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Physics 101

Achievement Standard AS90183

Demonstrate understanding of mechanics in one dimension

5 Credits

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Significant figures

Significant figures are important in physics and we need to understand what role 0 plays in this.Consider the following:210002400.00045all these have the same number of sig figs: 2

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When zero is not a place holder then it becomes significant

e.g. 23.00

0.330

22045

4 sig figs3 sig figs

5 sig figs

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Rounding

When rounding we need to be able to consider what is important and note when the zero is important or not:

try these

25.34 round to 2 sf

65.68 round to 3 sf

0.4997 round to 3 sf

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If we have to find a solution based on some rounded figures, then this will affect our final answer. Consider:

The answer can be no more accurate than the input data, thus 2 sf is the best we can do, giving 5.8

5.76923082.60

15

2 sf

3 sf

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Motion

The motion of an object, such as a runner or a car, is described using quantities like the distance covered, the time taken, speed reached and the acceleration required to achieve such a speed.

To define time and distance we generally use two well known and universal units.

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Motion

• The Second (s), this is the S.I. unit for time.Time is given the symbol t in formulas.

• The Metre (m), this is the S.I. unit for distance. Distance is given the symbol d in formulas

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Other units for distance include

Km, mm, µm

Other units for time include Min, hours

and days

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Motion

When we look at distance travelled in a given time we are investigating the speed of something.

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Motion

We may further qualify speedAverage speed:

This is the speed calculated over a defined distance.Instantaneous speed:

This is the speed at a particular point during a journey and can be described as the actual speed at a particular point in time.When the speed during a journey does not change then it can be described as a steady, uniform or constant speed.

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Motion

By the very definition of speed as distance covered in a given period of time we define the formula for speed as:

average speed = distance travelled

time taken to travel distance vav

d

t

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Motion

The units used to measure speed are related to the way in which the speed value is calculated. For example if we measure the distance in kilometres (km) and time in hours (h) then speed will be defined in km per hour. Often in physics and science since we measure in metres and seconds, speed is quoted in metres per second.

We write these units in a particular way:• km per hour = kmh -1

• metres per second = ms-1

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Motion

Examples:

Determine the average speed of a car traveling 128km between 2:15 pm and 4:15 pm one day.

Distance = 128 km

Time = 2 h

speed = distance

time

128km

2h64kmh 1

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Motion

Example:Determine the average speed of a bike wheeling down a slope of length of 525m in 25 s.Distance = 525 mTime = 25 s

speed = distance

time

525m

25s21ms 1

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Vectors

• In physics we often deal with specific vector values.

• Vectors have a size and a direction

• We consider initially two vectors:– Displacement (distance travelled

in a specific direction)

– Velocity (speed in a specific direction)

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To calculate displacement we just need to pay attention to the distance travelled and the direction. Opposite directions have negative effects

To calculate velocity we divide the displacement achieved during a period of time, by the time taken. The maths is the same as for speed.

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Distance Time (dt) graphs

Distance time graphs display information regarding the distance movement of an object over a period of time. The gradient (slope) of the line of the graph describes the speed of the object.

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The slope of any graph is determined as:

On a distance time graph, this becomes:

gradient change in y - axis

change in x - axis

Δt

Δd

in time change

distancein changegradient

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Time (s)

Dis

tanc

e (m

)

Time (s)

Dis

tanc

e (m

)

Time (s)

Dis

tanc

e (m

)

Object stationary, distance does not change over time

Object has a constant speed

Object has a constant

speed, faster than previous

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When a d-t graph does not have a straight line then the object concerned is changing speed.

Time (s)

Dis

tanc

e (m

)

Time (s)

Dis

tanc

e (m

)Speeding upaccelerating

Slowing downdecelerating

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Speed time graphs

Speed time graphs are used to give a more detailed and an accurate picture of the changing speeds of an object during a journeyThe gradient (or slope) of the line of the graph gives the acceleration of the object.

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Time (s)

Spp

ed (

ms-1

)

Time (s)

Spp

ed (

ms-1

)

Time (s)

Spp

ed (

ms-1

)

Constant speed Change speedAccelerating

Changing speedDeceleration

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Area under S-T Graph

We can determine the distance travelled by an object from the area under a speed time graph.Divide the area of the graph up into easily calculated areas (e.g. rectangles and triangles)Find the area of each subdivision and then sum all the areas together

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Area under S-T Graph

• Example: Find areas of sections A, B and C

Time (s)

Sp

ped

(m

s-1)

0

2

4

6

0 5 10 15 20

A B C

A B C

15 30 30

75m

A = 12 (5 6)

B = 5 6

C = 12 (10 6)

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Acceleration

• Acceleration is the rate of change of speed of an object.

• For example if the acceleration of an object is stated as 2 ms-2, then its speed is increasing by 2ms-1 every second.

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The formula to determine acceleration is defined by:

Where v1 is the starting speed and v2 the finishing speed

t1 is the start time and t2 the finish time

If the value for acceleration is negative then the object is slowing down or decelerating

achange in speed

time taken for that change

Vt

v2 v1

t2 t1

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Examples:1. Find the acceleration of a car starting from rest

at zero seconds and reaching a speed of 15ms-1 after 5 seconds.

V1=0, v2=15, t1=0, t2=5

a

av2 v1

t2 t1

vt

15 0

5 0

15

53ms 2

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• Examples:1. Find the acceleration of a skier going downhill. They

start at 7ms-1 and increase their speed to 13ms-1

between 28s and 31s after starting down the slopes.

V1=7, v2=13, t1=28, t2=31

a

av2 v1

t2 t1

vt

13 7

31 28

6

32ms 2

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Force Diagrams

We can represent the forces being applied to an object using what is called a force diagram. Arrows are used to represent the direction of a force and a value is written.

Forces in opposing directions subtract from each other

Force at right angles do not affect each other.

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Force Diagram Example

Applied force represented with an arrow pointing in the direction of the force.We identify the value with a number of Newtons (N).Equal forces from opposite directions are said to be balanced forces.

40 N600 N 40 N600 N2000 N 2500 N

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Illustrations

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5000N 5000N

400N400N

Balanced forces

• When the two forces applying in opposite directions are equal in size we say that the forces are balanced.

• If we consider the situation below, what will be the resulting motion of the object?

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Newton’s laws

• We can state that

“an object will remain stationary or move at a steady speed in a straight line unless

acted on by an unbalanced force”

• This is known as Newton’s 1st law of motion.

• We have already met his 2nd law, f=ma.

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Exploding trolley experiments

1. Place the trolley so that the plunger is facing into open space. Trigger the plunger and observe what happens.

2. Now place the trolley so that the plunger will strike a solid object, such as a wall. Trigger the plunger and observe what happens this time

3. Now place two trolleys so that the plunger will strike one of the trolleys while both trolley are free to move. Trigger the plunger and observe what happens this time.

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700N500N

Mass of car 275Kg

Direction of forces

• Forces are applied in a direction and can result in movement of an object.

• The direction of that movement will be in the direction of the resulting force

• Thus find the resulting force value direction and associated acceleration for the diagram below.

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Newton’s laws

Newton’s third law states:

“for every action force there is an equal and opposite

reaction force”

This means that when we apply a force against something, like pushing against a wall then the wall pushes back against us.

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Identify the action and reaction forces in the following

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Pressure?

What is pressure?

The application of a force over a specific area. If the area is very small then the pressure will be very large.

The formula to connect these is:

Where P= pressure, F=force (N) and A=area (m2)

A

FP

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• Consider an elephant weighs a lot, but has a large foot pad. The force of its weight is spread out and the animal can stand easily on its feet all day.

• A lady sometimes wears a stiletto heel shoe. Her weight will be significantly less than an elephant, but over the small area of the stiletto heel the pressure will be enormous.

• Moral your foot will hurt if stood on by an elephant, but a stiletto will pierce your foot

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example

What is the pressure experienced by a 15 Kg sledgehammer resting on the top of a tent peg size 2 cm x 1 cm.

P=F/A, F = 15x 10 = 150 NA = 0.02 x 0.01 =0.0002m2

P = 150/0.0002 = 750000 Nm-2 ( or Pa)

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The pressure of the atmosphere around us is 100 000 Pa. How many Kg of atmosphere must be pressing down on each square metre of Earth?P=F/A, F=P.A= 100000Pa .1 m2

F= 100 000 N, F=mg, thus m = F/g = 100 000/10 = 10 000 kg(10 tonne)

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Gravitational force

Gravity is a non–contact force that exists between two objects with a mass. The mass of the Earth is so big we state that an object is attracted to the Earth.An object with a big mass is attracted to the Earth by a bigger force. Thus weightlifters get a higher score for lifting a greater mass above their heads, it is more difficult.

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Mass and Weight

Mass describes the amount of matter in an object and is measured in Kilograms (kg)

Weight is a measure of the force due to gravity acting on an object.

We define:

W= m x g

W=weight (N)

m = mass (kg)

g= gravitational pull in N/Kg

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Weight on different places

On Earth the g= 10 N/kg, thus the weight of any object is 10 times the mass.

Different planets have gravitational pulls.

On Mars, Venus and the Moon it is less, on Jupiter, Saturn and the Sun it is greater.

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Weight on different places

Location GN/kg

Object mass (kg)

Object weight (N)

Earth 10.0 33.45

Moon 1.6 16

Mars 3.8 22

Saturn 26.0 5

Sun 275 0.02

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Weight on different places

Location GN/kg

Object mass (kg)

Object weight (N)

Earth 10.0 33.45 334.5

Moon 1.6 16 25.6

Mars 3.8 22 83.6

Saturn 26.0 5 130

Sun 275 0.02 5.5

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Force and distance

When a force is applied to an item we do work. Depending on how far the item is push and by what amount of force will determine the amount of work done.We summarise this by the following equation:

W= f dWhere W = work done in Joules (J) f = force applied in Newtons (N)d = distance travelled in metre (m)

W

f d

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Examples

1. How much work is done when pulling a 25 Kg bag of scoria stones with 200N 15m.W=fxd, f= 200N, d=15mW=200 x 15 =3000J

2. A 100Kg car is pushed by a force of 145N, find: a) the acceleration of the carf=ma, f=145N, m=100kg145=100.a, a=145/100=1.45 ms-2

b) The work done to move the car 0.5 kmW=fd, f =145N, d=500mW=145 x 500 = 72500J

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Watt is Power

Power is a measure of how much work is done in a given period of time.As usual time is measured in seconds and work in Joules.Thus power is defined as the number of joules used per second.P = W/tThe unit for power is the Watt (W) after James Watt and his work on the steam engine in 1770’s. Now do: Page 27 of blue book

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Potential energy

There are various types of potential energy and we have discussed these previously:

• Elastic

• Chemical

• Nuclear

• Gravitational

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Gravitational potential energy is defined by:• The height (h) of something above the ground in

metres• The mass (m) of something above the ground in

kg• The strength of gravity (g) at that point in space

in Nkg-1

This gives the formula Epg = mghg on Earth is 10 Nkg-1

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Kinetic energy

When an object is moving the energy it has will depend upon:

The mass of the object (m) in kg

The velocity or speed of the object (v) in ms-1

This give us the formula:

Ek = ½ mv2

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Changes in energy

We find that an object falling from a height will lose potential energy and gain kinetic. Ignoring effects of air friction then all PE will change to KE. The reverse of this will occur when something is thrown or projected into the air.

The conservation of energy allows us to equate Epg =Ek in these situations.

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Examples

A 4.6 kg rock is kicked off a 120m cliff

a) How much potential energy does the rock lose as it falls?

EPgrav = mgh = 4.6 x 10 x 120 = 5520J

b) How much kinetic energy does the rock have just before it hits the ground?

Loss of EPgrav = EK = 5520 J

c) What is the speed of the rock just before it hits the ground?

EK = ½ mv2 = 5520 (4.6)/2 *v2 = 5520 v = (5520/2.3) = 49.0 ms-1

d) What happens to all the kinetic energy when the rock hits the ground?

Turns to sound and heat energy

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Momentum

• Momentum is a quantity you may have heard of and even have a basic understanding of.

• It is related to the velocity and size of an object.• Small objects will require a lot of velocity to have

a lot of momentum and thus be difficult to stop.• Large objects even at slow velocities can be

hard to stop.• Momentum = mv

where m = mass in kgv = velocity in ms-1

Momentum is measured in kgms-1

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Density

• What do we mean when we describe something as light ?

• Which is heavier a tonne of feather or a tonne of coal?

• The real question is which would occupy the biggest volume, a tonne of feather or a tonne of coal? We know that a tonne of feather would occupy a larger volume.

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Density

Density can be described as the amount of mass of a material per unit volume.

The formula is:

Where m= mass in kgV= volume in m3

ρ = density in kgm-3

V

mρ

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Example

Find the density of the following:

a) Lump of metal weighing ½ kg with a volume of 5cm x 5 cm x 5cm

b) 1 tonne of a metal has a volume of 0.4 m3

c) a lump of wood weighing 25 kg is 1m square by 0.1 m in length