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1
NSS Physics Revision Notes (S.4 2
nd
term)
Topic 1: Momentum
- Conservation of momentum
➔ Momentum = mass × velocity ( p = mv )
➔ Momentum is a vector and is measured in kg m s
➔ The law of conservation of momentum states that the total momentum of a system is conserved,
provided that there is no external force acting on the system.
◼ It can be expressed mathematically as m (^) A uA + mBuB = mAvA + mBvB
◼ Note the following when applying the law of conservation of momentum:
An external force is exerted by an object outside a system.
The forces acting between object within a system are internal forces.
Only the total momentum of a system is conserved.
➔ Total momentum and total kinetic energy in different types of interaction:
Total momentum conserved? Total kinetic energy conserved?
Completely inelastic collision (^) ✔ ✘
Inelastic collision (^) ✔ ✘
Elastic collision (^) ✔ ✔
Explosion (^) ✔ ✘
➔ Examples of conservation of momentum:
a) Newton’s cradle
When one to four balls are released on one
side, the same number of balls rise to the
same height on the other side after the
collision. This shows that the total
momentum of the system is conserved just
before and after the collision.
b) Recoils of guns and cannons
When a bullet is fired forwards, the gun
recoils (moves backwards) so that the
momentum of the gun and the bullet remains
zero. The person holding the gun provides a
force to stop the gun from moving
backwards. Similarly, when a cannonball is
fired, the cannon recoils. The massive base
reduces the recoil velocity of cannon.
c) Spacecraft
SAFER (a safety measure for an astronaut
performing a spacewalk) applies the
principle of conservation of momentum. In
case the tether connecting an astronaut
becomes detached from the space station or
spacecraft, the astronaut can get back to the
station or spacecraft using SAFER which
can eject gas in different directions.
➔ If a projectile lands at the same level that it is launched from and air resistance is negligible,
◼ its trajectory is symmetrical about the vertical line passing through the highest point
◼ the magnitude of the velocity for the upward motion is the same as that for the downward
motion at the same height
◼ its time of upward flight is the same as its time of downward flight
◼ its range is at its maximum if the angle of projection is 45 ˚
◼ there are two possible angles of projection for the projectile to reach the same range, except 45˚.
➔ When a projectile lands at the same level that it is launched from,
g
u T
2 sin
g
u H 2
sin
2 2
g
u R
sin 2
2
=
➔ If air resistance is negligible, the sum of kinetic energy and potential energy of a projectile is
constant during its flight. If the projectile is projected with an initial velocity u and the potential energy
at the launching level is taken as zero, its energy changes with time as shown.
➔ In the presence of air resistance, a projectile has
◼ an asymmetrical trajectory
◼ a much reduced maximum height and range
➔ Experiments with related to gases:
Experiment Procedure and precautions of experiment
Boyle’s law experiment
Procedure:
Connect a pressure sensor to a syringe and a data-logger interface. Push
or pull the piston of syringe.
Precautions:
- The length of the rubber tubbing should be short to reduce the
volume of gas inside the tubbing.
- The piston should be moved slowly so that the temperature can be
kept constant.
- Do not take the readings immediately after the piston is moved.
Wait to ensure the temperature becomes steady.
- Well lubricate the piston to reduce friction between the piston and
the wall.
Charles’ law experiment
Procedure:
Set up the apparatus as shown. Heat the water bath. Record the lengths
of air column at different temperatures.
Precaution:
- The water should be well-stirred to ensure uniform temperature
before taking a reading.
- The gas column should be fully immersed in water.
- The thermometer should not touch the bottom of the beaker.
- Sufficient time should be allowed for the gas to acquire the
temperature of water.
- The capillary tube should have an open end to ensure that the
pressure of the trapped gas is constant and equal to the
atmospheric pressure.
Pressure law’s experiment
Procedure of set-up A:
- Heat a flask wrapped with cotton in an oven set at 150℃ for about
20 minutes. Then take out the flask and seal it.
- Measure the temperature and pressure of the gas inside the flask with
a temperature sensor and a pressure sensor.
Precaution of set-up A:
The flask is hot. Do not touch it with bare hands. Do not heat the flask in
an oven with an exposed heating coil. Such a heating coil mag ignite the
cotton.
Procedure of set-up B:
Precautions of set-up B:
- The water should be well-stirred to ensure uniform temperature
before taking a reading.
- The tube connecting the Bourdon gauge to the flask should be short.
- The glass flask should be fully immersed in water.
- The thermometer should not touch the bottom of the beaker.
- Sufficient time should be allowed for the gas to acquire the
temperature.
➔ The p - V relation due to molecular motion of the gas can be expressed as
2
3
1 (^) pV = Nmc , where
p means the gas pressure exerted on the wall of a container
V means the volume of the container
N means the number of gas molecules
m means the mass of a gas molecule
2 c means the mean-square-value of the velocities of all gas molecules
➔ Temperature and molecular motion
◼ Consider the general gas law and the formulae
2
3
1 pV = Nmc , we can conclude that:
◆ Total KE of one mole of gas = RT 2
3
◆ Average kinetic energy of a molecule = NA
RT
◆ Internal energy of a gas = nRT 2
3
◼ The molecules in a gas have a wide range of speeds. The distribution depends on the temperature.
◼ Consider the formulae
2
3
pV = Nmc and NA
RT
mc 2
= , we can conclude that:
N m
RT
Nm
pV c A
➔ Conversion between different quantities:
Quantity Physical meaning
n number of moles of gas molecules
N number of gas molecules
NA number of molecules in one mole of gas (Avogadro’s constant)
m mass of each gas molecule
Nm mass of all molecules in a gas (= mass of the gas)
NAm mass of one mole of gas molecules (= molar mass of the gas)
Therefore, we can conclude that Nm
m
N
N
n
A A
=^ =.
Mass Kinetic energy
1 molecule m
NA
RT
1 mole NAm RT 2
3
Total Nm = nNAm nRT 2
3
➔ Explaining gas laws using kinetic theory
◼ Mechanical simulator of kinetic theory:
◆ Physical quantities represented by the mechanical simulator
Physical quantities Mechanical simulator
Pressure Weight of piston
Temperature Voltage applied to the motor
Volume Height of piston
Charles law
As the temperature rises, the molecules move faster. As a
result, the frequency of collisions and the change in
momentum during each collision increases. If the pressure is
to remain constant, the volume must increase so that the
frequency of collisions is increased. Therefore, at a constant
pressure, an increase in temperature will results in an increase
in volume.
Relationship between number
of molecules and volumes
When the number of molecules increases, the frequency of
collisions increases. To maintain a constant pressure and
temperature, the volume must increase.
➔ Appendix:
➔ How do they vibrate:
Transverse wave Longitudinal wave
(2) Particle vibrations and wave motion
⇨ Terms for describing a transverse wave:
Term In terms of particle vibration In terms of wave motion Symbol Unit
Amplitude size of the maximum ffffffffffffffff
displacement of the particle from
its equilibrium position
size of the maximum
displacement measured
from the equilibrium
position
A meter (m)
Period time for the particle to make one
complete vibration
time for one complete cycle
of wave to be produced, or
time for the wave to travel a
distance of one wavelength
T second (s)
Frequency number of vibrations made in 1 s number of complete cycles
of wave produced in 1 s
f hertz (Hz)
Wavelength
minimum distance over
which the waveform repeats
itself
λ meter (m)
Wave speed
distance travelled by the
wave in 1 s
v
meter per
second (m s
⇨ All particles on a travelling wave vibrate with the same amplitude, frequency and period as the wave.
⇨ Period is equal to the reciprocal of frequency, f
T
⇨ The following relation applies to all kind of waves: v = f .
⇨ On a travelling wave, two particles that are separated by n are vibrating in phase, while two particles
that are separated by )
( n + are vibrating in antiphase.
in phase in antiphase
Topic 5 : Wave phenomenon
- Studying wave phenomena using water waves
➔ Water waves produced in a ripple tank can be projected onto a screen. The bright lines on the screen
correspond to wave crests and the dark lines correspond to wave troughs.
➔ There are two types of water waves: circular wave and straight wave.
Straight wave Circular wave
Set-up for producing
Pattern formed
➔ For both straight wave and circular wave, the distance between two adjacent bright lines (or dark lines)
is the wavelength of the water wave.
➔ When the depth of water in a ripple tank is constant, the speed of water waves v is constant, and the
frequency f is inversely proportional to the wavelength λ.
A water wave with frequency f****. A water wave with frequency to 2 f****.
➔ Waterfronts are lines of neighboring points on a wave which are vibrating in phase. They are always
perpendicular to the direction in which the wave travels.
