Module 5 - OCR (A) Physics A-Level

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It doesn’t arbitrarily depend on the properties of a given substance (eg. water’s melting and boiling point for the Celsius scale).

0K (absolute zero) means that the particles have minimum internal energy.

Solid - regular arrangement, vibrate around fixed point.

Liquid - close together, constantly moving past each other, random positions.

Gas - spaced very far apart, free to move in all directions.

Smoke particles suspended in air can be seen to move randomly in all directions. This must be as a result of random collisions with particles making up the air.

The sum of the potential and kinetic energies of a system.

False. The kinetic energies will be randomly distributed around a central ‘most likely’ amount.

We can increase it by heating it up or doing work on the object.

During change of state the potential energy of the particles change but the kinetic energies don’t change.

Q = mcΔ𝜭 Where Q = energy, m = mass, c = specific heat capacity, Δ𝜭 = temperature change.

The energy required to raise the temperature of 1kg of a substance by 1K.

Q=ml Where Q = energy, m = mass, l = specific latent heat (‘of fusion’ if melting/freezing, ‘of vaporisation’ if condensing/evaporating)

The energy required to change the state per unit mass of a substance, while keeping the temperature constant.

● An overestimate.

● Specific heat capacity is calculated as: c = Q / mΔ𝜭

● The energy input will be used, but the temperature change of the water will be lower than it should be due to the escaped energy - therefore c will be

The number of atoms there are in one mole of a substance.

6.022 × 10²³

● There are a large number of molecules in random, rapid motion.

● Particles are negligibly small compared to the total volume of the gas.

● All collisions are perfectly elastic.

● The time taken for a collision is negligibly small compared with the time between collisions.

● Between collisions there are no forces between particles.

● Gas particles collide with the surfaces of the container.

● The container exerts a force on the particles to change their direction. The particles exert an equal and opposite force on the container.

● Pressure is force applied per unit area.

A gas where that obeys the ideal gas laws.

pV=nRT Where p = pressure, V = volume, n = number of moles, R = the ideal gas constant, T = absolute temperature

Pressure is inversely proportional to volume, providing temperature is constant. i.e. pV = constant

They’re directly proportional.

● A temperature increase means the particles have more kinetic energy.

● More kinetic energy means a greater change in momentum during collisions with the container. There are also more frequent collisions.

● Change in momentum is proportional to force applied, and therefore to pressure as well

Where p = pressure, V = volume, N = number of particles, m = mass of a particle, ‘c’ = mean square speed.

The square root of the mean of the squares of the speeds of the molecules.

The total number of particles.

The average particle speed, and maximum particle speed both increase (curve shifts right). The curve becomes lower and more spread out.

JK^-1

1.5 kT

True.

In an ideal gas there is no ‘potential energy’ component in the internal energy. This means the internal energy is proportional to the kinetic energy (which is, in turn, dependent on temperature).

Angle.

multiply the number of degrees by π/180

The time taken for one full rotation.

The angle travelled through divided by the time taken. This is similar to linear speed, except we’re interested in rate of rotation rather than distance/time.

A constant centripetal force (a force applied always towards the centre of that circle)

False.

Velocity is always at a tangent to the circle, force is always along a radius. They are perpendicular.

v = ⍵r Where v = linear velocity, ⍵ = angular velocity, and r = radius.

False.

The direction is always changing hence the velocity always changing which means it is accelerating.

a=⍵²r

a = v²/r

F = mv²/r or F = m⍵²r

1. Setup:

   • Tie the bung to one end of the string.

   • Thread the string through a glass tube.

   • Attach the weight to the other end of the string.

   • Ensure that the tension in the string remains constant.

2. Whirling the Bung:

   • Hold the glass tube and whirl the bung in a circular path.

   • Record the time taken for one complete rotation (period).

3. Alter Mass of Weight:

   • Change the mass of the weight (M) by adding or removing weights.

   • Repeat the experiment for different masses.

4. Data Collection:

   • Measure the radius (r) of the circular path.

   • Note down the time for one complete oscillation.

5. Analysis:

   • Equate the centripetal force (F) to the gravitational force (Mg):

     • (F = Mg)

     • Also, (F = mv²/r)

   • Therefore, (Mg=mv²/r)

6. Graphical Analysis:

   • Plot (v²) against M.

   • The resulting graph should be a straight line passing through the origin.

● Displacement - distance from the equilibrium position (vector)

● Amplitude - maximum displacement

● Period - time taken for a complete oscillation

● Frequency - number of oscillations per second

⍵ = 2π/T Where ⍵ = angular frequency, T = time period

● Acceleration must be directly proportional to displacement and in the opposite direction: (a ∝ -𝑥)

● It must act towards equilibrium.

1. A mass-spring system

2. A pendulum

- ⍵²

𝑥 = Acos⍵t or 𝑥 = Asin⍵t (where A is amplitude)

False.

The velocity is minimum at the amplitude of oscillation, as the object changes direction. Velocity is maximum when the object passes through the equilibrium pos

v_max = ⍵A

Damping is the process by which the amplitude of the oscillations decreases over time. This is due to energy loss to resistive forces such as drag or friction.

Light damping occurs naturally (e.g. pendulum oscillating in air), and the amplitude decreases exponentially (but time period remains constant as A and T are independent). When heavy damping occurs (e.g. pendulum oscillating in water) the amplitude decreases dramatically. In critical damping (e.g. pendulum oscillating in treacle) the object is stopped in as short a time as possible without overshooting equilibrium.

When an object oscillates without any external forces being applied, it oscillates at its natural frequency. This is known as free oscillation. Forced oscillation occurs when a periodic driving force is applied to an object, which causes it to oscillate at a particular frequency.

When the driving frequency of the external force applied to an object is the same as the natural frequency of the object, resonance occurs. This is when the amplitude of oscillation rapidly increases, and if there is no damping, the amplitude will continue to increase until the system fails. As damping is increased, the amplitude will decrease at all frequencies, and the maximum amplitude occurs at a lower frequency.

● Suspend a mass between two springs attached to an oscillation generator and use a ruler parallel with the spring-mass system to record the amplitude.

● Increase the frequency of the generator slowly so that the amplitude increases, reaching maximum amplitude when the driving frequency is the same as the natural frequency of the system (after which, increasing the frequency will decrease the amplitude).

● Drag force damps the system so the amplitude should not continue to increase until the point of system failure.

● To increase accuracy, the system can be filmed and the amplitude value recorded from video stills, as it can be difficult to determine this whilst the mass is oscillating.

Gravity is the universal attractive force which acts between all matter.

The universal gravitational constant. Approx. 6.67x10^-11 m³ kg^-1 s^-2

The direction of the field and the strength of the field depending on the density of the field lines.

● 𝘨 is the force per unit area in a uniform gravitational field.

● In a radial field the magnitude of 𝘨 is the the proportionality constant at that point between force and mass.

● I.e. 𝘨 = GM/r²

Newton’s law of gravitation states that two point masses attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them.

Kepler’s first law states that the orbit of a planet is an ellipse, with the sun at one focus. The eccentricity of the ellipse is very low, so the motion can be modelled as circular.

Kepler’s second law states that a line segment joining a planet and the sun sweeps out equal areas during intervals of equal time. This is because the speed of the planet is not constant – the planet moves faster when it is closer to the sun.

Kepler’s third law states that the square of the orbital period T is proportional to the cube of the average distance r from the sun.

1. Because of Kepler’s third law, we can equate the formula for centripetal force with the formula for gravitational force to get mv²/r = GMm/r²

2. Rearrange to get v² = GM/r

3. Since velocity in circular motion is 2πr/T, you can substitute this into the previous equation to get 4π²r²/T² = GM/r

4. Rearrange this to get T² = 4π²r³ / GM

● Satellites are objects that orbit other, larger objects. These can include natural satellites like the moon, and artificial satellites that humans have sent into space.

● Uses include: communications, scientific research, and Global Positioning Systems (GPS).

● Geostationary satellites have a height so the orbital period is a day and they lay directly over the equator.

● They are useful for communications and surveying as they provide continuous coverage.

The work per unit mass needed to move an object from a fixed reference point to a specific point in space.

Gravitational potential difference is the difference in the gravitational potentials of two points in a gravitational field.

The work done per unit mass in moving object with from infinity to that point in the field.

● The minimum velocity an object requires in order to escape the gravitational field of an object when projected vertically from its surface.

● The formula for v_esc is derived from equating the kinetic energy and the gravitational potential energy required to reach infinity: ½mv² = GMm/r

○ Rearrange this to get v_esc = √2GM/r

Objects with mass sufficient for their own gravity to force them to take a spherical shape, where no nuclear fusion occurs, and the object has cleared its orbit of other objects.

Planets where the orbit has not been cleared of other objects.

Bodies that orbit a planet.

Objects which are too small and uneven in shape to be planets, with a near circular orbit around the sun.

Small, irregularly sized balls of rock, dust, and ice. They orbit the sun in eccentric elliptical orbits.

The systems containing stars and orbiting objects like planets.

A collection of stars, dust, and gas. Each galaxy contains around 100 billion stars and is thought to have a supermassive black hole at its centre.

Gigantic clouds of dust and gas. They are the birthplace of all stars.

In nebulae, there are regions that are more dense than others. Over time, gravity draws matter towards them and, combined with the conservation of angular momentum, causes them to spin inwards to form a denser centre.

GPE is converted into thermal energy, which heats up the centre. The resultant sphere of very hot, dense dust and gas is a protostar.

For a star to form, the temperature and pressure must be high enough for hydrogen gas nuclei in the protostar to overcome the electrostatic forces of repulsion and undergo nuclear fusion to convert hydrogen into helium. When fusion begins, the protostar becomes a main sequence star, where the outward pressure due to fusion and the inward force of gravity are in equilibrium.

Low-mass stars are classed as having a core mass between 0.5M☉ and 10M☉. As these stars have a smaller, cooler core, they remain in the main sequence for longer. Once the hydrogen supplies are low, the gravitational forces inwards overcome the radiation and gas pressures, so the core collapses inwards and the outer layers expand and cool. The core of the red giant becomes hotter (as GPE becomes thermal energy) and begins to fuse helium into heavier elements (up to carbon), as hydrogen continues to be fused in the layers around the core.

When the star runs out of fuel, it expels its outer layers, creating a planetary nebula. The core that remains contracts further, becoming a dense white dwarf. The white dwarf has a temperature of around 3000K, and no fusion occurs. Photons which were produced earlier in the evolution leak out, dissipating heat. As the star core collapses, electron degeneracy pressure (caused as two electrons cannot exist in the same state) prevents the core from collapsing. As long as the core mass is below 1.44M☉, then the white dwarf star is stable – this is the Chandraskhar limit.

Where a star’s mass in is excess of 10 M☉, its evolution takes a different path. As hydrogen supplies deplete, the core contracts. Since the mass is greater, when GPE becomes thermal energy, the core gets much hotter than a red giant, allowing helium fusion into elements heavier than carbon (up to iron) to take place. The outer layers expand and cool, forming a red supergiant.

When all of the fuel in a red supergiant is used up, fusion stops (as iron fusion does not release energy, it is unable to fuse further). Gravity becomes greater than the outward pressure due to fusion, so the core collapses in on itself very rapidly and suddenly becomes rigid (as the matter can no longer be forced any closer together). The outer layers fall inwards and rebound off of the rigid core, launching them out into space as a shockwave. The remaining core of a supernova is either a neutron star or black hole, depending on

If the remaining core mass is greater than 1.44M☉, gravity forces protons and electrons to combine and form neutrons. This produces an extremely small, dense neutron star. If the remaining core mass is greater than 3M☉, the gravitational forces are so strong that the escape velocity of the core becomes greater than the speed of light. This is a black hole, which even photons cannot escape.

Electrons bound to an atom can only exist in certain discrete energy levels. The electrons cannot have an energy value that is between two levels. Each element has its own set of energy levels. When an electron moves from a lower energy state to a higher energy state, it is ‘excited’. This requires the input of external energy (e.g. heating or absorbing a photon of the exact energy required).

True.

All energy level values are negative, with the ground state being the most negative. An electron that is completely free from an atom has energy equal to 0. This negative sign is used to represent the energy required to remove the electron from the atom.

● A series of coloured lines on a black background.

● When light passes through the outer layers of a star, the electrons in the atoms absorb photons and become excited. They then de-excite, releasing photons of specific wavelengths. These photons are detected on Earth and have wavelengths characteristic of the elements in the outer layers, shown as emission line spectra.

Continuous line spectra – where all visible wavelengths of light are present. They are produced by atoms of solid heated metals.

A series of dark spectral lines against the background of the continuous spectrum, with each line corresponding to a wavelength of light absorbed by atoms in the outer layers of a star. The dark lines are at wavelengths that are characteristic of the elements in the outer layers (as with emission spectra)

When an electron is de-excited, it releases energy as a photon with a specific wavelength. The energy released is the difference between the initial energy level of the electron, and the final energy level of the electron. This means that transitions between different energy levels produce photons with different wavelengths.

Components with regularly spaced slits that can diffract light.

Different colours of light have different wavelengths, and so will be diffracted at different angles.

The wavelength of emitted radiation at peak intensity is inversely proportional to the temperature of the black body.

λ_max T = 2.9 x 10^-3 m K

The power output of a star is directly proportional to its surface area and to its (absolute temperature)⁴ .

P = σAT⁴

The distance travelled by light in a vacuum in one year. In metres this is 9.46×10¹⁵m (speed of light multiplied by the number of seconds in a year).

The change in wavelength and frequency of a wave as the source moves away from or towards the observer.

The apparent shift in position of an object against a backdrop of distant objects due to the orbit of the Earth. It can be used to calculate distances of up to 100pc. Beyond this point, the angles involved are so small they are hard to accurately measure.