Understanding Pressure in Physics: Key Concepts and Applications

[Music] candidates are expected to have a thorough understanding of the syllabus

details outlined in the accompanying figure measuring length in physics experiments when we need to measure the

length of an object it is important to select a suitable instrument for the task different instruments offer varying

degrees of precision to suit the object's size lengths exceeding 100 cm we can be used the measuring tape its

Precision is 0.1 CM for example it is used to measure the waistline of a person or the dimensions

of a room lengths between 5 and 100 cm we can be used the meter rule or ruler its Precision is 0.1

CM for example it is used to measure the length of an object as pencils or wires lengths between 1 and 10

cm we can be used the Veria caliper its Precision is 0.01

CM for example it is used to measure the diameter of a beaker sphere or cylinder lengths less than 2

cm we can be use the micrometer its Precision is 0.01

CM for example it is used to measure the thickness of a wire paper or thin sheet of

material zero error zero error is caused by faulty equipment that doesn't reset to zer

properly zero error is simply the reading of the measuring device when input quantities are zero for example a

stopwatch that has not been reset to zero before use can give a zero error to minimize zero error it's important to

calibrate your instrument before use calibration ensures the instrument readings are accurate and

consistent Parallax error Parallax errors can occur during measurement for example incorrect positioning of the

eye this is wrong position of the eye this is wrong position of the eye this is right position of the eye we should

read the scale at perpendicular angle to the scale for avoiding The Parallax error the object is not touching the

marking of the scale this is wrong this is wrong this is right for the measuring tape meter Ru and ruler ensure that the

object is in contact with the scale more measurement techniques in an small length measure the diameter of a

ball bearing we can use the two wooden blocks to make it easier to measure the diameter of four ball bearing as shown

the blocks Mark the edges of the first and last ball bearings so the total diameter is

9.3 - 3 is equal to 6. 3 cm divide the total by the number of ball

bearings so diameter equals 6.3 to divide by 4 is equal to 1.6 CM measure the thickness of one paper

using a ruler measure the thickness of 500 sheets of paper using a ruler divide the thickness of 500 sheets by 500 to

get the thickness of one sheet repeat the reading at different positions of thickness of 500 sheets of papers and

find the average using the micrometer screw check the zero error of the micrometer measure the thickness of 20

sheets of paper using the micrometer divide the thickness of 20 sheets by 20 to get the thickness of one

paper repeat the reading of 20 sheets thickness at different positions of 20 papers and find the average

measure the volume of an object using the measuring cylinder fill the measuring cylinder with water read the

initial volume V1 by viewing the scale at perpendicular angle at the bottom of the meniscus as shown carefully place

the object into the water the water level rise as shown read to the final volume V2 by viewing the scale at a

perpendicular angle at the bottom of the meniscus the volume of the object is the final volume V2 minus the initial volume

V1 measure the time period of a pendulum the time period of a pendulum is the time taken for the pendulum to complete

one oscillation one oscillation is from A to B and back to a place the pin at here as

the fiducial mark for counting the number of oscillations set a stopwatch at zero

measure the time taken of a ball to complete and oscillations with a stopwatch an N should be about 10 to 20

oscillations in this experiment n equals 10 oscillations divide the time taken of n

oscillations by n to get the period of the pendulum for this example the period is 16.0 to divide by 10 which equals to

1.6 seconds repeat the reading at least three times and find the average of the

period to get the accurate value physical quantities there are two types of

physical quantities as scalar and Vector all physical quantities consist of a numerical magnitude and a unit for

example the volume of 150 cubic M the volume is the physical quantity it is a scalar quantity because the volume has

know the direction the Val Val of 150 represents the numerical magnitude or size of the volume the cubic meters

represents the unit of volume the weight of 500 Newtons the weight is physical quantity

it is a vector quantity because it has both magnitude and Direction the value of 500 represents the numerical

magnitude or size of the weight the Newton is the unit of weight the direction of weight is always down W

scalar and Vector a scalar quantity has only magnitude or size which is a numerical value a vector quantity has

both magnitude and direction for example some scalar quantities in physics include distance

speed time mass energy density and temperature for example some Vector quantities in physics include

displacement velocity acceleration force and weight momentum electric field strength and gravitational field

strength resultant Vector it is the total or net Vector which is the single Vector that all vectors are combined

Vector quantities are represented by arrows the Arrow Head indicates the direction of the vector the length of

the arrow represents the magnitude there are two methods that can be drawn to determine the resultant

Vector as the triangle method and the parallelogram method to add the vector a and Vector B using the triangle method

link the head of vector a to the tail of vector B the resultant Vector is formed by connecting the tail of the vector a

to the head of the vector B to add the vector a and Vector B using the parallelogram method link the taals of

the vector a and Vector B draw a parallelogram with Vector a and Vector B are sides the resultant Vector is the

diagonal of the parallelogram determine the resultant of two vectors at right

angles find the resultant velocity of an airplane flying at 80 km per hour in a 60 km/h

crosswind find the resultant velocity using the calculation draw a parallelogram with 80

km per hours and 60 km/s or sides which form to the rectangular the resultant velocity is

the diagonal of the parallelogram we can calculate the magnitude of the resultant velocity

using the Pythagorean theorem resultant velocity S = 80 2 + 602 resultant velocity = < TK 802 + 602

= 100 km hour we can calculate the direction of the resultant velocity by the tangent ratio the direction of the

resultant velocity is the angle Theta to the direction of wind's velocity so the direction of the resultant velocity is

tan power minus 1 8/ 60 is equal to 53° to 60 km/h find the resultant velocity using

the graphically set the scale 1 cm to 10 km/ hour draw the velocity of 60 km per hour

to right for 6 cm measure angle at the head of the 60 km per hour velocity using a protractor

as 90° link the head of the 60 km per hour velocity to the tail of the 80 km/h

velocity draw a velocity of 80 km per hour for 8 cm the resultant velocity is formed by

connecting the tail of the 60 km perh velocity to the Head of the 80 km/ hour measure the length of the resultant

velocity so magnitude of the resultant velocity is 10 cm * 10 km per hour = 100 km/ hour measure the angle between the

60 km per hour and resultant velocity so the direction of the resultant velocity is 53° to 60 km/ hour

[Music] candidates are expected to have a thorough understanding of the syllabus

details outlined in the accompanying figure distance and displacement you don't need to know

about displacement for igcs but it useful to know it when a ball travels along a circular track from

point A to point B the distance traveled from A to B is half of the circumference of the circle the displacement is the

diameter of a circle and its direction point from A to B or downward or South when a ball travels back to point a the

distance traveled from point A to return at Point a is equal to the circumference of a circle the display placement is

equal to zero this is because the ball has returned to its original position therefore we can deduce that

distance is the total length of the path traveled by an object distance is a scalar quantity which means that it has

only magnitude and no direction and its unit is meter the displacement is the directed distance from the start to the

end points displacement is a vector quantity which means that it has both magnitude and Direction and its unit is

meter speed and velocity speed is the distance moved per unit time speed is a scalar quantity

which has only magnitude its unit is me/ second the average speed is the total distance

moved to divide by total time velocity is a change in a displacement per unit time velocity is a vector quantity which

has both magnitude and direction in one-dimensional motion the sign positive or negative in front of the Velocity

indicates the direction of the object's motion the unit of velocity is the same as the unit of speed which is

m/s the magnitude of velocity is equal to speed when an object travels in a straight line and does not change its

direction a car travels with constant speed up and down the hill as shown while its speed remains constant its

velocity is not constant due to the changing direction of movement a car traveling at an initial speed of U for T

seconds reaches a final speed of v and covers a distance of s m and its acceleration is constant in a diagram

the average speed is U + V / 2 total distance moved is s total time is T therefore U Plus V / 2 = s / T If U

equals V this means a car is traveling with constant speed so the average speed is V total distance moved is s total

time is T therefore V equal s / T acceleration acceleration is change in

velocity per unit time acceleration is a vector quantity which has both magnitude and

Direction its unit is m/s squared therefore the equation of acceleration is a = vus u / t a is

acceleration in m/ second squared V is final velocity in m/s U is initial velocity in

m/s and T is time taken in seconds When U equals V it it indicates the car is traveling at a constant speed

the change in velocity is zero the acceleration is also zero when V is more than U it indicates the car is speeding

up this positive change in velocity is called acceleration when V is less than U it

indicates the car is slowing down this negative change in velocity is called deceleration if an object decelerates we

must put the negative sign into this equation and positive if it accelerates if a car moves the same

distance as 5 m every second this means that a car is traveling with constant speed of 5 m/s an acceleration is zero

if a car moves with increasing distance every second this means that a car is traveling with increasing speed and it

is accelerating if a car moves with decreasing distance every

second this means that a car is traveling with decreasing speed and it is

decelerating distance time graph the graph of distance Against Time as shown here we draw a right

triangle here is change in X and the x- AIS represents time here is change in y and the y- AIS represents distance the

gradient of graph is the ratio of the change in y- AIS to change in x-axis so it is the ratio of the change

in distance to change in time since the gradient of the graph is the speed of the object a horizontal line graph with

zero gradient indicates the speed is zero and no acceleration so the object is at rest a

straight line graph with constant gradient indicates the object is moving at a constant speed and no acceleration

a is steeper than b so a has a higher speed than b a curved graph with an increasing gradient indicates the object

is moving at increasing speed and it is accelerating a curved graph with a decreasing gradient indicates the object

is moving at decreasing speed and it is decelerating finding the speed and average speed using distance time graph

the distance time graph is shown here between a to B shows that the gradient is increasing so the speed is also

increasing and the object is accelerating between B to C shows that the gradient is constant so the speed is

also constant and the acceleration is zero we can find the constant speed by the gradient between B to C we draw a

right triangle here is change in X or run is equal to 20 - 7.5 is equal to

12.5 here is change in y or rise is equal to 45 - 10 is equal to 35 therefore the speed is equal to 35 /

by 12.5 is equal to 2.8 m/s between C to D shows that the gradient is decreasing so the speed is

also decreasing and the object is decelerating between D to e shows that the gradient is zero so the speed is

zero no acceleration and the object is at rest we can find the average speed between a to e by the total distance

divided by total time taken the total distance is 60 M the total time is 35 seconds therefore the average speed is

equal to 60 / 35 is equal to 1.71 m/s speed time graph the graph of speed Against Time as shown here we draw a

right triangle here is change in X and the x- AIS represents time here is change in y

and the y- AIS represents speed the gradient of speed time graph is the ratio of the change in y- AIS to the

change in x-axis so it is the ratio of change in speed to change in time the velocity is

speed in a given Direction their magnitudes are equal when an object travels in a straight line and does not

change its direction since the gradient of the graph is the acceleration of the object

the area under graph is the half of U + V * T this is the average speed since the area under graph is the

distance moved a horizontal line graph at the x-axis with zero gradient indicates the acceleration is zero and a

speed is zero so the object is at rest a horizontal line graph with zero gradient indicates the acceleration is zero and

the object is moving at constant speed of U since the distance moved is the area under graph which is U * t a

StraightLine graph with a positive constant gradient indicates the acceleration is constant and the OB

object is moving at increasing speed we can find the acceleration from V minus U / T and the distance moved is the area

under the graph which is half of sum of u and v * t a straight line graph with a negative constant gradient indicates the

deceleration is constant and the object is moving at decreasing speed we can find the acceleration from V minus u/ t

and the distance moved is the area under the graph which is half of sum of u and v * t a curved graph with an increasing

gradient indicates the acceleration increases and the object is moving at increasing speed a curved graph with a

decreasing gradient indicates the acceleration decreases and the object is moving at increasing

speed finding the acceleration and distance moved using speed time graph the speed time graph is shown here

between a to B shows that the gradient is increasing so the acceleration is also increasing and the speed

increases between B to C shows that the gradient is positive constant so the acceleration is also constant and the

speed increases we can find the constant acceleration by the gradient of graph we

draw a right triangle here is changing X or run is equal to 20 - 7.5 is equal to

12.5 here is change in y or rise is equal to 50 - 10 is equal to 40 since the acceleration is equal to 40 / 12.5

is equal to 3.2 m/s squared between C to D shows that the gradient is decreasing so the acceleration decreases and the

the speed increases between D to e shows that the gradient is zero so no acceleration and

the speed is constant at 60 m/s between e to F shows that the gradient is negative constant so the

deceleration is constant and the speed decreases we can find the constant deceleration by the gradient of graph we

draw a right triangle here is change in y or rise is equal to 0 - 60 = - 60 here is change in

X or run is equal to 45 - 32.5 is equal to 12.5 since the deceleration is equal to

-60 / 12.5 = -4.8 m/s SAR we can find the average speed by the total distance moved divide by total time taken

the total distance moved is equal to the area under graph the area under between a to B is approximately to area at here

so we combine area under graph between a to B with area under between C to d as a rectangle since the area of this

rectangle is equal to 60 * 7.5 is equal to 450 M area under graph between B to C forms a trapezium shape shape so it is

equal to 0.5 * sum of 10 and 50 and * 12.5 is equal to 375 M area under graph between D to e to F

form a trapezium shape so it is equal to 0.5 * sum of 5 and 17.5 * 60 is equal to 675

M the total area under graph is equal to 3 75 + 450 + 675 is equal to

1,500 the average speed is equal to 1500 / by 45 is equal to 33.3 m/s rounded to three significant

figures Free Fall is the motion of an object under the influence of gravity only if a feather and a bowling ball are

dropped at the same time from the same position in air the bowling ball will reach the ground first this happens

because air resistance has a greater effect on the feather due to its larger surface area if a feather and a bowling

ball are dropped at the same time from the same position in a vacuum they will reach the ground at same time and same

speed this is because air resistance has no effect on them this is called Free Fall that applies to all objects

regardless of their mass in a vacuum free fall describes the motion of an object under the influence of gravity

only we can conclude that there is no air resistance and only weight acting on the object the object accelerates

constantly towards the ground due to gravity this acceleration is typically denoted by the symbol G and has a value

of approximately 9.8 m/s squared when a ball is moving as free fall it's speed increases by 9.8 m/s

every second this is because its acceleration is approximately constant at 9.8 m/s squared a ball is dropped at

rest its initial speed is zero and its initial acceleration is 9.8 m/s squared after 1 second the ball has descended

and its speed increases from 0 to 9.8 m/s after 2 seconds the ball has descended a greater distance than it did

first second and its speed increases to 19.6 m/s after 3 seconds the ball has

descended a greater distance than it did between 1 and 2 seconds and its speed increases to 29.4

m/s after 4 seconds the ball has descended a greater distance than it did between 2 and 3 seconds and its speed at

4 seconds increases to 39.2 m/s the speed time graph of a free fall the speed of a ball increases 9.8 m/s every

second therefore we plot the graph with the following points Time 1 second speed is

9.8 time 2 seconds speed is 19.6 time 3 seconds speed is 29.4 Time 4 seconds speed is 39 two then

we draw a straight line from the origin the speed time graph shows that the gradient is constant which indicates

that speed increases with constant acceleration of 9.8 m/s squared we can find the distance moved of the ball from

the area under the graph distance moved between 0 and 1 second equals 0.5 * 1 te 9.8 is equal to 4.9 m

distance moved between 1 and 2 seconds equals 0.5 * sum of 9.8 and 19.6 and * 1 is equal to 14.7

M distance moved between 2 and 3 seconds equal 0.5 * sum of 19.6 and 29.4 and * 1 is equal to 24.5

M distance moved between 3 and 4 seconds equals 0.5 * sum of 29.4 and

39.2 and * 1 is equal to 34.3 M you see that the distance moved of a ball increases for 9.8 M every second

the distance time graph of a free fall we can plot the graph at 1 second the distance 4.9 M at 2 seconds the distance

is 14.7 + 4.9 is equal to 19.6 M at 3 seconds the distance is 19.6 + 24.5 is equal to 44.1 M at 4 seconds the

distance is 44.1 + 34.5 is equal to 78.4 M then we draw a best fit curve from the

distance time graph shows that the gradient is increasing which indicates that the speed is also increasing with

constant acceleration of 9.8 m/s [Music] squared candidates are expected to have

a thorough understanding of the cabus details outlined in the accompanying figure

mass and weight mass is a measure of the quantity of matter in an object it resists change in its state of motion

this is called inertia mass is a scalar quantity with only

magnitude its unit is kilogram mass is constant anywhere in the

universe weight is the gravitational force on an object that has mass due to the gravitational field strength it's in

weight is a vector quantity having both magnitude and Direction its unit is

Newton weight varies depending on the gravitational field strength which can change throughout the

Universe gravitational field strength is the force per unit Mass the equation of gravitational field strength is G equal

W / M where G is the gravitational field strength in Newton per kilogram it is equal to 9.8 Newton per kg at the

Earth's surface it is equivalent to the acceleration of Free Fall which is 9.8 m/s squared on the Earth's

surface gravitational field strength is a vector quantity that points towards the center of mass W is a gravitational

force or weight in Newton m is a mass in kilogram we can rewrite this equation to find weight as W equal m MTI G

gravitational field is a region in which a mass experiences a forc due to gravitational

attraction we can measure mass using an electric balance weight can be measured by a Newton meter or Force

meter weight is affected by the gravitational field strength on a mass so it will vary depending on the

location however mass is not affected by gravitational field strength and will remain constant regardless of

location when an astronaut is on Earth their mass is 75 Kg the gravitational field strength at

the earth's surface is 9.8 Newtons per kgam therefore his weight is 75 * 9.8 is equal to 735

Newtons when an astronaut is on the moon their Mass remains at 75 Kg however their weight is less than on

Earth by a factor of six this is because the gravitational field strength on the moon is 1.6 Newtons per kilg which is

six times less than on Earth therefore their weight is 75 * 1.6 is equal to 120 Newtons any planet or star have

different gravitational field strength which depends on its mass the gravit ational field strength of the Sun and

its planets are shown therefore gravitational field strength varies depending on the mass and size of each

planet the greater the mass of a planet the stronger its gravitational field strength

[Music] candidates are expected to have a thorough understanding of the syllabus

details outlined in the accompanying figure density density is defined as mass per

unit volume we can express density with the symbol row and the following equation row equals m / V where row is

density in kilog G per cubic meter or G per cubic cm m is mass in kilogram or gam V is

volume in cubic meters or cubic cm density is specific value for each material meaning that same material will

always have the same density for example let's say we know an unknown material with a mass of 2.41 kg and its volume of

125 cubic cm to determine which material our unknown material is made of we know the

densities of gold aluminum and silver as shown in the table convert the Mass from kilog to G first as 2.41 * 1,000 is

equal to 2,410 G so the density of unknown material

equals 2,410 g / by 125 cubic cm equal 9 19.3 G per cubic

cm therefore our unknown material is made of gold the density of an object can explain whether it will float or

sink in a liquid if the density of an object is more than the density of liquid the object will sink if the

density of an object is less than the density of the liquid the object will float for example a block of aluminum

will sink and settle to the bottom of a liquid this shows that aluminum's density is

more than liquid's density a block of ice will float at the surface of liquid but will be totally

submerged this shows that Ice's density is equal to the liquid's density a block of cork will float at the surface of a

liquid with some of it submerged this shows that Cork's density is less than liquid's

density experiment to investigate the density of a regular object one measure the mass of a regular object using an

electric balance or a Newton meter if a scale balance is used the reading will be the mass of the regular object if a

Newton meter is used the reading will be the weight of the regular object then dividing it by 9.8 to get its mass two

find the volume of a regular object by measuring its dimensions and calculating the volume using the formula

for example a cube measure the length of each side with a ruler calculate its volume using V equal side cubed a cuboid

measure the length width and height with a ruler calculate its volume using V equals length time width time height a

cylinder measure the height with a ruler measure its diameter using a ruler and wooden blocks as shown view the top and

measure the distance between blocks at different positions to check for consistency calculate the radius of the

cylinder by dividing the diameter by 2 calculate the volume of cylinder using V = < r^ 2 h a sphere measure the radius

using the same method as for the cylinder calculate the volume of the sphere using V = 4 over 3 pi R cubed we

should measure each length at different positions and find the average to get an accurate value view the scale at a

perpendicular angle to avoid Parallax error three we can calculate the density of each object using roll equals m /

V experiment to investigate the density of an irregular object that sinks in water such as a stone one we measure the

mass of a stone using an electric balance or a Newton meter as shown two two we measure the volume of a stone

using a measuring cylinder as follows fill the measuring cylinder with water read the initial volume V1 by viewing

the scale at perpendicular angle at the bottom of the meniscus as shown carefully place the stone into the water

the water level rise as shown read the final volume V2 by viewing the scale at a perpendicular angle at the bottom of

the meniscus the volume of the stone is the final volume V2 minus the initial volume

V1 three we can calculate the density of a stone using roll equals m / V how to determine the volume of a piece

of wood that floats in the water such as a cork fill a measuring cylinder with water tie a thread to a stone and place

it into the water read the initial value V1 by viewing the scale at a perpendicular angle at the bottom of the

meniscus as shown remove the Stone from the measuring cylinder by lifting it up by the thread tie the cork to the end of

the thread lower the Cork and stone into the measuring cylinder read the final volume V2 by viewing the scale at a

perpendicular angle at the bottom of the meniscus as shown the volume of the cork is the final volume V2 minus the initial

volume [Music] V1 candidates are expected to have a

thorough understanding of the syllabus details outlined in the accompanying figure

forces force is a vector quantity that has both magnitude and Direction its unit is the

Newtons effects of the forces on object when forces act on an object they can cause the object to change in shape

direction of moving speed forces can be categorized into two main types contact forces and

non-c contct forces a contact force is a force that acts between two objects that are physically touching each other when

two objects Collide or come into contact they exert a force on each other this force can cause a change in motion

direction or shape of the objects when your hand pushes the Box a contact force propels the Box forward this is called

the pushing force normal reaction force is the perpendicular force that act on an object when it is in contact with a

surface when you place a box on a table the table exerts an upward Force normal force to hold the book Against Gravity

tension is the force in a string spring rubber band or wire when it is stretched or compressed when you pull a box with a

rope to create tension in the Rope this tension is the pulling Force transmitted through the length of the Rope friction

is the force that opposes the relative motion between two surfaces in contact when you push a box or pulling a box

along the floor with a rope friction acts in the opposite direction of your applied force air or liquid resistance

also known as drag force is a resistive force that acts on an object moving through air or liquid up thrust force or

buoyancy force is the upward force that acts on an object that is partially or fully submerged in a fluid

a non-con force is a force that acts between two objects that are not physically touching non-con forces act

through a field which is an invisible region of space that surrounds an object and exerts a force on other objects

within that field the gravitational force or weight due to the gravitational field strength of Earth its direction is

always downward Earth's gravity pulls objects towards its Center even without touching them we can calculate the

weight of the object using the equation W equals mg where W is weight in Newtons m is mass in kilogram and G is

gravitational field strength in Newtons per kilogram electrostatic force is the force between the charged objects

charged objects attract or repel each other depending on their charges and distance between them like charges repel

unlike charges attract magnetic force is the force between the

magnets magnets attract or repel each other without physical contact like poles repel unlike poles

attract when a car is moving to the right as shown there are the forces acting on a car

including the weight acts downward the total normal reaction force is acting Upward at its Wheels the force from the

engine acting forward the air resistance acting backward when a box is at rest on a rough incline as shown there are the

forces acting on a box including the weight acts downward the normal reaction force acts upward

perpendicular to the slope the friction acts upward parallel to the slope when we pull a box with a rope along the

incline causing the box to move up the incline there are forces acting on the box

including the tension acts up along the slope the friction acts downward parallel to the slope because the box is

moving up the slope the weight acts downward the normal reaction force acts upward perpendicular to the slope when a

box floats on the water there are forces acting on the box including the weight acts downward the

up thrust acts upward when a metal sphere is moving downward through the water there are forces

acting on the metal including the weight acts downward the up thrust acts upward the water

resistance acts upward resultant Force the resultant force or net force is the single force

that has the same effect as all the other forces acting on an object combined if the the resultant force is

zero it is called balance force if the resultant force is not zero it is called unbalance Force we can find the

resultant force that acting on the object for example a box a has forces acting on it as shown the forces on the

left and right sides of the Box are balanced this means the net force acting on the box in the horizontal direction

is zero in the vertical Direction the resultant force can be found by subtracting the downward Force 22

Newtons from the upward Force 14 Newtons so a resultant force is 8 Newtons acting downwards a box B has the

forces acting on it as shown the resultant force can be determined by adding the two forces acting to the

right 300 Newtons and 60 newtons so a resultant force is 360 Newtons AC to the right a box C has the

forces acting on it as shown the resultant force can be found by adding the two rightward forces 2 Newtons and

four Newtons and subtracting the leftward force five Newtons so a resultant force is one

newton acting to the right a box D has the forces acting on it as shown the resultant force can be found by

subtracting the leftward force of 70 Newtons and the leftward force 30 and 20 newtons so a resultant force is 20

newtons acting to the left calculate the magnitude and direction of the resultant force of two

forces acting at right angle as shown first method calculate using trigonometry join the tail of 10 Newton

and 8 Newton forces at right angle draw a parallelogram with 10 Newtons and 8 Newtons as side

which form to the rectangular the resultant force is the diagonal of the

parallelogram we can calculate the magnitude of the resultant Force using the Pythagorean

theorem resultant force equal 10^2 + 8^2 = 12.8 Newtons we can calculate the direction

of the resultant Force by the tangent ratio the direction of the resultant force is the angle Theta to 10 Newtons

for so the direction of the resultant velocity is tan power - 1 8 / 10 is

equal to 39° to 10 Newton Force second method find the resultant Force using the graphical diagram set

the scale 1 cm to 2 Newtons parallelogram diagram draw the force of 10 Newtons for 5

cm measure angle at the tail of the 10 Newtons Force using a protractor as 90° link the tail of the 8 Newton Force

to the tail of the 10 Newton Force draw a force of 8 Newtons for 4 cm draw a parallelogram with 10 Newtons

and 8 Newtons are sides which form to the rectangular the resultant force is the

diagonal of the parallelogram measure the length of the resultant Force so magnitude of the

resultant force is 6 .4 CM * 2 Newtons = 12.8 Newtons measure the angle between the 10

Newtons Force resultant Force so the direction of the resultant velocity is 39° to 10 Newtons Force

triangular diagram draw the force of 10 Newtons for 5 cm measure angle at the head of the 10

Newtons Force using a protractor as 90° link the tail of the 8 Newtons Force to the head of the 10 Newtons Force draw

a force of 8 Newtons for 4 cm the resultant force is formed by connecting the tail of the 10 Newtons

Force to the head of the 8 Newtons Force measure the length of the resultant Force so magnitude of the resultant

force is 6.4 CM * 2 new equal 12.8 Newtons measure the angle between the 10 Newtons for Force resultant

Force so the direction of the resultant force is 39° to 10 Newton Force the three laws of motion also

known as Newton's Laws of Motion Newton's first law of motion the forces on an object are all balanced then it

will just stay still or else it is already moving it will just carry on at the constant velocity when a car is at

rest then the force on it must be balanced so car's weight acts downward to equal the total normal forces acting

upward when you pushes a car with a force 500 Newtons to the right and a car stay still this causes the total

friction between the tires and the road's surface to act to the left 500 Newtons for balancing with the pushing

force when a car is moving with constant velocity then the forces on it must be balanced so car's weight acts downward

to equal the total normal forces acting upward the force from engine 2500 Newtons acting forward is balanced

with the fair resistance 2,500 Newtons acting backward when a ball is falling down with constant velocity then the

forces on it must be balanced the downward weight 10 Newtons is balanced with the total upward up thrust 1 Newton

and a resistance 9 Newtons since we can conclude that when no resultant force or balanced force the

object is stationary or moving with constant velocity and its acceleration is

zero Newton's second law of motion if there is a resultant Force unbalanced force then the object will accelerate in

that direction this acceleration can be done by changing the object's velocity

the change in velocity caus the object to start speeding up slowing down stop and changing direction if a resultant

Force acts on an object at rest the object will accelerate starting to move increasing its speed if a resultant

Force acts on an object in the opposite direction of its motion the object will decelerate eventually coming to a stop

if a resultant Force acts on an object in the same direction of its motion the object will accelerate further

increasing its speed if a resultant Force acts on an object at a perpendicular angle to its direction of

motion the object will change direction while its speed Remains the Same the acceleration of an object is directly

proportional to the resultant Force the bigger the force the greater the acceleration the acceleration is

inversely proportion to mass of the object the bigger the mass the smaller the

acceleration this can be expressed mathematically as F equal m a where f is the resultant force in

Newtons m is the mass in kilogram a is the acceleration in m/s squared for example find the resultant

force and acceleration of the box with magnitude and Direction like as shown the resultant force is the subtracting

the leftward force 15 Newtons with the rightward forces 4 Newtons and 2 Newtons resulting 9 Newtons to the left

calculate the acceleration using f = m a substitute F = 9 Newtons Mass = 2 kg then a = 9 / 2 is equal to 4.5 m/s

squar to the left Newton's third law of motion when when object a exerts a force on object B

then object B exerts an equal an opposite force on object a a pair of forces must be equal in magnitude

opposite in direction and act on different objects for example a book lying on a table exerts a downward force

on the table this is the action force the table also exerts an equal and opposite force on the book in the upward

Direction This is the reaction Force the Earth exerts a downward force on the book this is the action force the

book also exerts an equal and opposite force on the earth in the upward Direction This is the reaction force

while moving on the ground we push the ground backward with our feet this is the action force the ground also exerts

a forward force on our feet of equal magnitude in the opposite direction which makes us move forward this is the

reaction force a man's hand exerts a force on the wall this is the action force the wall also exerts an equal an

opposite force on a man's hand in the backward Force this is the reaction force a

rocket exerts a downward force on the burnt gases this is the action

force the burnt gases also exerts an equal and opposite force on the rocket in an upward

Direction This is the reaction force friction friction is a force that

opposes the movement of an object it acts in the direction opposite to the motion friction is present almost

everywhere and it can slow down or even stop moving objects this happens because friction

converts kinetic energy into thermal energy if there's no Force propelling an object object forward friction will

eventually slow it down to a complete stop this is true on Earth but in a frictionless environment like outer

space objects can continue moving indefinitely to maintain a constant speed an object needs a continuous

driving force to overcome friction there are three main types of friction static

friction this occurs between two Solid Surfaces that are at rest and not moving relative to each other it prevents an

object from slipping static friction is usually the greatest Force you need to overcome to get an object moving kinetic

friction sliding friction this occurs between two Solid Surfaces that are sliding past each other it is the force

you feel when you rub your hands together or slide a box across the floor kinetic friction is usually slightly

less than static friction you you can reduce both static and kinetic friction by using lubricants like oil or grease

between the surfaces fluid friction also known as drag this is the resistance an object experiences when moving through a

fluid liquid or gas there are two main factors affecting fluid friction the surface area of the object

in contact with the fluid increases drag also increases streamlined shapes like those

of race cars or boat hulls experience less drag this is because they deflect the fluid more smoothly resulting in

less resistance to the object's movement the object's speed increases drag also increases terminal velocity is the

maximum speed an object reaches when moving through a fluid liquid or gas due to the balance forces no resultant Force

when an object is moving through a fluid there is a drag force due to the fluid this drag force can increase when the

speed of the object increases and the surface area of the object increases right now we will use the

symbol of Sigma F to represent the resultant Force consider the terminal velocity of a

skydiver when a skydiver jumps out of airplane they are initially at rest drag force is zero because their speed is

zero only weight acts on them downward so the resultant force is equal to their weight since their initial acceleration

is 9.8 m/s squared this cause their speed to increase is from zero and the drag Force also

increases as time passes drag Force acts upward to increase as speed increases the resultant force is equal

to their weight minus drag Force which acts down downward to decrease this causes their acceleration

also decreases as drag Force increases until it equals their weight this causes the

resultant force is zero since their acceleration also is zero this causes their speed is constant this is called

terminal velocity when a parachute is opened the large surface area increases the drag Force to act upward this causes

the resultant force to be drag Force minus their weight which acts upward since the acceleration is also upwards

so the sky diver decelerates and their speed decreases as time is passes the drag

Force acts upward to decrease as speed decreases since the resultant Force acts upward to decrease and their

deceleration also decreases as the drag Force decreases until it equals their weight so the

resultant Force is zero this causes their acceleration is also zero and their speed is constant again this speed

is called terminal velocity the speed time graph of the skydiver's motion is shown on the screen

we known that the gradient of speed time graph is the acceleration at Point a initial speed is

zero and initial gradient is 9.8 this is because the initial acceleration is 9.8 m/s squared between points A and B the

gradient decreases this means that the acceleration also decreases while the speed still

increases between B and C the speed is constant and this speed is called terminal velocity the gradient of graph

is zero this means that the acceleration is also zero at Point C the parachute is opened large surface area of the

parachute causing large drag Force this causes the speed to decreases rapidly between C and D the speed

decreases the gradient is negative so the parachutist decelerates the steepness of the

gradient decreases so the deceleration also decreases between d and e the speed is

constant which is terminal velocity the gradient is zero this means that the acceleration is also zero the

parachutist reaches is the ground at Point e the speed time graph showing the

difference between free fall and terminal velocity of a ball when a ball falls through a vacuum there is no air

resistance acting on it this is called Free Fall the speed time graph of this scenario is a straight line passing

through the origin the constant gradient represents the ball's constant acceleration due to gravity which is

around 9 .8 m/s squared this is because only force acting on the ball is its weight acting downwards so the resultant

force is the weight when a ball falls through air there is air resistance acting on it the speed time graph of

this scenario is a curve with a decreasing gradient that eventually becomes

horizontal the initial gradient is around 9.8 m/s squared represents the ball's acceleration due to gravity

this is because at the beginning the only force acting on the ball is its weight acting downwards making the

weight the initial resultant force over time the decreasing gradient of the graph shows that the acceleration

of the ball decreases this is because as the ball Falls faster air resistance also

increases this air resistance acts in the upward Direction opposing the weight so the resultant force is the weight

minus the air resistance becomes smaller as air resistance increases when the gradient reaches zero

it indicates that the acceleration is also zero this causes the speed of the ball is constant and reaches its

terminal velocity at terminal velocity the air resistance acting upwards is equal to the weight acting

downwards since the resultant force is zero a ball falling through air will take longer and reach the ground at a

slower speed compared to a ball falling through a vacuum from the same height deformation of

material investigate how extension varies with applied force for helical Springs set up the apparatus as shown

measure the original length of the unstretched spring using a ruler hang a Load One North on the spring and then

measure the length of the spring calculate the extension by subtracting the length from from the original length

repeat the experiment for addition loads of 2 Newtons 3 Newtons 4 Newtons 5 Newtons and 6

Newtons record the results of the length of the spring and its extension in the table plot the graph of the load in

Newtons against the extension in centimeters as shown we can conclude the results from the graph as follows here

the result is a straight line graph passing through the origin of the axis this shows that the spring obeys hooks

law hooks law states the extension of the spring string or wire is directly proportional to the force or load in

this region the spring is not OB Bays hooks law at this point is called the limit of proportionality it is the point

where the spring stops obeying hooks law and starts to stretch more for each increase in the load

Force at this point is called the elastic limit if the spring is stretched Beyond its elastic limit it will not

return to its original length when the weights are removed investigate how extension varies

with applied force for elastic bands we set up the apparatus as shown to investigate how an elastic band

stretches under load if you stretch an elastic band with increasing load forces we get a graph of load against extension

like as shown the graph is not a straight line showing that elastic bands do not obey

hooks law if the graph of load against extension of material when it loaded and unloaded like as shown this shows that

this material stretches elastically this is called elastic deformation this means that a wire

spring or rubber band that stretches elastically will return to its original length once the stretching force is

removed if the graph of load against extension of material when it loaded and unloaded like as shown this shows that

this material stretches plastically this is called plastic deformation this means that a wire

spring or rubber band that stretches plastically will not return to its original length once the stretching

force is removed circular motion when a resultant force or Sigma F acts on a ball in

perpendicular angle to the direction of motion this causes the direction of motion to change but the speed remains

constant if this resultant Force acts on a ball continuously this causes the ball to move in a circular path as shown on

the screen we can conclude the following about Circle motion there is the resultant Force known as the centripedal

force it acts on an object at a right angle to the direction of motion this Force always acts towards

the center of the circle this resultant Force changes the direction of the object's motion at any

point in the circular path while the object's speed remains constant this continuous change in direction is what

keeps the object in the circular path this resultant force causes an acceleration that is directed towards

the center of the circle this acceleration is called the centripedal acceleration if this resultant Force

absent the object will escape from the circular path along a tangent line at the point where it leaves the circle the

resultant force or centripedal force is increased as the speed of an object increases the mass of an object

increases the radius of the circular path decreases vertical circular motion of a

ball that attaches to a string the resultant Force also known as the centripedal force is provided by the

tension in the string and the component of weight if the speed of the ball increases the resultant Force needs to

increase as well to keep the ball moving in a circular path this increase in speed also causes the tension in the

string to increase if the tension increases until it can no longer support the resultant

Force the string breaks the ball then escapes from the circular path along a tangent line at the point of breakage if

the string breaks at Point a this causes the object escapes from the circular path along the tangent line at the point

a and then it is pulled downward from the weight to the ground this cause the traveling path is curve as shown if the

string breaks at point B this cause the object escapes from the circular path along the tangent line at the point a

and then it is pulled downward from the weight to the ground this cause the traveling path is curve as shown if the

string breaks at Point C this caused the object escape from the circular path as shown horizontal circular motion

horizontal circular motion of a ball that is attached to a string the resultant force or centripetal force is

provided by the tension in the string if the speed increases the resultant force and tension increase with mass and

radius remain constant if the radius decreases the resultant force and tension increase with mass and speed

remain constant if the mass increases the resultant force and tension increase with speed and radius remain constant a

car is moving on a circular Road the resultant force or centripetal force is provided by the sideways friction

between the surface of the car's tires and the road if the speed of a car increases the resultant Force increases

which causes is the sideways friction between the surface of the car tires and the road to

increases if the sideways friction is not enough to support the resultant Force this caused the car to escape from

the circular Road the moon orbits the earth in a circular path the resultant force is provided by the gravitational

force between the Moon and the Earth [Music] [Music]

candidates are expected to have a thorough understanding of the syllabus details outlined in the accompanying

figure turning effect of forces is a measure of the moment forces when forces act around a fixed

Point called a pivot they have turned burning effects called moments we use these effects all the time in everyday

life for some everyday examples as a spanner or wrench uses to loosen a nut you apply a force that creates an

anticlockwise moment helping you turn the nut a claw hammer uses to remove a nail the force applied on the handle to

create the moment of force a scissors work by applying two opposing forces that create a moment causing the blade

to come together and cut through material a cail pivots on a central point and the moment created by children

sitting on either end determines its clockwise or anticlockwise movement a lever is tools that utilize the concept

of moment of force to amplify the applied force making it easier to lift or move heavy objects a door is opened

by pushing or pulling on a door knob you create a moment of force that causes the door to rotate on its hinges a

wheelbarrow distributes the weight of a heavy object allowing you to apply a smaller Force at the handles to move it

with a larger moment steering wheels of a car is turned to create a moment that alters the direction of the wheels

ultimately controlling the car's Direction moment of forces is defined as the product of force and perpendicular

distance between line of action and pivot we can write the equation as m equals

FD where m is the moment of force in Newton meter f is force in Newtons D is perpendicular distance from

pivot in meters for first example A4 Newton's Force acts on the light beam at a perpendicular distance of 3 m from the

pivot this causes the clockwise moment to be three * 4 is equal to 12 Newt M about the

pivot second example A3 Newton's Force acts on the light beam at a perpendicular distance of 2 m from the

pivot this causes the anticlockwise moment to be 3 * 2 is equal to 6 Newton M about the

pivot third example A4 Newton's Force acts at the end of beam along pivot as shown this causes the moment is zero due

to the force acting along the pivot causing perpendicular distance from pivot to be zero fourth example

A5 Newton Force acts at the end of beam and 2 m perpendicular distance between line of action and pivot this causes the

anticlockwise moment to be 5 * 2 is equal to 10 Newt M about the pivot fifth example a diagram shows the

forces acting on a light beam and distance of each force from point P calculate the sum or resultant moment

about P clockwise moment about P causes by forces 3 Newtons 1 M from p and 4 Newtons 3 m from P so total clockwise

moment equal 4 * 3 + 3 * 1 is equal to 15 Newtons M anticlockwise moment about P causes by only 2 Newtons 1 M from P so

anticlockwise moment equals 2 * 1 is equal to 2 Newtons M you see that larger total clockwise moment than anti

clockwise moment so the resultant moment equal 15 - 2 is equal to 13 Newtons m in clockwise the principle of moment states

that if an object is in equilibrium the total of clockwise moment is equal to the total anticlockwise moment about the

pivot the conditions for equilibrium of an object are there is no resultant force acting on the object there is no

resultant moment acting on the object this is the principle of moment for example someone is trying to balance a

plank with particles A and B the plank has negligible weight calculate the moment of the forces about Point O and

determine if the plank will balance if not calculate the force acting on the plank at P calculate the moment of 4

Newtons Force about Point O which is 4 * 4 is equal to 16 Newt m in clockwise calculate the moment of 6

Newtons Force about Point O which is 2 * 6 is equal to 12 Newt m in anticlockwise since the clockwise moment

is greater than the anticlockwise moment the plank will rotate clockwise resultant moment equal 16 - 12

is equal to 4 Newtons M to balance the plank we need to add an additional downward Force at Point P that will

create anticlock wise moment of 4 Newton M perpendicular distance between point P to Pivot o is 4

M so Force F = 4 / 4 is equal to 1 Newton therefore the plank will balance if a force of 1 Newton is applied

downward at Point p [Music] [Music]

candidates are expected to have a thorough understanding of the syllabus details outlined in the accompanying

figure center of gravity the center of gravity is sometimes called the center of mass it is the point where the whole

of the weight of the object appears to act the weight of all object Acts through the center of

gravity for example the center of gravity of the human is about here the center of gravity of an apple is about

here the center of gravity of a magnet is here a uniform object's center of gravity is at the middle of the object

for example a uniform cylinder has its center of gravity at here a uniform sphere has its center of gravity at the

center a uniform Cube has its center of gravity at here a uniform wooden meter rule has

its center of gravity at the 50 cm Mark the object will always balance around its center of gravity for example the

wooden meter rule is balancing on the pivot at the 50 cm Mark like as shown you can try balancing a pencil on your

finger like as shown the people is walking on the Rope like as shows an object will be nice and stable

if it has low center of gravity and wide base area for example a conical frustum placed with its wider base on the ground

is more stable than when flipped upside down in the first case the center of gravity is lower and the base area is

wider so more stability the second case the center of gravity is higher and the base area is smaller so less stability a

racing car has a lower and wider base area than the family car so the racing car is more stable an object will topple

over if a vertical line drawn downward from its center of gravity falls outside its base area as shown for example a bus

on an incline Road will stay on the incline as long as the vertical line from the center of gravity falls on its

base however if the slope increases until the vertical line Falls outside its base area the bus will topple

over experiment to investigate the center of gravity of an irregular lamina hang up the lamina as shown suspend a

plum line from the same plane Mark the position of the thread as shown the center of gravity is along the line of

the thread repeat the experiment with the lamina suspended from the different places the center of gravity is where

these line cross someone of weight 500 Newtons is standing on a uniform plank 6 M long and

weighing 250 Newtons the plank is supported by two trestles as shown calculate that the

upward forces X and Y exerted by the trestles on the plank the plank is uniform so the center of gravity is the

middle of the plank equals 2.5 m from Trestle y the plank is equilibrium because it is at rest and not turning so

the principle of moments can be applied finding X let's take Trestle y as the pivot the total clockwise moment

about y equals the total anticlockwise moment about y total clockwise moment 5 * X and equal to Total anticlockwise

moment 500 * 3 + 250 * 2.5 we will get 5x = 2,125 so x = 425

Newtons finding Y using total upward force on the plank equals total downward force on the plank because no resultant

Force acts on the plank total upward force is 425+ y equal total downward force is 500

+ 250 so y equal 325 Newtons a diagram shows an arm with the

hand holding a weight of 120 Newtons the 20 newtons force is the weight of the forearm acting at the

center of gravity f is the force in the muscle of the upper arm p is the point in the elbow about which the arm pivots

the distances of the forces from point P are shown by taking moments about Point P calculate the force f a diagram shows

an arm is equilibrium or balance so total clockwise moment equals total anticlockwise moment total clockwise

moment causes by 20 newtons Force 15 cm from p and 120 Newtons Force 33 cm from P so total clockwise moment is 20 * 15 +

20 * 33 is equal to 4,260 Newt M total anticlockwise moment is force f * 2 therefore Force f is

4,260 / 2 is equal to 2,130 newtons a force acts on the forearm at

Point P calculate this force and state its direction we can apply the total upward acting on arm equals total