Post on 16-Nov-2021
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
week 5 week 6 week 7 week 8
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
week 9 week 10 week 11 week 12
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
week 13 week 14 week 15 week 16
Ideal gases
Equation of state
Kinetic theory of gases
Pressure of an ideal gas
Past-paper questions
K.E. of a gas molecule
Past-paper questions
Temperature
Temperature scales
Thermometers
Thermal properties of matter
Specific heat capacity
Specific latent heat
Determining specific heats
Past-paper questions
Internal energy
Simple kinetic model of matter
1st law of
thermodynamics
Past-paper questions
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
Prepared by Sir A. N. Chowhan (Headstart School, Islamabad)
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
Now do the following workbook questions (of chapter 8) in the same order:
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
Now do the following workbook questions (of chapter 8) in the same order:
6, 18, 19, 20, 16, 12, 9
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