A2 Physics Plan of Work (of

A2 Physics Plan of Work (of Sir A. N. Chowhan’s online class)

Sir A. N. Chowhan’s lecture notes (covering 100% syllabus) and solutions to topical-workbook questions (2013 to 2018) will be WhatsApped/WeChatted (in the form of pdf files).

Online test will take place at the end of each chapter. The test will cover ALL topics of the chapter.

For registration and further queries, WhatsApp/WeChat us at +92 307 5059 857

week 1 week 2 week 3 week 4

Motion in a circle

Angular displacement and angular speed

Centripetal force

Gravitational fields

Newton’s law of gravitation

Motion of satellites

Gravitational field strength

Gravitational potential

Gravitational potential energy

Electric fields

Coulomb’s law

Electric field strength (E)

Electric potential (V)

Determining resultant E and V due to two charged bodies

Oscillations

Simple harmonic motion (SHM)

Displacement, velocity and acceleration in SHM

Energy in SHM

Damped oscillation

Resonance


Waves

Ultrasound production

Acoustic impedance and intensity reflection coefficient

Ultrasound scanning

Communication

Modulation

Digital transmission

Communication channels

Satellite communication

Attenuation, gain and signal-to-noise ratio (SNR)

Capacitance

Capacitors in series and parallel

Energy stored in a capacitor

Electronics

Electronic sensors

Ideal op-amp

Inverting op-amp

Non-inverting op-amp

Relay and LED

Magnetic fields

Force on a current-carrying conductor in a magnetic field


Measuring magnetic flux density by a current balance

Velocity selection of moving charges

Hall voltage

Determining charge-to-mass ratio of electron

MRI scanning

EM induction

Laws of EM induction

Alternating current

Root-mean square current and voltage

Power in a.c. circuits

Transformer

Rectification of a.c.

Quantum physics

Particulate nature of EM radiation and photon

Photoelectric effect

de Broglie wavelength and electron diffraction

Line spectra

Band theory

X-ray and CT scanning

Particle and nuclear physics

Nuclear binding energy

Nuclear Fusion and fission reactions

Radioactive decay

Activity, decay constant and half-life


Ideal gases

Equation of state

Kinetic theory of gases

Pressure of an ideal gas

Past-paper questions

K.E. of a gas molecule


Temperature

Temperature scales

Thermometers

Thermal properties of matter

Specific heat capacity

Specific latent heat

Determining specific heats


Internal energy

Simple kinetic model of matter

1st law of

thermodynamics


CONTENTS

Prepared by Sir A. N. Chowhan (Headstart School, Islamabad)

Chapter 10 Ideal gases 1 - 22

Chapter 11 Temperature 23 - 30

Chapter 12 Thermal properties of materials 31 - 68

Chapter 7 Motion in a circle 69 - 76

Chapter 8 Gravitational fields 77 - 120

Chapter 17 Electric fields 121 - 164

Chapter 13 Oscillations 165 - 218

Chapter 14 Waves 219 - 240

Chapter 16 Communication 241 - 289

GRAVITATIONAL FIELDS CHAPTER 8


1 Gravitational Field

Figure 8.1

Gravitational field is the region of space where a mass experiences a force. [1]

Representation of Gravitational Field

Figure 8.2 (a) Figure 8.2 (b)

Notes

The field lines in Fig. 8.2 (b) are radial, and appear to come from the centre of the sphere. So, for a point outside a uniform sphere, the mass of the sphere may be considered to be a point mass at its centre. [2]

At a point, the direction of gravitational field line indicates the direction of force (that would act) on a small mass (if placed at that point). [1]

Important Notes

The formulas/equations with borders (rectangles) drawn around them are very important from the examination point of view, but the formula sheet of paper 4 (theory paper) does not contain these formulas; so students are advised to memorise them.

Keywords have been underlined throughout the text. Definitions/statements lacking keywords are not awarded full marks (as indicated, in blue, at the end of definitions/statements); so students are advised to pay special attention to the keywords (as they memorise the definitions/statements).

Bracketed information only serves as an additional detail that is not required (in order for the examiner to award the intended marks).

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Gravitational Field Strength (g)

If:

Figure 8.3

then gravitational field strength at point A (due to mass M) is given by:

=F

gm

(where F is the force acting on mass m at A)

So, at a point, gravitational field strength may be defined as:

force

gravitational field strength =mass

[1]

2 Newton’s Law of Gravitation

If:

Figure 8.4

then by Newton’s 3rd

law of motion: F1 = – F2

The experimental results show that

F m1m2 (where F is the magnitude of gravitational force between m1 and m2) and

F 2

1

r

Combining the above relationships gives:

F 1 2

2

m m

r

1 2

2=Gm m

Fr

where G is the gravitational constant (6.67 10–11

N m2 kg

–2).

So, Newton’s law of gravitation states that the force between two point masses is directly proportional to the product of their masses, and inversely proportional to the square of their separation. [2]

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3 Circular Motion of Satellites

For a satellite orbiting the Earth as shown below:

Figure 8.5

the gravitational force (Fg) provides the required centripetal force (Fc). So:

Fg = Fc

2

2 =GMm mv

rr or 2

2 =GMm

m rr

where is the angular speed (or angular frequency) of the satellite, given by:

= 2f or 2

=T

where f is the frequency and T is the period of circular motion of the satellite.

Geostationary Satellite

Figure 8.6

A satellite orbiting in geostationary orbit always appears stationary to an observer on the Earth. This happens because a geostationary satellite orbits:

1 in the plane of the Equator

2 in the direction of Earth’s rotation

3 with a period of 24 hours. [3]

Classwork/homework

Now do the following workbook questions (of chapter 8) in the same order:

21, 14, 13, 7, 11, 3, 4, 10

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Important Note

In all solved past-paper questions throughout the text, things (such as text/formula/drawing) written/drawn in red serve as additional explanations only, so students are not required to write/draw them in order to score the intended marks.

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4 Gravitational Field Strength (g) due to a Point Mass (M)

If:

Figure 8.7

then gravitational field strength at point P due to point mass M is given by:

=F

gm

(where:2= )

GMmF

r

2/=

GMm rg

m

2=GM

gr

………. (i)

Note

For a point outside a uniform-density sphere, the sphere may be treated as a point mass (by assuming that its mass is concentrated at its centre). This implies that the above expression for g can also be used for a uniform sphere if the point at which g is to be determined lies outside the sphere.

Variation of g with Height

Figure 8.8

From Eq. (i), it follows that as we go up from the surface of the Earth (i.e. r increases), g decreases.

Variation of g with Depth

Figure 8.9

As we go down from the surface of the Earth towards its centre, g decreases (this time too) because the effective mass Me of the Earth decreases.

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Apparent g at the Equator

If:

Figure 8.10

then for mass m: Fnet = Fc

Fg – R = Fc ………. (ii)

where R is the normal reaction on mass m which is equal to the ‘apparent weight’ of the mass m. So, putting R = mg into Eq. (ii) gives: Fg – mg = Fc

Fg – Fc = mg

g c

=F F

gm

Classwork/homework


2, 8, 17, 5, 1, 15

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5 Gravitational Potential () due to a Point Mass (M)

If:

Figure 8.11

then gravitational potential at point P is given by the expression:

=W

m (where W is the work done by force F)

So, gravitational potential at a point may be defined as the work done per unit mass in bringing a small test mass from infinity to the point. [2]

It can be shown that gravitational potential at a point (P) due to a point mass (M) is given by the expression:

=GM

r

where r is the distance of the point (P) from the point mass (M).

Sample Question

Explain why gravitational potential at any point inside the field is always negative. [2 or 3]

Answer

Gravitational potential at a point is the work done (by external force F) per unit mass in bringing a mass from infinity to the point. Now, as gravitational force is always attractive, so the work done (by force F) is always negative (because force F and motion are in opposite directions (see Fig. 8.11)).

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6 Gravitational Potential Energy (Ep)

If:

Figure 8.12

then gravitational potential energy stored in mass m at point P is given by the expression:

p =E m (where at P: = )GM

r

p = .( )

GME m

r

p =GMm

Er

Example 1

If:

Figure 8.13

then find an expression for vR, where vR is the minimum speed to be given to mass m, at the surface of the Earth, so that it can escape the Earth’s field. [3]

Solution

As air resistance is negligible, so by energy conservation:

total energy at the surface = total energy at infinity

KER + PER = KE + PE

2

R

1+( )

2

GMmmv

R = 0 + 0

2

R

1=

2

GMmmv

R

R

2=

GMv

R

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Example 2

If:

Figure 8.14

then show that near the Earth’s surface (i.e. for h << rA and h << rB):

∆Ep = mgh

where ∆Ep is the change in gravitational PE of mass m between A to B. [4]

Solution

∆Ep = EpB – EpA

=B A

( ) ( )GMm GMm

r r

=A B

GMm GMm

r r

=A B

1 1 ( )GMm

r r

=B A

A B

( )r r

GMmr r

(where: rB – rA = h)

∆Ep =A B

mGMh

r r ………. (i)

Now as h << rA and h << rB, so we may use the approximation:

rA rB

rA rB r2 (where:

A B+

= )2

r rr

Putting rA rB = r2 into Eq. (i) gives:

∆Ep = 2.( ).GM

m hr

(where: 2 = )GM

gr

∆Ep = mgh

Classwork/homework


6, 18, 19, 20, 16, 12, 9

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A2 Physics Plan of Work (of