spring is 6cm, find the energy stored in the spring.

Answer:
The energy stored in the spring is the elestic potential energy.




Conservation of Energy and Work Done
During a conversion of energy,
Amount of Work Done = Amount of Energy Converted




Example 8
A trolley of 5 kg mass moving against friction of 5 N. Its velocity at
A is 4ms-1 and it stops at B after 4 seconds. What is the work done to
overcome the friction?

2.12 Power and Efficiency

Power
Power is the rate at which work is done, which means how fast a work is done.

Formula:




Example 1
An electric motor takes 20 s to lift a box of mass 20kg to a
height of 1.5 m. Find the amount of work done by the machine and hence
find the power of the electric motor.




Efficiency

The efficiency of a device is defined as the percentage of the energy input that is transformed into useful energy.






Efficiency

In
the example above, the input power is 100J/s, the desire output power
(useful energy) is only 75J/s, the remaining power is lost as undisire
output. Therefore, the efficiency of this machine is
75/100 x 100% = 75%





Air conditioner

• Switch off the air conditioner when not in use.
  
• Buy the air conditioner with suitable capacity according to the room size.
  
• Close all the doors and windows of the room to avoid the cool air in the room from flowing out.
  

Refrigerator

• Always remember to close the door of refrigerator.
  
• Open the refrigerator only when necessarily.
  
• Always keep the cooling coil clean.
  
• Defrost the refrigerator regularly.
  
• Choose the refrigerator with capacity suitable for the family size.
  
• Refrigerator of large capacity is more efficient compare with refirgerator of small capacity.
  

Lamp or Light Bulb

• Use fluorecent bulb rather than incandescent bulb. Fluorescent bulbs are much more efficient than incandescent bulbs.
  
• Use a lamp with reflector so that more light is directed towards thr desirable place.
  

Washing Machine

• Use front-loading washing machine rather than top-loading wahing machine because it uses less water and electricity.
  
• Use washing machine only when you have sufficient clothes to be washed. Try to avoid washing small amount of clothes.
  

2.13 Elasticity

Elasticity
Elasticity is the ability of a sub-stance to recover its original shape and size after distortion.



Forces Between Atoms

The intermolecular forces consist of an attractive force and a repulsive force.

• At the equilibrium distance d, the attractive force equal to the repulsive force.
  
• If the 2 atoms are brought closer, the repulsive force will dominate, produces a net repulsive force between the atoms.
  
• If the 2 atoms are brought furhter, the attractive force will dominate, produces a net attractive force between the atoms.
  

Graph of Forces Between 2 atoms
x0 = Equilibrium Distance
When the particles are compressed, x < x0, the repulsive force between the particles increases.
When the particles are stressed, x > x0, the attractive force between the particles increases.
If the distance x exceeds the elastic limit, the attractive force will decreases.






Hooke's Law
Hooke's Law states that if a spring is not stretched beyond its elastic limit, the force that acts on it is directly proportional to the extension of the spring.





Elastic Limit
The elastic limit of a spring is defined as the maximum force that can be applied to a spring such that the spring will be able to be restored to its original length when the force is removed.





Equation derived from Hooke's LawFrom Hook's Law, we can derived that







Spring Constant
Spring constant is defined as the ratio of the force applied on a spring to the extension of the spring.


It is a measure of the stiffness of a spring or elastic object.





Graph of Streching Force - Extension
Gradient = Spring constant
Area below the graph = Work done






F-x graph and spring constant
The higher the gradient, the greater the spring constant and the harder (stiffer) spring.
For example, the stiffness of spring A is greater than spring B.






System of Spring
Arrangement in series:
Extension = x × number of spring
Stiffness decreases
Spring constant = k/number of spring
Arrangement in parallel:
Extension = x ÷ number of spring
Stiffness increases
Spring constant = k × number of spring





Factors Affecting the Stiffness of Spring

	Stiffer	Less stiff
Material type of spring
Diameter of wire of spring
Diameter of the spring
Length of the string