IB Physics HL Resonance

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A tutorial sheet of resonance questions from the Engineering Physics option is given below.

  1. An oscillator is subject to no damping. Describe its motion if its natural frequency is 2𝜔 and the driving frequency is 𝜔.
  2. An oscillator undergoes damped oscillations. Is the frequency of the damped oscillations the same as the undamped oscillations?
  3. An oscillator has a natural frequency 𝜔 and is subject to a damping acceleration that is proportional to its velocity with a proportionality constant 2k. Write down the condition for (a) damped oscillations (b) critically damped oscillations (c) overdamping.
  4. An oscillator has damping. When the damping is increased does the frequency at which the maximum forced oscillations occur increase or decrease? Give a reason.

IB Physics Resistors and Capacitors

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A tutorial sheet of resistor and capacitor questions follows.

  1. An uncharged 6.0 mF capacitor is placed in series with a battery of emf 12 V. Find the charge on the capacitor after 6.0 min.
  2. A 20 pC capacitor is connected in series to a 20Ω resistor. The initial charge on the capacitor is 2.0 mC. Find the charge on the capacitor after 20.0 s.
  3. A battery of emf 12.0 V and internal resistance 2.0 Ω is used to charge a 600 pF capacitor for 5.0 min. The capacitor is initially uncharged. Find (a) the work done by the battery in the 5.0 min, (b) the energy stored in the capacitor after 5.0 min.

IB Physics Viscosity

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A tutorial sheet on viscosity is given below.

  1. Is viscosity a force?
  2. What is the cause of viscosity?
  3. State the SI unit for viscosity.
  4. A small sphere of radius r is falling vertically in a fluid of viscosity 𝛈 and density 𝜌. Find an expression for the terminal speed of the sphere.
  5. A viscous fluid flows steadily through a horizontal pipe. Does the pressure exerted by the fluid change along the pipe?

IB HL Physics Time Dilation

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The new HL Physics course includes special relativity for all students. Below is a tutorial sheet on time dilation.

  1. Do moving clocks run slower?
  2. Define proper time.
  3. A particle has a lifetime of 2.0 µs in its rest frame. The particle moves at 0.8c relative to a laboratory. Find the lifetime of the particle according to an observer in the laboratory reference frame.
  4. Two detectors in a laboratory are 20.0 cm apart. A particle moving at a constant speed of 0.9 c relative to the laboratory passes through the detectors. What is the time of passge between the detectors as measured in the reference frame of the particle?

IB Physics EMF of a cell

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Which of the following is/are correct regarding the emf of a cell?

  1. The voltage of the battery.
  2. The potential difference across the terminals of the cell when zero current passes through it.
  3. The work done in moving unit charge through the cell.
  4. The work done in moving unit charge around the circuit.
  5. The chemical energy changed to thermal energy when unit charge moves through the cell.
  6. The power per unit current passing through the cell.

IB HL Physics Electric Field in a Moving Conductor

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A conductor moves in a magnetic field. Is the electric field in the conductor zero? A tutorial sheet follows.

  1. State Ohm's law in terms of electric field (E) and current density (J).
  2. A current flows through a stationary conductor that obeys Ohm's law. Is there an electric field inside the conductor? Outside of the conductor?
  3. A straight metal rod of length L is a perfect conductor (zero resistance). The rod moves at a constant velocity v along the x-axis through a uniform magnetic field B along the z-axis. The length of the rod is along the y-axis. Find the electric field in the rod in the (a) reference frame of the laboratory, (b) reference frame of the rod.
  4. In the previous question find the force acting on a charge q in the rod relative to the reference frame of the rod.
  5. In question 3 the rod has a constant non-zero resistance. Find the force on a charge q in the rod relative to the reference frame of the rod.

IB Physics Work Done on a Moving Charge in a Magnetic field

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A common question is finding the work done on a charge as it moves in a magnetic field. Is it always zero? A tutorial sheet of questions investigates this concept.

  1. A constant, uniform magnetic field B acts along the x-axis. A charge q enters the field at a velocity v at an angle 𝜃 to the x-axis. Is work done on the moving charge?
  2. A constant current flows along a long straight wire that is along the x-axis. At a certain instant a charge q is moving along the x-axis at a speed v towards the wire. Is work done on the charge?
  3. A magnetic field increases at a rate proportional to the time, B = kt, and its direction is parallel to the x-axis. Does the magnetic field do work on the moving charge in question 1? Does the associated electric field do work on the moving charge?

IB Physics Collision rate in an ideal gas

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A tutorial sheet on particle collisions in an ideal gas is given below.

  1. The temperature of an ideal gas is doubled, the volume of the container being kept constant. Describe the change in the rate of collision of the particles with the walls of the container.
  2. The pressure of an ideal gas is tripled, the volume being kept constant. Describe the change in the rate of collision of the particles with the walls of the container.
  3. The volume of an ideal gas is reduced by one-quarter, the temperature of the gas being kept constant. Describe the change in the rate of collision of the particles with the walls of the container.
  4. At what conditions does a real gas behave closest to an ideal gas?

IB Physics Gravitational field strength

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A tutorial sheet of questions on gravitational field strength is below.

  1. The mass of the Moon is 1/81.3 that of the Earth. Assuming a model in which the bodies are considered to be point particles at rest, find the location of the point in space where the resultant gravitational field is zero.
  2. In question 1 consider of model in which the Moon moves in a circular path about the centre of the Earth. Does the zero field point move closer, stay the same or move further away from the Earth? Calculate its position assuming an orbital period of 27.32 days.
  3. In question 1 is/are there points inside the Earth or the Moon where the resultant gravitational field strength is zero?

IB Physics Relativity of E and B fields

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A tutorial sheet of questions on E and B fields is given below.

  1. A uniform magnetic field is along the z-axis. A reference frame moves relative to the magnetic field with its velocity vector parallel to the x-axis. Describe the fields according to an observer in the moving reference frame.
  2. A uniform electric field is along the z-axis. A reference frame moves relative to the electric field with its velocity vector parallel to the x-axis. Describe the fields according to an observer in the moving reference frame.
  3. Without special relativity there is no magnetism. Magnetic effects are a consequence of Einstein's special theory of relativity. True or false?
  4. Does Newton's third law apply in special relativity?

IB Mathematics Normal Distribution

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A tutorial sheet of practice questions on the normal distribution is given below.

  1. In a nation wide exam µ=65 and σ=15. Find (a) the percentage of marks greater than 70. (36.9) (b) the percentage of marks between 40 and 70. (58.3) (c) the probability that at least one of three randomly selected students scored more than 70. (d) the probability that two of three randomly selected students scored more than a certain score is 1/5. Find the score.
  2. More to come

IB Physics Engineering Mechanics

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A tutorial sheet of questions for the engineering physics topic is given below.

  1. A uniform spherical shell of mass M has an inner radius a and an outer radius b. Find the moment of inertia of the shell about an axis through its centre.
  2. What is the difference between torque and work done by a force?
  3. Does the angular momentum of a spinning object always have the same direction as its angular velocity?
  4. A disc of moment of inertia 3I has angular velocity ⍵ about its axis in a horizontal plane. Another disc of moment of inertia I is placed from a state of rest on the first disc with their axes coincident. After a short time both discs have a common angular velocity. Find the kinetic energy "lost" in this interaction. Where does it go?

HSC Physics Cavity Resonance Measurement of the Speed of Light

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Some questions on the measurement of the speed of electromagnetic waves using standing waves in a cylindrical metal cavity are given below. The method is that of Essen and Gordon-Smith (1947).

  1. How can a cylindrical cavity have a resonant frequency?
  2. Essen and Gordon-Smith (1947) state the following equation for the speed of electromagnetic waves in an evacuated cylindrical cavity. What do the symbols mean?