# Form 4 -notes [chapter 1 &2 ]

## Form 4 -notes [chapter 1 &2 ]

1.1

==what are Physical Quantities==

==what are 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==

==what is derived quantities?==

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?==

==what are prefixes?==

==what are scalar quantities?==

==what are Physical Quantities==

__Physical Quantities__- A physical quantity is a quantity that can be measured.

==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 Quantities__A derived quantityis 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 Unit__The derived unit is a combination of base units through multiplying and/or dividing them.==what are prefixes?==

__Prefixes__Prefixes 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.

__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.

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## 回复： Form 4 -notes [chapter 1 &2 ]

1.2 Error Analysis

==What is error?==

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

==What is 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.==

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

==What is meant by zero error?==

==Define random Error==

==State the causes of random error==

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

instrument due to the eye of the observer and pointer are not in a line

perpendicular to the plane of the scale.

==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 to avoid random error__- Taking repeat readings
- Find the average value of the reading.

__Parallax Error__A parallax error is an error in reading aninstrument due to the eye of the observer and pointer are not in a line

perpendicular to the plane of the scale.

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## 回复： Form 4 -notes [chapter 1 &2 ]

1.3 Measurement

==What is meant by 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?==

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.==

==How the accuracy of a measurement can be increased?==

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

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

(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

==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.==

__Accuracy__The 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

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## 回复： Form 4 -notes [chapter 1 &2 ]

1.4 Scientific Investigation

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:

__Scientific Report__A 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.

__Inference__Inference is a statement to state the relationship between two visible quantities observed in a diagram or picture.__Hypothesis__Hypothesis is a statement to state the relationship between two measurable variables that can be investigated in a lab.__Variables__A 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 Data__A 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 Graph__Graphsare 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

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## 回复： Form 4 -notes [chapter 1 &2 ]

__Chapter 2 Force and Motion__

__2.1 linear motion__

__Linear Motion__

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

__Distance__The

**distance**traveled by an object is the

**total length**that is traveled by that object.

Unit:

**metre (m)**

Type of Quantity:

**Scalar quantity**

__Displacement__

**Displacement**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

__Speed__Speed is the

**rate of change**in

**distance**.

Formula:

Unit:

**ms-1**

Type of quantity:

**Scalar quantity**

__Velocity__Velocity is the rate of change in displacement.

Formula:

Unit:

**ms-1**

Type of quantity:

**Vector quantity**

__Acceleration__Acceleration 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.

- the
- An object that experiences
**changes in velocity**is said to have**acceleration**. - An object traveling with a constant acceleration,
if the velocity changes at a constant rate.*a,*

__4 Equations of Uniform Acceleration__

The above equation is for solving numerical problems involving uniform acceleration.

__Summary__

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## 回复： Form 4 -notes [chapter 1 &2 ]

__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 Velocity__Velocity 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 Acceleration__Acceleration 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,

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## 回复： Form 4 -notes [chapter 1 &2 ]

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

Velocity - Time Graph

Analysing Velocity - Time Graph

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.

Launching Object Upward

Object falling and bounces back

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 |

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## 回复： Form 4 -notes [chapter 1 &2 ]

2.4 Inertia Mass

Mass is the amount of matter.

Unit: kilogram (kg)

Type of quantity: Scalar quantity

Inertia

Inertia is the

Newton's First Law

In the

Jerking a Card

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

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

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

Tension at A = Weight of the load + Pulling Force

Larger Mass - Greater Inertia

Bucket filled with sand is

Object with more mass offers a greater resistance to change from its state of motion.

Object with

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

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: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.****The**

Explanation:

Explanation:

**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

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## 回复： Form 4 -notes [chapter 1 &2 ]

__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.

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## 回复： Form 4 -notes [chapter 1 &2 ]

2.6 Effects of Force

The

When there is

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

(IMPORTANT: F Must be the net force)

When there is a

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.

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?

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.

**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.

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## 回复： Form 4 -notes [chapter 1 &2 ]

__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 × t**Impulse = 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.

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## 回复： Form 4 -notes [chapter 1 &2 ]

__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.

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## 回复： Form 4 -notes [chapter 1 &2 ]

**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

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## 回复： Form 4 -notes [chapter 1 &2 ]

**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

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## 回复： Form 4 -notes [chapter 1 &2 ]

**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?

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## 回复： Form 4 -notes [chapter 1 &2 ]

**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.

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## 回复： Form 4 -notes [chapter 1 &2 ]

**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 |

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