Physics Preparatory Course 2021 Part 1 PDF

Preview

Summary

Physics Preparatory Course Lesson 1: Introduction / BasicsDr Ho Shen Yong Lecturer, School of Physical and Mathematical Sciences Nanyang Technological University2 Jul 2021"Although no one can go back and make a brand new start, anyone can start from now and make a brand new ending.” - Carl BardConte...

Description

A (L1 – L3) Physics Preparatory Course Lesson 1: Introduction / Basics Dr Ho Shen Yong Lecturer, School of Physical and Mathematical Sciences Nanyang Technological University 2 Jul 2021

"Although no one can go back and make a brand new start, anyone can start from now and make a brand new ending.” - Carl Bard

Content

Online 7:00 pm – 10:00 pm

L1: Introduction / Diagnostics / Basics

2 July 2021 (Fri)

L2 / L3 : Forces, Pressure and Thermal Physics

5, 7 July 2021 (Mon/Wed)

L4 / L5: Mechanics – 1D Kinematics, Momentum, Newton’s Laws

9?, 11 Jul 2021 (Fri/Mon)

L6 / L7: Mechanics – Vectors, 2D Mechanics

14, 16 Jul 2021 (Wed/Fri) Short Assessment 15 Jul

L8 / L9: Mechanics – Work, Energy and Power

19, 20 Jul 2021 (Mon/Tue)

L10: Gravitational Fields

23 Jul 2021 (Fri)

L11: Electric Fields

26 Jul 2021 (Mon)

L12: Magnetic Fields and Electromagnetic Induction

28 Jul 2021 (Wed)

1

Units and Measurements 1.

List the seven SI Base quantities and their units

2.

Write down the prefix for each decimal sub-multiple and multiple

 1012

 109

 10 6

 10 3

 101

 10 12

 10 9

 10 6

 10 3

 10 2

 10 1

2

Units and Measurements 3. a.

Express 0.0000156 m in mm.

b.

17829000J in MJ

4.

Convert

a.

23 cm3 to m3

b. 0.98 g cm-3 in kg m-3

c.

the speed limit on the expressway in m s-1.

d.

your average speed when you run the 2.4 km for your NAFA test in km h-1 and m s-1.

3

Pause to Ponder: Are you able to lift up 1 m3 of seawater? Density of seawater is 1.03 g/cm3 .

Pause to Ponder: How does Usain Bolt’s top speed compare with a car moving on the expressway?

The Scale of Things http://htwins.net/scale2/

4

Atomic Structure

http://en.wikipedia.org/wiki/Rutherford_model

Mass (kg)

Charge (C)

Proton

1.6726 × 10−27

+1.602 × 10−19

Neutron

1.6749 × 10−27

0

Electron

9.109 × 10−31

-1.602 × 10−19

Matter is made up of atoms. Each atom is made of protons and neutrons which forms its core – the nucleus with electrons moving round it. For example, in a carbon-14 atom .14 6 𝐶, it

has

𝑍 = 6 protons and 𝑁 = 14 − 6 = 8 neutrons Here, 𝑍 is the atomic number which gives the number of protons and the element. All carbon atoms have 6 protons. The mass number A gives the total number of protons and neutrons. Here, 𝐴 = 14. The number 𝑁 gives the number of neutrons. In an electrically neutral atom, the number of electrons is the same as the number of protons. The size of the nucleus is about 10−15 m and the size of the atom is about 10−10 m. 5

Pause to Ponder: Some NTU students do part-time driving with Grabcar during vacation. In some cars, some statistics (such as duration of trip, distance covered in a trip and fuel consumption) related to a trip are collected and that allows us to do some simple calculations. A particular trip from Bukit Panjang to NTU is 15.0 km and the journey takes about 20 min. The average fuel consumption for this whole journey is recorded as 7.0 litres per 100 km. The price of petrol is $2.5 per litre. The price he collect from the passenger is fixed at $14. Using the information provided, determine i. ii. iii.

the average speed in km/h, the number of litres of fuel used, the cost of the fuel used for the journey.

iv.

If there is a slightly longer route from Bukit Panjang to NTU, say 16.5 km but the journey takes about 18 min instead, should he take this route instead of the original route? Give your reasons.

6

Units and Measurements Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units. For example Physical Quantities

Units

Symbols

area volume speed, velocity acceleration mass density

square meter cubic meter meter per second meter per second squared kilogram per cubic meter

m2 m3 m/s m/s2 kg/m3

current density magnetic field strength

ampere per square meter ampere per meter

A/m2 A/m

For ease of understanding and convenience, 22 SI derived units have been given special names and symbols (taken from http://physics.nist.gov/cuu/Units/units.html):

Derived quantity Name radian plane angle

Symbol rad

In terms of other SI units -

force newton pressure, stress pascal energy, work, joule quantity of heat power, radiant watt flux

N Pa

N/m2

m·kg·s-2 m-1·kg·s-2

J

N·m

m2·kg·s-2

W

J/s

m2·kg·s-3

In terms of SI base units m·m-1 = 1

7

Units and Measurements

Derived quantity electric charge, quantity of electricity electric potential difference, electromotive force capacitance electric resistance

Name

Symbol

In terms of other SI units

In terms of SI base units

coulomb

C

-

s·A

volt

V

W/A

m2·kg·s-3·A-1

farad

F

C/V

m-2·kg -1·s4·A2

ohm

Ω

V/A

m2·kg·s-3·A-2

Wb

V·s

m2·kg·s-2·A-1

T

Wb/m2

kg·s-2·A-1

°C

-

K

magnetic flux weber magnetic flux tesla density Celsius temperature degree Celsius

8

Units and Measurements The importance of consistency

The formula for the period 𝑇 of a small pendulum swing is 𝑇 = 2𝜋

𝑙 𝑔

. Here, 𝑙 is

the length of the pendulum and 𝑔 is the acceleration of free fall with a value 9.81 𝑚/𝑠 2 . Calculate the period of a pendulum with length 𝑙 = 50 𝑐𝑚.

𝑙

The dimensions of a piece of gold is 56 cm × 28 cm × 22 cm. What would the mass be? The density of gold is 19.3 × 103 kg / m3 .

9

Units and Formulas Homogeneity of Units

Given an equation 𝐴+𝐵+

𝐶 +𝐸×𝐹 =𝐺 𝐷

𝐶

The units of 𝐴, 𝐵, , 𝐸 × 𝐹 and 𝐺 must be the same. 𝐷

Mathematical functions can only operate on pure numbers with no physical units. For example, cos 𝜃, here 𝜃 has no units (rad is not a physical unit). Other examples include ln 𝑥 and 𝑒 𝑥 . Here, 𝑥 must be a number with not units.

Example An equation often used in fluid mechanics, known as Bernoulli’s equation is given by 1 𝜌𝑣 2 + 𝜌𝑔𝑧 + 𝑃 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 2 Here, 𝑣 is velocity in m/s. The unit for density 𝜌 is in kg/m3 and the unit for acceleration of free fall 𝑔 in m/s 2 . What are the units for the variables 𝑧 and 𝑃?

10

Units and Formulas Homogeneity of Units

Example The formula for the remaining charge 𝑄 in the capacitor in a discharging RC (Resistor-Capacitor) circuit at any time 𝑡 (in s) is given by 𝑄 = 𝑄𝑜 𝑒 −𝑡/𝜏 where 𝑄𝑜 is the original charge. What is the unit for the variable 𝜏?

Example Newton’s law of gravitation states that the mutual force 𝐹 of attraction between two objects of masses 𝑚1 and 𝑚2 separated by a distance 𝑟 is given by 𝐹=

𝐺𝑚1 𝑚2 𝑟2

where 𝐺 is a universal constant. What is the SI unit of 𝐺 ?

11

Units and Measurements Estimate a. the cruising speed of an plane in km s-1.

b. the linear speed at the equator when the Earth spins about its axis in km h-1. (Radius of Earth is 6400 km)

The Mole Concept

Estimate the number of water molecules you swallow when you drink one cup of water.

12

Solid, Liquids and Gases Particles in a solid are tightly packed, usually in a regular pattern. They vibrate (jiggle) but generally do not move from place to place.

Particles in liquid state are close together with no regular arrangement. They liquid vibrate, move about, and slide past each other.

Particles in a gaseous state are well separated with no regular arrangement. They vibrate and move freely at high speeds.

Giancoli Fig 17.2

https://phet.colorado.edu/en/simulation/legacy/states-of-matter 13

Metals

http://www.texasgateway.org/resource/chemical-bonding-metallic-bonds

14

Mass and Weight Mass •

is understood as the quantity of matter in the object. It is a scalar quantity.

•

is a property of an object and does not change with location.

•

measured in kilograms.

•

is a measure of inertia of an object.

Mass is not weight. Weight •

is the force exerted on that object by gravity. It is a vector quantity and has both direction and magnitude.

•

is obtained by multiplying the mass of the object m by acceleration due to gravity g.

•

the unit for weight is Newton (N).

The value of g near Earth’s surface is 9.8 𝑚/𝑠 2 . If the mass of an object is 5.0 kg, then its weight near Earth’s surface is 5 × 9.8 = 49𝑁.

If you go to the Moon, where acceleration due to gravity is about 1.6 𝑚/𝑠 2 , you will weigh much less. Your mass, however, will be the same.

Pause to Ponder: Where does the mass of trees come from?

15

Density The density ρ of a substance is its mass per unit volume: 𝑀𝑎𝑠𝑠 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 = 𝑉𝑜𝑙𝑢𝑚𝑒 𝜌=

Giancoli

𝑀 𝑉

The SI unit for density is kg/m 3. To convert g/cm3 to kg/m3, multiply by 1000. Water at 4°C has a density of 1 g/cm3 = 1000 kg/m 3. Specific Gravity The specific gravity of a substance is the ratio of its density to that of water. Example [G13.5] A bottle has a mass of 35.00 g when empty and 98.44 g when filled with water. When filled with another fluid, the mass is 89.22 g. What is the specific gravity of this other fluid?

16

Exercise 1. [G1.48] Estimate the number of gumballs in the machine.

2. [G1.33] Many sailboats are moored at a marina 4.4 km away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the water’s edge, you can just see its deck but none of the side of the sailboat. You then go to that sailboat on the other side of the lake and measure that the deck is 1.5 m above the level of the water. Using the figure, where ℎ = 1.5 𝑚, estimate the radius R of the Earth.

17

3. [G1.68] One mole of atoms consists of 6 × 1023 individual atoms. If a mole of atoms were spread uniformly over the surface of the Earth, how many atoms would there be per square meter?

4. You can obtain a rough estimate of the size of a molecule with the following simple experiment: Let a droplet of oil spread out on a fairly large but smooth water surface. The resulting ”oil slick” that forms on the surface of the water will be approximately one molecule thick. Given an oil droplet with a mass of 8.85 × 10−7 kg and a density of 923 kg/m3 that spreads out to form a circle with a radius of 43.2 cm on the water surface, what is the approximate diameter of an oil molecule? Answer in units of m.

18

5. [G13.7] The Earth is not a uniform sphere, but has regions of varying density. Consider a simple model of the Earth divided into three regions—inner core, outer core, and mantle. Each region is taken to have a unique constant density (the average density of that region in the real Earth): Region Radius (km) Inner Core 0 – 1220 Outer Core 1220 – 3480 Mantle 3480 – 6371

Density (kg/m3) 13,000 11,100 4,400

Use this model to predict the average density of the entire Earth.

𝑟2

𝑟1

19

6. [G13.6] If 5.0 L of antifreeze solution (specific gravity = 0.80) is added to 4.0 L of water to make a 9.0-L mixture, what is the specific gravity of the mixture?

7. A 2.00 m by 3.00 m plate of aluminum has a mass of 324 kg. What is the thickness of the plate? (The density of aluminum is 2.70 × 103 kg/m3.)

20

Physics Preparatory Course Lesson 2: Forces, Pressure, Fluids Dr Ho Shen Yong Lecturer, School of Physical and Mathematical Sciences Nanyang Technological University 5 Jul 2021

I think I have never met a person who could not teach me something. J. Dan Gill

Key things to committed to long term memory

21

∘

∘ 𝐶 − (−30)∘ 𝐶 1: Weight Normal Δ𝑙 = 𝛼𝑙𝑜Forces Δ𝑇 =−212 × 10−6 and 𝐶 200𝑚 20Force = −12.0 × 10 𝑚

Weight 𝑊 is the force exerted on an object by gravity. Near the surface of the Earth, where the gravitational field is nearly constant, the weight of an object of mass 𝑚 is: 𝑊 = 𝑚𝑔 where

𝑔 = 9.8 𝑚/𝑠 2

𝑊 = 𝑚𝑔 This force acting on the ball at the point of contact is known as the ‘Normal Force’ 𝐹𝑁 . It is a force due to contact and acts perpendicular to the surface.

𝑊 = 𝑚𝑔

When the ball is in equilibrium, an equal and opposite normal force 𝐹𝑁 is acting downwards on the ground. Force is a vector. It has a magnitude and direction. 22

∘ Tension Force Δ𝑙 = 𝛼𝑙𝑜 Δ𝑇 = 12 × 10−6 𝐶 200𝑚 20∘ 𝐶 − (−30)∘ 𝐶

= −12.0 × 10−2 𝑚

•

When a string or rope or wire pulls on an object, it exerts a contact force that we call the tension force.

•

The direction of the tension force is always in the direction of the string or rope.

•

The direction of the tension is always pointing away from the object.

Identify the forces in each of the object, labelled X below:

X

23

∘

Pressure Δ𝑙 = 𝛼𝑙𝑜 Δ𝑇 =−212 × 10−6 𝐶 200𝑚 20∘ 𝐶 − (−30)∘ 𝐶 = −12.0 × 10 𝑚

Pressure is defined as the force per unit area.

Pressure is a scalar; the units of pressure in the SI system are pascals: 1 Pa = 1 N/m2. Giancoli Table 13.2

Giancoli Example 13-2: The two feet of a 60-kg person cover an area of 500 cm2. (a)

Determine the pressure exerted by the two feet on the ground.

(b)

If the person stands on one foot, what will the pressure be under that foot?

24

∘

Pressure Δ𝑙 = 𝛼𝑙𝑜 Δ𝑇 =−212 × 10−6 𝐶 200𝑚 20∘ 𝐶 − (−30)∘ 𝐶 = −12.0 × 10 𝑚 http://en.wikipedia.org/wiki/Highheeled_footwear#mediaviewer/File:Stilettos-heels-b.JPG

http://certs-tabletop.blogspot.sg/2013/11/weekly-walking-on-thin-ice.html

Exercise: Giancoli Ex 13.9 Estimate the pressure exerted on a floor by (a) one pointed chair leg (66 kg on all four legs) of area 0.020 𝑐𝑚 2 and (b) a 1300-kg elephant standing on one foot. (area = 800 𝑐𝑚 2 )

25

∘

Δ𝑙 = 𝛼𝑙𝑜 Δ𝑇 =−212 ×Pressure 10−6 𝐶in Fluids 200𝑚 20∘ 𝐶 − (−30)∘ 𝐶 = −12.0 × 10 𝑚 Giancoli Chap 13 Pressure is the same in every direction in a static fluid at a given depth; if it were not, the fluid would flow. For a fluid at rest, there is also no component of force parallel to any solid surface—once again, if there were, the fluid would flow.

The pressure at a depth h below the surface of the liquid is due to the weight of the liquid above it. We can quickly calculate:

This relation is valid for any liquid whose density does not change with depth. Exercise: Giancoli Ex 13.15 (a) Determine the total force and the absolute pressure on the bottom of a swimming pool 28.0 m by 8.5 m whose uniform depth is 1.8 m. ( b) What will be the pressure against the side of the pool near the bottom?

26

∘

Δ𝑙 = 𝛼𝑙𝑜 Δ𝑇 =−212Atmospheric × 10−6 𝐶 Pressure 200𝑚 20∘ 𝐶 − (−30)∘ 𝐶 = −12.0 × 10 𝑚 At sea level the atmospheric pressure is about 1.013 x 105 N/m2; this is called 1 atmosphere (atm). Another unit of pressure is the bar: 1 bar = 1.00 x 105 N/m2. Standard atmospheric pressure is just over 1 bar. This pressure does not crush us, as our cells maintain an internal pressure that balances it.

Knight Fig 15.9

At sea level the atmospheric pressure can balance the pressure due to a column of mercury of height 760 mm.

http://www.chem.uiuc.edu/rogers/ Text9/Tx94/tx94.html

Most pressure gauges measure the pressure above the atmospheric pressure— this is called the gauge pressure. The absolute pressure is the sum of the atmospheric pressure and the gauge pressure.

27

−6 ∘bottom Exercise: Giancoli A house at the of a hill a full∘ 𝐶 tank of water Δ𝑙 = 𝛼𝑙13.16 𝐶 200𝑚 20is∘ 𝐶fed − by (−30) 𝑜 Δ𝑇 =−212 × 10 = and −12.0 × 10 to 𝑚the house by a pipe that is 110 m long at an angle of 5.0 m deep connected 58° from the horizontal. Determine the water gauge pressure at the house.

Exercise: The mercury in the tube is in equilibrium and the height difference between the mercury level in the two limbs is 4.0 cm. Determine the gas pressure in the tank. Density of mercury is 13 600 kg m -3.

Δℎ = 4.0 𝑐𝑚

Exercise: Giancoli Ex 13.17 Water and then oil (which don’t mix) are poured into a U-shaped tube, open at both ends. They come to equilibrium as shown in Fig. 13–49. What is the density of the oil?

28

Forces 2: Upthrust Pause to Ponder: The density of iron is 7.86 g cm-3. The density of sea water to be 1.03 g cm-3. Can iron float in sea water?

http://en.wikipedia.org/wiki/Rubber_du ck#mediaviewer/File:Rubber_Duck_%28 8374802487%29.jpg

[email protected]

29

Upthrust When an object is partially immersed in a fluid, it will experience an upward force. When the object is immersed further in a fluid, the upward force will increase correspondingly until it is fully immersed. This force is known as upthrust. It originates from the pressure difference between the bottom (larger pressure) and top side of the object.

Archimedes' Principle Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Remarks: 1. Volume of object submerged in the fluid=Volume of fluid displaced; 2. Knowing the displaced volume Vsubmerged and density rfluid of the fluid, we can compute the weight of fluid which gives the upthrust: 𝑈𝑝𝑡ℎ𝑟𝑢𝑠𝑡 = (𝜌𝑓𝑙𝑢𝑖𝑑 𝑉𝑠𝑢𝑏𝑚𝑒𝑟𝑔𝑒𝑑 ) 𝑔 From here, we can derive the law of flotation: A floating object displaces its own weight of fluid. For example, if an object weighs 1.2 N, for it to float, it has to be able to displace at least 1.2 N of fluid, i.e. giving an upthrust equivalent to 1.2 N. If the duck displaces 0.15 𝑚 3 of water (assuming density 𝜌 = 1.00 𝑔/𝑐𝑚 3 ), calculate the upthrust acting on it. Since it is floating, deduce the weight of the duck. (use 𝑔 = 10 𝑚/𝑠 2 for simplicity.)

[email protected]

30

A piece of material with density 0.70 g cm-3 is partially immersed in oil with density 0.85 g cm-3. i.

What is the volume of oil displaced by the block of material?

ii.

What is the weight of oil displaced b...