PHYSICS SPM 2010

REVISION NOTES PREPARED BY: MR. PEETER CHAPTER 1.1.1 BASE QUANTITIES AND DERIVED QUANTITIES.

1. A quantity that be measured are physical quantity: examples are area of rectangle – area is the quantity and the rectangle is the physical object.

2. Physical quantities are divided to BASE and DERIVED QUANTITIES. A BASE quantity is a quantity that cannot be defined in terms of other physical quantities. Units for BASE quantities are called SI units.

3. LIST OF BASE QUANTITIESBase quantity SI unit SymbolMass, m kilogram kgLength, l meter mTime, t seconds sTemperature, T (thermodynamic temperature) kelvin K Electric current, I ampere AQuantity of matter mole mole

4. DERIVED quantities are derived by multiplications and divisions of BASE quantities. It’s a combination of various basic quantities. Units are known as derived units.

5. LIST OF DERIVED QUANTITIESDerived quantity Relationship with the base quantity Derived unit

Power

Pressure

Scientific notation Prefixes .Prefix Multiple In scientific notation SYMBOLTERA 1 000 000 000 000 10 12 TGIGA 1 000 000 000 10 9 GMEGA 1 000 000 10 6 MKILO 1 000 10 3 kHECTO 100 102 hDECA 10 101 da

Sub-multipleDESI 0.1 10 –1 dCENTI 0.01 10 –2 cMILLI 0.001 10 –3 mMICRO 0.000 001 10 –6 μNANO 0.000 000 001 10 –9 nPICO 0.000 000 000 001 10 -12 p

1.2 MEASUREMENTS.

1. PRECISION is the degree of uniformity or reproducibility of the measurements.Is the ability of an instrument in measuring a quantity in a consistent manner with only a small relative deviation between readings.

A high precision indicates a small deviation. And a low precision indicates a large deviation. Absolute deviation is the difference between a value and the mean value for the whole measurements.Relative deviation is the percentage of mean deviation for a set of measurements.

Relative deviation = mean deviation X 100 % mean value

2. ACCURACY is the degree of closeness of the measurements to the true or accepted value. Is the approximation of the measurement to the actual value for a certain quantity of physics.Accuracy of a measurement can be increased by:a. taking a number of repeated readings to calculate the mean value of the readingsb. avoiding the end errors or zero errorsc. taking into account the zero and parallax errorsd. using more sensitive equipment such as a vernier caliper to replace a ruler.

3. SENSITIVITY of an instrument is its ability to detect small changes in the quantity that is being measured. Measuring instruments that have smaller scale parts are more sensitive.

MEASURING INSTRUMENTSa. VERNIER CALIPER

The reading of vernier caliper.CALIPER READING = MAIN SCALE READING + VERNIER SCALE READING

ZERO ERROR ( of vernier caliper ).

The reading of the vernier caliper in the next figure is :Main scale = 5.30cmVernier scale = 0.04cmVernier caliper reading = 5.30cm + 0.04cm

= 5.34cm.0

An instrument which does not register a zero reading when the true reading is zero has a zero error defect. A vernier caliper has a zero error if the ‘0’ mark on main scale is not in line with the ‘0’ mark on the vernier scale of the calipers when the jaws are fully closed . To eliminate zero error: Correct reading = caliper reading – zero error.REAL READING = CALIPER READING – ZERO ERROR

Type of zero error:

b. MICROMETER SCREW GAUGE

The reading of micrometer screw gauge.

ZERO ERROR ( of a micrometer screw gauge ).

The reading of the micrometer screw gauge :

Reading = main scale + thimble scale

The accuracy of the micrometer screw gauge is also affected by zero errors. If the micrometer shows zero errors then all the readings have to be corrected. To eliminate zero error: Correct reading = micrometer reading – zero error.

Type of zero error:

CHAPTER 2.2.0 FORCES AND MOTION

EQUATIONS FOR LINEAR MOTION WITH UNIFORM ACCELERATION.

LINEAR MOTION EQUATIONS.

b. v = u + atc. s = 1 x (u + v) t 2DERIVE ALL THESE EQUATIONS, from the above formulae. d. s = ut + 1 at 2

2e. v 2 = u 2 + 2as

2.1 Analysing Motion Graphs 1. Displacement-time graphs 2. Velocity-time graph

1a. the displacement stays the same, the object is at rest, velocity is zero (gradient is zero)

2a. object is not moving, velocity is zero, (gradient is zero) acceleration zero

1b. the displacement is increasing uniformly with time, object moving with constant velocity (constant gradient)

2b. constant velocity, (gradient is zero) acceleration is zero

[displacement of the object = area under the graph]1c. the displacement is increasing (not uniformly with time) velocity is increasing (gradient is ncreasing) object moving with constant acceleration

2c. velocity is increasing uniformly with time, (constant gradient) acceleration constant

[displacement of the object = area under the graph]

1d. the displacement is increasing (not uniformly with time) velocity is decreasing (gradient is decreasing) the object is moving with constant deceleration

2d. velocity decreasing uniformly with time, (constant negative gradient) object moving with constant deceleration

[displacement of the object = area under the graph]

2. Acceleration-time grapha. object not moving, acceleration zero

b. constant velocity, acceleration zero

c. object moving with constant acceleration ( positive acceleration)

d. object moving with constant deceleration ( negative acceleration)

INERTIAInertia = of an object is the tendency of the object to remain at rest or if moving to continue its motion. = is the property of matter that causes it to resist any change in its motion or state of rest.

The charecteristics of inertia can be described by NEWTON’S FIRST LAW OF MOTION. STATES:

every object will continue in its state of uniform velocity or at rest unless it is acted upon by an external force.

o ( MASS DETERMINE THE AMOUNT OF INERTIA ). o AN OBJECT WITH A LARGER MASS HAS A LARGER INERTIA.

Ways of reducing the effects of inertia. a. Seat belt – the seat belts secure the passengers to their seats and prevent them from being thrown forward or head long

into the windscreen.b. Air bag system – mounted on the steering or dashboard, expands automatically during collisions protects the driver and

passenger during collision.c. Lorries carrying heavy loads ( petrol tanks ) will have following structures:

i. a strong iron structure behind the drivers cabin, to stop the inertial movement of the heavy load towards the driver when the lorry is stopped suddenly.

ii. If it is a petrol tanker the inside tank is divided internally into compartments. This is to lessen the impact of the inertial movement of the liquid forward.

THE PRINCIPLE OF CONSERVATION OF MOMENTUM.States: that the total momentum of a system is always fixed if there is no external force acting on the system

THE TOTAL MOMENTUM OF THE OBJECT BEFORE COLLISION IS THE SAME AS THE TOTAL MOMENTUM AFTER COLLISION PROVIDED THAT THERE IS NO EXTERNAL FORCE ACTING ON IT.

TYPES COLLISIONS:

A. ELASTIC COLLISION: After collision the objects move seperately. Both objects move independently at their respective velocities after collision.Momentum is conserved, kinetic energy is conserved and total energy is conserved.

B. INELASTIC COLLISION: After collision objects stick together and moves with a common velocity. The two objects combine and move together with a common velocity after collision. Momentum is conserved, kinetic energy is not conserved and total energy is conserved.

C. EXPLOSION: The total momentum before explosion is equal to the total momentum after explosion because the total momentum is conserved during explosion. The total momentum is zero before and after collision.Momentum is conserved.

4. B. Unbalanced Forces . When the forces acting on an object is not at balance the object will accelerate or decelerate. The net force is known as the unbalanced force or the resultant force. Net force occur when there is unbalanced forces acting on an object.

Fb > Fs Fb – Fs = ma

Net force = ma.

RELATIONSHIP BETWEEN FORCE, MASS, AND ACCELERATION.1. The acceleration of a body is directly proportional to the force applied if the mass of the object is constant.

F ∞ a

2. The acceleration of a body is directly proportional to the force applied if the mass of the object is constant. F ∞ a

F = k a k = mF=ma

NEWTON’S SECOND LAW OF MOTION.Formula for force, F=ma. This relationship is known as Newton’s second law of motion.

Newton’s second law of motion states that the rate of changes of momentum of a moving body is proportional to and in the same direction as the net force acting on it.

Free Fall.- objects falls without encountering any resistance from a height towards the earth with an acceleration due to gravity, the

object is said to be free falling.- All objects which free fall from the same height have the same gravitational acceleration, g. But a free fall can only occur

in vacuum.

MASS AND WEIGHT.1. Mass is the amount of matter content in an object(body).2. Weight is the gravitational force exerted on an object by the earth.3. Weight is therefore a force and measured in Newton, N. Weight is a vector quantity.

Weight = mg

2.9 PULLEY SYSTEM

1. If M1 > M2 ( mass of load M1 is bigger than mass of load M2),The formula of net force(resultant force) will be:

M1g - T = M1a.T - M2g = M2 a.M1g - M2 g = (M2 + M1 )a.

2.10 WORK, ENERGY AND POWER. WORK.a. Work done is the product of an applied force and the displacement of an object in the direction of the applied force.b. Work is defined as the product of the applied force and the displacement of an object in the direction of the applied force. c. Work is defined as the product of the acting force and the distance travelled in the direction of that acting force. The S.I.

unit for work is Nm or Joule and work is a scalar quantity.

Work done, W = F X s F = force, s = displacement= Nm.= J.

Energy is defined as the capacity for doing work. The S.I. unit for energy is Joule.

Types of Energy.a. Gravitational potential energy

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Gravitational potential energy is the energy of an object due to its higher position in the gravitational field. Gravitational potential energy is the energy possessed by a body due to its location.

b. Elastic potential energy Elastic potential energy is the energy that is due to a state of compression or stretching.The elastic potential energy =

c. Kinetic energy Kinetic energy is the energy of an object due to its motion.

The principle of conservation of energyThe principle of conservation of energy states that energy can be transferred from one form to another, but it cannot be created or destroyed.

The Principle of Conservation of Energy states that energy cannot be created or destroyed but it can be converted from one form into another.The conservation of energy benefits humans. On the other hand, the abuse of energy can bring about danger.

POWERPower is defined as the rate at which work is done, or the amount of work done per second.

POWER = WORK TIME

Efficiency =

2.11 Elasticity The forces of repulsion act when solids are compressed and forces of attraction act when solids are stretched.The resultant force is zero when the particles are in a state of equilibrium. Therefore, in such a case, the force of attraction is equal to the force of repulsion.

Elasticity is the characteristic of a solid to return to its original shape and size after a stretching or compressive force is removed.The forces of repulsion act when solids are compressed and forces of attraction act when solids are stretched.

Hooke's lawHooke's law defined that the extension of a spring is directly proportional to the applied force provided that the elastic limit is not exceeded. It can be written as:F= k xwhere, F is the force on the spring, k is the spring constant and x is the extension of the spring.The elastic potential energy stored in a stretched spring is given by: ______________________

The spring constant, k is a value that depends on the(a) type of substance(b) diameter of the spring(c) diameter of the wire from which the spring is made.

(d) original length of the spring.

The elastic limit is defined as the maximum force which can be acted upon a given elastic substance before the substance loses its elastic characteristics.

CHAPTER 3.3.0 FORCES AND PRESSURE

3.1 PRESSURE IN LIQUIDS 1. Pressure in liquids caused by the weight of liquids. The pressure at a point in a liquid, at a particular depth, acts equally in

all directions. The pressure in a liquid increases with depth. The pressure at a point in a liquid depends on its vertical distance from the surface of the liquid.

2. Deriving a Formula for Pressure in a liquid.

Methods to measure Air(Gas) and Atmospheric Pressure.1. To measure gas pressure instrument used are:

a. manometer

b. and Bourdon gauge

2. To measure atmospheric pressure instrument used are:

a. Aneroid barometer

b. And Fortin’s Barometer A Simple Barometer

3.2 PASCAL’S PRINCIPLE Pascal’s Principle states that when pressure is applied to an enclosed fluid, the pressure will be transmitted equally throughout the whole enclosed fluid. Pascal’s Principle states that in a confined fluid, an externally applied pressure is transmitted uniformly in all directions. It is also known as the principle of transmission of pressure in a liquid.

Application of Pascal’s Priciple:1. A Basic hydraulic system works with the Pascal’s principle.2. Mechanism of a hydraulic system.

When a small force of F1 is exerted at the small piston a larger force of F2 will be exerted at the larger piston.

3. Examples of hydraulic systems.A hydraulic brake system.

3.3 ARCHIMEDES’ PRINCIPLES - states that for a body immersed wholly or partially in a fluid, the upward buoyant force acting on the

body is equal to the weight of the fluid displaced. ( buoyant force is an upward force resulting from an object being wholly or partially immersed in a fluid)

BUOYANT FORCE = WEIGHT OF LIQUID DISPLACED= p V g

p = density of the liquid V = volume of liquid displacedG = gravity

1. if objects are freely floating on water( liquid ):weight of object = buoyant force

2. when weight of object is equal to the buoyant force than the :weight of object = weight of liquid displaced[weight of liquid displaced = buoyant force]

Formula for buoyant force:

3.4 BERNOULLI’S PRINCIPLE - states that when the velocity of a fluid is high, the pressure is low and when the velocity is low, the pressure is high.

Applications of Bernoullis Principle.A. Aerofoil

- the aerofoil shape of the wing of an aeroplane , causes the lifting of an aeroplane- when the plane is moving horizontally , air flows over the aerofoil- the velocity of the air at the top is greater then at bottom. - The difference in the velocity of air at the top and bottom has caused lower air pressure at the top compared to

the bottom. The higher air pressure at the bottom created a net upward force or lift is resulted.-

CHAPTER 4.

HEAT

4.1 TEMPERATURE, HEAT AND THERMAL EQUILIBRIUMTemperature The degree of hotness or coldness of an object, it is expressed as a number on the

temperature scale. SI unit is Kelvin (K).Is a measure of the average kinetic energy of the atoms or molecules in a substance.

Heat Heat is energy transfer from a higher temperature substance to a lower temperature substance. Heat is the energy transfers from one object to another because of the differences in temperature. Unit of measurement is Joule (J).

Thermal Equilibrium When objects in thermal contact reach the same temperature, these objects are in thermal equilibrium. There is no net heat flow between them.

The amount of heat energy flowing out of one object is the same as the amount flowing in.

The rate of heat absorption equals to the rate of heat dissipation at the same temperature

e.g. a thermometer is read when it has reached thermal equilibrium with the substance being measured

4.2 UNDERSTANDING SPECIFIC HEAT CAPACITY

Different substance will have different ability to transfer heat energy, the specific heat capacity is used to compare these ability.The Specific Heat Capacity of a material is defined as the amount of energy that must be transferred to change the temperature of one kilogram of a material by 1oC or 1K.

A substance with a larger heat capacity will experience a smaller temperature rise when absorbing heat. Specific Heat Capacity

Q=mcӨ

C = Q_ mӨ

C = specific heat capacityQ = amount of energy absorbed or released( J )Ө = changes in temperature ( OC)m = mass of the object / material (Kg)

4.3 UNDERSTANDING LATENT HEAT 1. Latent heat is the energy transferred during the change in state of matter at a constant temperature.

2. SPECIFIC LATENT HEAT OF FUSION, lf (L) of a substance is the amount of heat energy required to change 1kg of a substance from solid state to liquid state without a change in temperature.The SI unit for SPECIFIC LATENT HEAT OF FUSION, lf is joule per kilogram ( JKg-1)Q = m L.

3. SPECIFIC LATENT HEAT OF VAPORIZATION, lV (L) of a substance is the amount of heat energy required to change 1kg of a substance from liquid state to gas state without a change in temperature.The SI unit for SPECIFIC LATENT HEAT OF VAPORIZATION, lV is joule per kilogram ( JKg-1)Q = m L.

GAS LAWS

A. BOYLE’S LAW .a. Boyle’s Law : states that the pressure of a fixed mass of a gas is inversely proportional to the volume of the gas, provided

the temperature of the gas is constant.

b. When the temperature of a constant mass gas is constant , the average kinetic energy of all the gas particles are constant too. If the volume of the gas is reduced , the number of gas particles per unit volume will increase. This will increase the frequency of collision of the gas particles with the wall of the container which will increase the gas pressure.

B. CHARLES LAW.a. Charles’s Law: states that for a fixed mass of ideal gas , the volume is directly proportional to its absolute temperature at

constant pressure.

b. When the mass and the pressure of a gas are fixed, frequency of collision between the gas particles and the wall of the container are constant. If the temperature is increased then the kinetic energy of the gas particles will increase, this will increase the number/frequency of collision between the gas particles and the wall of the container, so the pressure exerted by the gas particles on the wall of the container is increasing. The container at first will expand due to the increase in the pressure but when the pressure becomes the same as before the expansion, the expansion will stop and the gas will have a new different volume( an increased volume), when the temperature is increased.

C. PRESSURE LAW.a. Pressure Law: states that the pressure of an ideal gas is directly proportional to its absolute temperature at constant

volume

b. When the temperature of a fixed volume and mass of a gas is increased the kinetic energy of the particles will increase. The increase in the kinetic energy will increase the frequency of collision, thus this will increase the gas pressure.

CHAPTER 5 LIGHT IMAGE FORMED BY A CONVEX MIRROR

1. Characteristics of the image formed by convex mirror , a. virtualb. uprightc. diminished in sized. image behind the mirror

5.2 REFRACTION OF LIGHTa. Law’s of refraction Snells Law.-two laws of refraction - A. the incident ray and the refracted ray are on the opposite sides of the normal at the point of incidence, and all three lie in the same plane ( phase ).B. The value of sin i / sin r is a constant this known as snell’s law.

C. Refractive index, n i. refractive index , n = sin i

sin r ii. refractive index , n = speed of light in vacuum

speed of light in a medium iii. refractive index , n = real depth

apparent depth iv. refractive index , n = 1

sin c

D. Critical angle = C , an angle of incidence when the refracted ray’s angle is 90o . The refracted ray travels along the two mediums boundary.E. Total Internal Reflection is the total reflection of a beam of light at the boundary of two mediums, when the angle of incidence in the optically denser medium exceeds a specific critical angle. The boundary between two mediums acts like a perfect plane mirror where total internal reflection occurs.

PRACTICE 1: 1. Draw image formed by a concave mirror when :

a. when the object is at C

b. when the object is between F and C

UNDERSTANDING TOTAL INTERNAL REFLECTION OF LIGHT1. Critical angle an angle of incidence that cause a refracted light ray with an angle of 900. If the angle of incidence is allowed to exceed the critical angle, it is found that light rays are not refracted. This is because all of the light rays are reflected. This is named total internal reflection. 2. Total internal reflection can happen when:

a. light rays travel from a denser medium to a less dense mediumb. the angle of incidence is greater than the critical angle

3. refractive index , n = 1 sin c

4. Light Diagram for total internal reflection.b. light ray with total internal reflection

c. total internal reflection in a glass prism

d. Applications of Total Internal Reflection:i. mirageii. periscopeiii. binocularsiii. fibre optics

Linear Magnification.

i. linear magnification , M = height of image height of object

ii. linear magnification , M = distance of image (v) distance of object (u)iii. 1 = 1 + 1

f u v

Lens PowerPower ( D ) = 1

Focal length(m)

i. convex lens power = + ___ Dii. concave lens power = - ___ D

5.5 OPTICAL DEVICES

1. Slide Projector.Components Functionsslide Placed at a distance between 2F and F from the projector lens . As an object ,

placed invertedProjector lens To focus a clear image on the screen

Can be adjusted Condenser Consisting 2 plano-convex lenses to focus all the light on the object to obtain a

clear image on the screenConcave mirror To reflect all the light ray and to focus all the light ray to the slide .

* the slide is placed inverted so that the image will be upright

3. Compound Microscope

a. Focal length of the eye lens is longer than the focal length of an objective lens

Fe > Fo

b. Eye lens works as a magnifying glass c. Power of the eye lens is smaller than the power of the objective lensd. The final image formed by the eye lens are virtual, magnified and invertede. Magnification of the microscope : M = m0 X me

[The first image from the object lens is used as image for the eye lens][The height of the first image is the same height of the object of eye lens]

4.Astronomy Telescope.

a. Focal length of the eye lens is shorter than the focal length of the objective lens Fo > Fe

b. Power of the eye lens is bigger/higher than the power of the objective lensc. Magnifications of the telescope : M = focal length of the objective lens , fo

focal length of the eye lens(eyepiece) , fe

M = Height of the image Height of the object

PHYSIC FORM 4. PREPARED BY: CIKGU PEETER 017 3820248