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Important Graph 1: Draw the graph for magnitude of the electric field strength (E) vs distance (r)

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Important Graph 1: Draw the graph for magnitude of the electric field strength (E) vs distance (r)

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Important Graph 2: Draw the graph for magnitude of the electric field strength (E) vs distance (r)

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Important Graph 2: Draw the graph for magnitude of the electric field strength (E) vs distance (r)

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Why are some isotopes more stable than others?

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Why are some isotopes more stable than others?

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Some atoms with larger nucleus needs a higher neutron-proton ratio so that the strong nuclear force can counteract the repulsive electrostatic forces between the protons, which is why isotopes with a larger neutron-proton ratio are more stable.

Isotopes with a higher binding energy per nucleon will be more stable as it takes more energy to "split" the nucleus apart.

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Moderators: slows down fast-moving neutrons so they are more likely to be absorbed by U-235 nuclei (water, heavy water, graphite)

Control rods: absorbs excess neutrons to regulate or shut down the reaction if needed (boron, cadmium, hafmium)

Shielding: protect the workers, the public and the environment using thick material designed to block ionizing radiation (concrete, lead, water)

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There are two copper coils, one in the wireless charger, and one inside the phone.

By applying an alternating current through the copper coil in the wireless charger, it induces a magnetic flux, and the magnetic flux will change due to AC changing the direction of the current.

The change in the magnetic flux, will allow the copper coil in the phone to have an induced current, and this current goes on to charge the battery pack in the phone.

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Simple harmonic motion refers to the periodic motion, where the restoring force is proportional to the distance from the displacement from the point of equilibrium.

An example of this would be a simple pendulum. It has a periodic oscillation, and the period of oscillation is proportional to the root of the length of the string. The restoring force is always in the direction of the equilibrium point, and is caused by gravity.

Another example would be a mass-spring system. It also has a periodic oscillation, but in real life, the dampening effect is more apparent. The restoring force is caused by the deformation of the string, and can be described by Hooke's Law. The point of equilibrium for this type of system is where the mass would be when the only force acting on a fixed spring is the weight of the mass.

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Lenz's Law states that the current induced in a conductor will be in the direction that will generate a magnetic field that is able to resist (oppose) the change in magnetic flux.

For example, if I put a sheet of copper into a space where there is a magnetic field facing to the right, the current that is induced in the copper will be in the direction where the magnetic field generated by the current will be towards the left to counteract the change. We can find the direction of the current by using the right hand rule and the fact that the magnetic field generated must be facing the opposite direction of the existing field.

Another example that can show this is if a magnet was dropped through a conductive coil. As the falling magnet gets closer to the ring, it will induce a current in the coil to generate a magnetic field that repels the magnet, slowing the fall of the magnet. A similar case happens when the magnet falls away from the coil, the coil will want to oppose the change in the magnetic field field, wanting to keep the magnet near, so it will generate a magnetic field that attracts the magnet.

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The similarity between SHM and Lenz's Law is that both wants to oppose a change to the system. For SHM, the change refers to the displacement of the system, whereas in Lenz's Law, the change is the change in magnetic field.

I think that this connection is easiest to show using a mass-spring system.

Where the restoring force is proportional to the displacement:

F = -kx

And connecting Faraday's law:

ε = -NdΦ/dt

We can see that both equations have a negative sign to show that it is opposing change, and that both are proportional to some change.

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I think that Lenz's Law is just the Law of Conservation of Energy, because:

A magnetic field cause a current to be induced in a conductor.

A conductor with a current will induce a magnetic field.

If the magnetic field is in the same direction, it will strengthen the magnetic field.

Magnetic field becomes stronger, change in magnetic field continues to induce a current in the conductor, and then we will have infinite energy, which breaks physics (which would be revolutionary if it happened)

Therefore, Lenz's Law explains how energy is conserved as a current is induced in a conductor due to magnetic fields.

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There will be an induced emf for the left and right position. This is because there will be a force acting on the charge due to the magnetic fields. Using the formula F=BIL sinθ. There will be no induced emf for the top and bottom positions as the angle between the magnetic field and the solenoids are very small.

The direction of the induced EMF for the right and left position would be counter-clockwise.

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Following Faraday's Law, if there is a potential difference, then there will be a change in the magnetic flux, which will then lead to the following happening:

The current from the battery will induce a magnetic field in the coil of the solenoid. This magnetic field will then induce a current, which will induce a secondary magnetic field around the wire.

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Answer is D, because by convention, the current is the direction that the positive charges are moving in, following the right hand rule, the current was determined to be moving towards the right.

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Questions sometimes asks for either of the two, and their difference is as follows:

Instantaneous velocity refers to the velocity at a certain point of time. This is usually expressed as the rate of change in displacement over time.

Average velocity refers to the velocity had the object been travelling at a constant speed, and can be expressed as the total displacement divided by the total time.

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Displacement is a vector quantity, and often refers to the distance between some reference point and the current position.

Velocity is also a vector quantity, refers to the rate of change of the displacement over time.

Acceleration is also a vector quantity, this is the rate of change of the displacement over time.

Some properties of the graphs if these values were graphed against time:

If acceleration is constant, and non-zero

Velocity would be a linear graph

If acceleration is 0

Velocity would be constant

Displacement would be a linear graph

Acceleration is 0

Velocity is 0

Displacement would be constant

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The most common way to describe Newton's Second Law of motion is through the formula F=ma.

However, it is more accurate to describe it as the rate of change in momentum over time, resulting in the following formula:

F = dmv/dt

Therefore, it can be said that the net external force acting on an object is equal to the rate of change of the momentum of the object.

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Complete this ASAP (then ask for the worked solution)

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Complete this ASAP (then ask for the worked solution)

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A4 Rigid Body Motion Paper 2 Exam Question

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Angular momentum is conserved when there are no external torques acting on a system.

Lets say that there is a disc rotating at some speed, if we placed an object on the disc, the object gain some angular momentum due to the rotation of the disc, but the disc will lose some speed. The loss in angular momentum in the disc is equal to the gain in angular momentum in the object. In this case, angular momentum is conserved.

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There are some graphs in A2 where the area under the graph represents another value:

Area under a force vs distance graph = Work done

Area under a acceleration vs time graph = change in velocity

Area under velocity vs time graph = change in displacement

Area under power vs time graph = work done

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When an object in motion collides with another object that is not in motion, the total momentum of the two objects will be the same before and after the collision.

We can find the amount of momentum being transferred from its impulse, which is the change in momentum. It is calculated by multiply the force by the interval of time the force is acted on the object.

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Kinetic Energy of Molecules and Temperature

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Kinetic Energy of Molecules and Temperature

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The average kinetic energy of molecules can be calculated using:

Ek = 3/2(kB)T

Where kB is the boltzmann constant.

It is seen that the average kinetic energy is proportional to the temperature. I think that when heat is transferred to a molecule, we are giving it more kinetic energy, rather than thinking about heat and kinetic energy separately.

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When the sun shines light on earth's surface, some energy is transferred to the surface of the earth.

Consider the case where the greenhouse effect does not take place.

The energy transferred to the ground will have some of it reflected due to the albedo effect, and some energy is inputted into the earth. However, the input of energy into the Earth must equal to the output of energy from the earth. Therefore, there will be radiation from the ground back into the space, equal to the input that the earth received after considering the albedo effect.

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States that the current entering a circuit and exiting the circuit must be equal.

Basically, lets say we have a circuit that is parallel. When the current reaches the point where it has to split into two different wires due to the parallel circuit, the sum of these two currents must be equal to the current that is entering the parallel circuit.

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Electrons exists in energy levels, very cool.

The implications of this is that we can excite the electron of an atom by giving it a specific amount of energy, and then after a while, it will deexcite and release the same amount of energy. The energy release and absorption usually happens in the form of photons of a specific wavelength.

If we give enough energy we are able to ionize the electron, ionized electrons will not go back to its ground state.

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The experimental proof to show that light behaves as a particle.

Shine light with enough energy on a metal surface and it will release electrons. Metals have a work function that is determined by what metal it is. The released electrons will have the energy of the light minus the work function of the surface.

We can also prevent electrons from being released if we run a conventional current in the direction of the electron's motion, then it will "decrease" the energy of the electrons. We call the voltage that completely stops the electrons from being ejected the stopping voltage, and it depends on the frequency of the light and/or the work function of the metal.

I think that if we made it such that the conventional current opposes the motion of the electrons, it would make the electrons go faster instead, and makes it easier to eject electrons, but I am not very sure.

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This shows the luminosity of the stars graphed against its surface temperature.

Something to mention is that the further to the right you go, the lower the temperature, unlike conventional graphs.

Stars that are on the same diagonal line usually have the same size, and the main sequence stars usually have the same size, and are seen from the main diagonal of the diagram. Many supergiants are above the diagonal line of main sequence stars.

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We use the right hand rule to determine the direction of the magnetic field, force and the velocity. It is rather similar to using the right hand rule for the vector product.

Of three of these quantities are vectors, and are all perpendicular to each other. For a positively charge, we say that the thumb is the direction of the velocity, the fingers (stretch out straight) are the magnetic fields, and the palm is the direction of the magnetic force.

Left hand rule is used for negative charges, the same rules applies here.

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electric force and some relations to other formulas

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electric force and some relations to other formulas

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So we know the typical formula to calculate electric force, kqq/r^2.

If we multiply it by r, we get the potential energy, which is similar to gravitational potential, as we multiply the force by some distance.

If we instead divide by one of the charges, we instead get the electric field strength, and this relates to the potential difference, as the field strength is simply the difference divided by some distance.

Pretty useful to know in tests in case i forget

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Basically, doppler effects states that there will be a change in the frequency of a wave if the source of the wave is in motion relative to an observer.

If the source is moving towards the observer, perceived frequency will become higher, and results in a higher pitch.

Whereas if the source is moving away from the observer, the perceived frequency will be lower, and results in a lower pitch

This is commonly experienced when we hear the sirens of the ambulance. Sometimes I wonder if they did this intentionally to help drivers know if there is an ambulance coming towards them.

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If it isn't already known, the orbital velocity is only affected by 2 things, the mass of the object being orbited (the sun for example), and the distance to the object.

The closer the object, the faster it will need to rotate to be able to stay in orbit, otherwise it will just crash into the object it was orbiting.

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This states the relationship between the frequency/period of a wave and its wavelength, and the product of the wavelength and the frequency will result in the velocity of the wave.

This is usually connected back to E2 because we relate the energy of a photon with its wavelength.

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Refraction happens when travelling light changes medium.

When less dense to more dense:

Refracted light goes towards medium

When more dense to less dense:

Refracted light goes away from medium

When light travels from a much denser medium, something known as total internal reflection, where the light will be reflected back.

This happens at a large angle, and the angle where this will happen is the critical angle. The critical angle is where the angle of incidence will result in the refracted light to be 90 degrees away from the medium

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Damping refers to the dissipation of energy within an oscillating system, usually happening due to resistive forces, causing the system to go back into its equilibrium position.

There are three types of damping

Critical damping

Goes back to its equilibrium position very fast without oscillating

Light damping

Continues to oscillate, and will eventually return to equilibrium after a long time

Heavy damping

Goes back to equilibrium without oscillating, but takes a long time.

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Since mechanical waves requires a medium to travel through, when the source moves, there will be relative motion between the medium and the source. In this case, the perceived frequency and the wavelength will be different.

However, if it was the case for a stationary source and an observer in motion instead, since the medium isn't squished together due to the motion of the source, the distance between the waves will remain the same, therefore the wavelength remains the same. However, because the observer will still be able to perceive a change in frequency

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The change in frequency or wavelength perceived by an observer due to being in relative motion to the source of a wave. We consider the component of velocity that is parallel to the observer's line of sight.

These are some of the more common cases:

Stationary observer and source

Stationary observer and source moving towards observer

Stationary observer and source moving away from observer

Observer moving towards stationary source

Observer moving away from stationary source

Keep in mind of the direction of the velocity of the moving component because you don't want to perform the wrong operation (plus minus) during calculations.

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This question involves wave interference, and asks us to find when we would get a maximum intensity at point P, this means that we have constructive interference at point P.

The question is asking for the wavelength, which we can connect to the requirements for constructive interference, which the phase difference between the two sources must be a whole multiple of the wavelength out of phase.

After this, the phase difference that were given from the question and the phase difference that was caused by the path difference needs to be equal to some multiple of the wavelength.

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This question is about how there will be a continuous range of wavelengths due to the component of velocity to our line of sight changing.

The trick to this question is to recognize that there will be a larger shift in wavelength for larger wavelengths, therefore B is correct.

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We need to consider that the reflected wave is actually being emitted by a moving source, so, we need to consider the perceived frequency by the moving observer and also the frequency that would be observed at the original source due to the movement of the observer.

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The position of the source when a wavefront is emitted would be the center of that wavefront regardless of whether the source is in motion or not.

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For this case, since the train does not decelerate, and is coming at a constant speed, there would be a constant frequency being observed, and the graph would look like a step function, as the train will immediately start to move away from the observer after passing the observer.

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There will be no change in perceived frequency when observing from a direction perpendicular to a source's motion. Also, because wavefronts are centered around the source, there is no relative motion, so any wavelengths the source measures would be exactly the same.

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An object's resistance to a change in rotation.

This is the angular equivalent to mass.

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Finding time using known final velocity and torque

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Finding time using known final velocity and torque

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Use newton's second law to find the angular acceleration

Apply kinematics equation for angles to find final velocity, in this case, we would want the equation without an angular displacement component as it is unknown.

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There are two types of moment of inertia:

Shapes

Discrete points

For shapes, we are usually given the formula.

For discrete points, we have to sum the moments for each of these points using the formula ML^2

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We can calculate the angular displacement as we know the time, initial velocity, final velocity and acceleration.

Since angular displacement is given in radians, and there are 2pi radians in a full circle, we just take angular displacement divided by 2pi.

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You know that sound is a longitudinal wave. However, sometimes we use a sine wave or cosine wave graph to describe sound wave. What exactly is this graph? What quantities would go on the y-axis and x-axis?

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Question from Teacher Joshua: Changes during refraction?

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Question from Teacher Joshua: Changes during refraction?

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When light passes across a boundary into water or glass in undergoes refraction. Refraction doesn’t change the colour of light, but its wavelength does change during refraction.

Explain how is this possible.

Hint: 1. What stays constant during refraction and what changes?

2. Think about topic E1 atomic physics and the cause of colour.

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This questions require us to realize that when we refer to maximum in this context, we mean that constructive interference happens, whereas a minimum would be where destructive interference happens. In this case, we see that at point P, two crests are overlapping each other, so it is a maximum. At point Q, we see that two troughs are overlapping each other, so it is a maximum as well.

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In this question, we are asked to find the albedo of the surface. First, we need to see the incident intensity on the surface, this would be the amount of radiation absorbed by the clouds. Then we can divide the amount of reflected light by the amount of radiation that is incident to the surface.

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Surfaces and absorbed incident intensity

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Surfaces and absorbed incident intensity

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This question requires us to recognize that snow is white, and this means that it reflects most of the light that is incident on it. So, if snow reflects more light, then the rainforest must absorb more intensity

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This question is kind of misleading due to the diagram, but the question is actually asking for the intensity of radiation incident on the planet's surface averaged over the entire surface, not just where the incident light is affecting.

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Assumptions of the Kinetic theory of an Ideal gas

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Assumptions of the Kinetic theory of an Ideal gas

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We assume that:

Molecules are in constant, random motion

The particles have a negligible total volume

No intermolecular forces

The collisions between particles are perfectly elastic

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In E2, we learned that molecules have discrete energy levels, this means that they only interact with photons that carry a specific amount of energy. In this case, greenhouse gases interact with infrared radiation, if we convert the wavelengths of IR radiation, we get around 1eV, this is why B is the correct answer.

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Adiabatic processes are a type of thermodynamic process where there is no heat loss or gain.

However, heat loss or gain does not mean that there is no change in temperature, but instead refers to that there is no change to the internal energy of the system.

Adiabatic processes, when graphed, are usually steeper than isothermal processes.

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Looking at this question, we already know that cloud formation is definitely affects the albedo of the planet from other questions regarding the energy balance. Same for the nature of surfaces, different materials reacts to light differently. The wavelengths of the incident radiation also is a factor, because light of certain wavelengths have special interactions with different materials. Therefore, the albedo of a planet is independent of the intensity of the incident radiation.

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“Using the first and second laws of thermodynamics, explain why Earth’s surface temperature is higher than the temperature predicted for a planet without an atmosphere.”

Explain why the energy radiated by Earth has a much higher entropy than the energy received from the Sun, making reference to the number of available wavelengths.

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“Explain why greenhouse gases absorb IR but not visible light, using harmonic oscillator models of molecular bonds.”

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To solve a question where we consider the internal resistance of a battery, we need to understand that we would consider the internal resistance of the battery would be connected in series with the rest of the circuit, which we then apply Ohm's Law and the formula to calculate the total resistance.

For a real battery, we consider the internal resistance, whereas for an ideal battery, we assume that there is negligible or no internal resistance. The terminal voltage is the actual voltage of a source, so it considers any internal resistances that it may have, whereas emf is just the energy that is provided by the source.

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For adiabatic expansion, the pressure will decrease as volume increase, the arrow goes to the right, so work is done by the gas, so W > 0. If we compared the work done by adiabatic processes and isobaric processes, given that they start at the same state, and reach the same final volume, the isobaric process will have done more work as it is a horizontal line, whereas the adiabatic curve goes downwards to the right.

For the change in temperature, external heat is required to be added to the system for isobaric expansion, using ideal gas law, so the change in temperature > 0. For adiabatic expansion, Q = 0, so since W > 0, then delta U < 0 must be true, since the internal energy of a monoatomic gas is related to its temperature, then the change in temperature must be negative as well.

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For variable resistors where the resistance is increased, the current running through the circuit would be lower, emf remains the same, but because there will be less potential difference across the cell, the terminal voltage would be higher, this is described by the equation:

V = ε - Ir

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This question mainly relies on how well we can understand what is being described. So the wave tells us the leftward and rightward displacement using up and down.

We want to find the displacement at time t, which is the dotted line. Notice that it mostly goes below the solid line, so its arrow would be down, which is a displacement to the left.

And for its velocity, since its displacement is to the left, then its velocity should be in the same direction as it was moving at time t.

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I find this question kind of weird, but this question requires us to understand that the melted spots are where constructive interference is taking place. We can approximate the wavelength by taking the distance between the center of the left and right melted spots, which then can find the frequency using v = f*lambda.

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Given that the system is closed, and in thermal equilibrium. We know that the gray body radiates the same intensity as it absorbs, so T(in) = T(out) for the grey body. The intensity entering the grey body would then be equal to the intensity radiated by the black body, multiplied by the emissivity of the grey body, and using Stefan's Law, we can find the relationship between the temperature of both bodies

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Reference frames are defined as "a set of coordinates to record the position and time of events". It can be thought of a perspective, as different observers may record down different positions due to having different perspectives.

Inertial reference frames refers to a non-accelerating reference frame (in a state of inertia), so either it is at rest, or staying at a constant velocity.

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The concept where Newton's Laws of Motion are identical within all inertial frames.

This is because if an experiment was conducted within a laboratory and in a moving ship, both experiments will yield the same result.

Take Newton's First Law for example, when a ship is moving at constant velocity, an object within the ship that was at rest will remain at rest, given that there is no external acceleration acting on the object.

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Position and Time in Galilean Relativity

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Position and Time in Galilean Relativity

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In Galilean Relativity, for two different inertial reference frames, the time observed for an event will be the same for both inertial frames. But the position recorded will be different as a result of relative velocity between the two reference frames.

The formula to calculate the position of an event would be given as:

x'=x-ut

Where u is the velocity measured in the stationary reference frame.

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The position and time axes will change as a result of relative velocities between two IRFs.

The position axes will change and the gamma factor is required as a factor compared to the galilean relativity

For the time axes, rather than using the time dilation formula, we need to use the Lorentz transformation for the time coordinates

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To measure parallax angle, I assume that the measurements of distance should be equal, so B may not be the correct answer, A doesn't sound correct either, because I remember the Sun being involved and the astronomical unit being involved. So I think C is the correct answer

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This just memorization, but the correct answer is C