IB Physics Binding Energy per Nucleon

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Tutorial questions on binding energy are below.

  1. Define nuclide.
  2. The atomic mass of the N-14 atom is 14.003074 u. Determine the atomic mass of the nucleus, the mass defect of the nucleus and the binding energy per nucleon of the nucleus. [13.999231 u, 0.112363 u, 7.48 MeV per nucleon]
  3. The atomic mass of the B-10 atom is 10.012939 u. What is the binding energy per nucleon of the B-10 nucleus? [6.475 MeV per nucleon]
  4. Which nuclide has the largest total binding energy? [Ni-62]
  5. Which nuclide has the largest binding energy per nucleon? [Fe-56]
  6. List the three largest binding energies per nucleon. [Fe-56, 1.082 MeV, Ni-62 1.077 MeV, Fe-58 1.071 MeV]
  7. Which term is more significant, total binding energy or biding energy per nucleon? [binding energy per nucleon, see note by Hans A Bethe in Physics Today April 1991 page 15]
  8. The binding energy per nucleon of a nucleus is negative in sign. Why is this? [See Physics Education, Vol 36 No 5 p375 Sep 2001, article by George Marx]

IB Physics River Crossing Problems

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A tutorial sheet of harder questions on this topic follows and will be added to. A reference is Physics Education Vol 34 Number 3 May 1999, p 148

  1. A boat leaves point P on one side of a river bank and travels with a constant speed u relative to the water in a direction toward Q on the other side of the river directly opposite P and distant d from it. If r is the distance of the boat from Q and the angle between r and PQ is 𝜽, show that r = dsec𝜽/(sec𝜽+tan𝜽)u/v, where v is the speed of the river.

  2. In question 1 if u = v show that the path is an arc of a parabola.

  3. A boat crosses a river of width w with velocity of constant magnitude u always aimed toward a point on the opposite shore directly opposite its starting point. If the water flows at a constant speed u how far downstream does the boat arrive on the opposite shore? [w/2]

IB Physics Melting Icebergs

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A tutorial set of questions on floating objects is given below.

  1. An ice cube floats partially submerged in a container of water. Does the water level rise when the ice melts? See Physics Education 36, no 1, p75 Jan 2001 .

  2. An iceberg floating in the sea melts. Does this cause the sea level to rise?

  3. A steel ball bearing floats in a beaker of mercury. Water is now poured on top of the mercury. Does the ball bearing sink, rise or stay the same depth in the mercury?

IB Physics Galileo's Dying Breath

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A tutorial sheet of estimation questions is given below.

  1. Estimate how many molecules of air exhaled by Galileo during his dying breath you are likely to breathe during one breath. Surface area of the Earth = 5x108 km2.
  2. Estimate the time taken by a ray of light to travel the diameter of a hydrogen atom.
  3. Estimate the number of oxygen molecules in the air in a science laboratory.
  4. Estimate the number of atoms in a grain of sand.
  5. (After Enrico Fermi) Estimate the number of piano tuners in Chicago.
  6. Enrico Fermi was 10 miles from the blast site of the first atomic bomb. He released pieces of paper from rest and found that they travelled 2.5 m as the blast wave passed. Estimate the energy released in the blast. 1 ton of TNT yields 4x109 J of energy. [equivalent to 10 kilotons of TNT]

IB Physics Critical Angle

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A tutorial sheet on critical angle, a topic in SL waves, is given below.

  1. Define the term critical angle.
  2. Why can total internal reflection only occur if the wave speed in the first region is less than the wave speed in the second region?

  3. A diver is at a depth of 3.0 m in water of refractive index 1.3. The diver looks upwards. What is the diameter of the image of the horizon that they see?

  4. An electromagnetic wave strikes the end of an optical fibre at an angle 𝜽 to the normal. The refractive index of the cladding layer is n 2 and the refractive index of the optical fibre is n 1 . Show that the maximum value of 𝜽 which allows transmission of light along the fibre is given by sin𝜽 = (n1 2 -n2 2 ) 1/2 .

  5. For more applications of critical angle see Physics Education Vol 17, No 2, March 1982, p 86

IB Physics Capacitance

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A tutorial sheet on capacitance, a section in HL topic 11, is given below.

  1. What is the meaning of the term capacitance?
  2. For a given capacitor at a constant temperature, is the "capacitance" constant?
  3. Write down an expression for the capacitance of a charged sphere of radius R in a vacuum.
  4. Express the unit of capacitance in terms of SI base units.
  5. An uncharged capacitor of capacitance C is connected in series with an open switch across a 12 V DC battery of zero internal resistance and a resistance R. The switch is now closed. Describe the build up of charge on the capacitor.
  6. A capacitor of value C has a charge Q. It is connected in series to a resistor R and an open switch. The switch is now closed. Describe the current through the resistor.
  7. Two capacitances C1 and C2 are connected in series across a battery. Find an expression for the total capacitance. Show your working.

  8. Two capacitances C1 and C2 are connected in parallel across a battery. Find an expression for the total capacitance. Show your working.

  9. An uncharged capacitor is charged by being connected by wires to a battery of constant emf and zero internal resistance. (a) Is the current in the connecting wires equal to the rate of increase of charge on the plates? (b) Is there a current in the space between the plates? (c) Is there a magnetic field in the space between the plates? (d) Is the work done by the battery equal to the energy stored in the capacitor?

  10. In the IB Physics Data Booklet a formula is given for the capacitance of a parallel plate capacitor. What are the assumptions for this formula?
  11. To take into account the finite area of the plates of a capacitor see the Berkeley Physics Course Volume 2 Electricity and Magnetism by E M Purcell (red version page 97, blue version page 105) for a table of end correction values. Another reference is Physics Education, Vol 17, Number 2, March 1982, page 35.

HSC Physics Bouncing Superballs

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A tutorial sheet involving collisions is given below.

  1. A tennis ball is dropped from a height h1. It bounces to a height h2. Is momentum conserved in the collision? Is kinetic energy conserved in the collision? Is energy conserved in the collision?
  2. A steel ball bearing of mass M moving at a speed U collides in a line with two balls of mass M that are at rest. Why doesn't each ball move at U/3 after the collision?
  3. Imagine two superballs, of different mass, placed one on top of the other and dropped from a height H very large compared to the radius of each ball. Assuming an elastic collision with the ground, what is the maximum height to which the top superball can bounce? [9 H]
  4. For more multi-highball problems see Anthony Anderson, Physics Education, vol 34, number 2, March 1999, page 76.

IB Physics Phase Difference

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A tutorial sheet on phase difference is given below.

  1. What does the term "in phase" mean?
  2. What does the term "180 degrees out of phase" mean?
  3. How do we define phase difference?
  4. Are points on a progressive wave all in phase?
  5. A progressive wave has a wavelength of 1.0 m. What is the phase difference between two points on the wave that are 0.8 m apart?
  6. Are points on a standing wave on a string all in phase?
  7. The wavelength of the standing wave on a string is 1.0 m. What is the phase difference between two points on the string that are 0.8 m apart?
  8. In an AC transformer are the primary and secondary voltages in phase?
  9. In an AC transformer are the primary and secondary currents in phase?
  10. For application to transformer problems see S J Osmond, Physics Education, vol 17, no 5, Sep 1982 p236

IB Physics Why is it Hotter in Summer than in Winter?

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A tutorial sheet of true/false questions on this work in topic 8 is given below.

  1. Summer occurs when the Earth in its orbit is closest to the Sun.
  2. The angle of the Sun above the horizon causes less energy to strike the surface of the Earth in winter.
  3. The low Sun angle causes a bundle of Sun's rays to be spread over a larger area of the surface of the Earth in winter than summer.
  4. The Sun is lower above the horizon in winter causing a lower amount of energy to enter the atmosphere.
  5. The Sun is above the horizon for a shorter time in winter reducing the time for a bundle of Sun's rays to heat the surface of the Earth.
  6. The atmosphere is not heated by the Sun but by reflected longer wavelength radiation from the Earth. In winter each square metre of surface reflects less energy and so the surrounding atmosphere is at a lower temperature.
  7. The variation in the maximum angle made by the Sun above the horizon during the year is due to the inclination of the Earth's spin axis at 66.5° to the plane of the Earth's orbit.
  8. People at the equator experience 12 hours of night and day every day of the year.
  9. Sunset in Melbourne on January 1 is before sunset in Sydney.
  10. Sunrise in Melbourne on January 1 is after sunrise in Sydney.
  11. See Roy L Bishop, Journal of the Royal Astronomical Society of Canada vol 87 No 5 p346 1993

HSC Physics Does ∆U always equal mg∆h?

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A tutorial sheet of gravitational potential energy questions is below.

  1. What do the symbols in the equation ∆U=mg∆h mean?
  2. When is it correct to use the equation ∆U=mg∆h?
  3. What is the meaning of the equation U=-GMm/r?
  4. When should we use the equation U=-GMm/r?
  5. An object of mass m is lifted through a vertical height ∆h from the surface of the Earth. If the radius of the Earth is R shew that ∆U=mg∆hR/(R+h), where g is the acceleration due to gravity at the surface of the Earth.
  6. An apple of mass 85 g falls from a height of 2.5 m to the ground. What is the change in gravitational potential energy of the apple? [0.99999961mg∆h ≅ mg∆h, -2.08 J]
  7. Mt Everest is 8848 m sbove sea level. If the radius of the Earth is 6400 km show that the increase in gravitational potential energy of a climber of mass m in going from sea level to the top of Mt Everest is 0.9986mg∆h.
  8. The International Space Station (ISS) orbits the Earth at an average altitude of 408 km. If its mass is 419,700 kg determine the gain in gravitational potential energy in lifting this mass from the surface of the Earth to its final height.[0.9401mg∆h, 1.58x1012 J]

IB HL Physics Resolution

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Image resolution is a poorly understood topic in IB HL Physics. A tutorial sheet is given below.

  1. A double star is examined through a telescope. The stars appear too close together to be resolved. To resolve the image of the stars a coloured filter is placed in front of the telescope. Which coloured filter could allow the images to be resolved? Red or violet?
  2. Two stars are observed through a telescope and appear too close together to be resolved. Does increasing the magnification of the telescope resolve the images?
  3. The headlights of a stationary car subtend an angle of 1" at a distant point. The human eye can distinguish between two images that are 1' apart. If the wavelength of the light is 550 nm, determine the minimum diameter of a telescope that can allow the headlights to be resolved as separate images.
  4. A satellite is in orbit 350 km above the surface of the Earth. Newspint has a size of 3.0 mm. Determine the diameter of the aperture of a camera in the satellite that will allow a newspaper on the Earth to be read from orbit in light of wavelength (a) 600 nm, (b) 400 nm. The resolution of the human eye is 1'.
  5. If we increase the amount of light entering a telescope, keeping the diameter and the wavelength constant, does this improve the image resolution? Why?

HSC Physics Rutherford's Nuclear Atom

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A tutorial sheet of miscellaneous questions on Rutherford’s nuclear model is given below.

  1. What is a spinthariscope?
  2. At which university was Rutherford a professor when his model was proposed (1911)?
  3. Why were alpha particles used in the famous experiment?
  4. Why was a gold foil used?
  5. Do the alpha particles hit the gold atoms in the foil?
  6. Where are the electrons in Rutherford's model of the atom and what are they doing?
  7. Did most of the alpha particles pass through the gold foil with small amounts of scattering? Give a reason.
  8. Some alpha particles were scattered through angles greater than 90°. Give the approximate number and give a reason for this.
  9. In an alpha particle scattering experiment the speed of the alpha particles is doubled. Will the number of scattered alpha particles at a particular angle increase, decrease or stay the same?
  10. In an alpha particle scattering experiment the thickness of the foil is doubled. Will the number of scattered alpha particles at a particular angle increase, decrease or stay the same?
  11. An alpha particle scattering experiment is repeated with a pure thin metal sheet of double the atomic number of the first case. Will the number of scattered alpha particles at a particular angle increase, decrease or stay the same?
  12. Draw the famous diagram showing the scattering of an alpha particle by a positively charged gold nucleus. (Many people draw this diagram incorrectly, be careful).
  13. In question 12 draw the diagram for a negatively charged particle fired at a gold nucleus. Is the path of a negatively charged particle, fired with the same initial kinetic energy, the same as that of a positively charged particle of the same magnitude?
  14. Is the scattering of alpha particles proof that the nucleus is positively charged?
  15. Rutherford's scattering equation was deduced using classical physics and then later quantum mechanics, an example of classical physics principles giving the correct result for an atomic process. State this equation and find out who derived it for Rutherford. Use the equation to sketch the graph of s(𝜽), where 𝜽 is the angle through which an alpha particle is deflected.
  16. How did Geiger determine the number of alpha particles scattered through each angle?

IB Physics Voltage

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A tutorial sheet on voltage and potential difference is given below.

  1. Is voltage the same as potential difference?
  2. Define electric potential.
  3. Define electric potential difference.
  4. Point A in an electric field has a potential of +15V. Point B in this field has a potential of -12V. (a) What is the potential difference between A and B? (b) What work is done by an external force in moving a +1C charge at a constant speed from A to B? (c) what work is done by the field when a proton moves from A to B?
  5. Is voltage the same as energy? Explain.
  6. Is potential difference the same as energy? Explain.
  7. Sketch the equipotential lines around the point charges +Q and -Q.
  8. Sketch the equipotential lines around the point charges +4Q and -Q.
  9. Can electric field lines ever intersect?
  10. Can equipotential lines ever intersect?

HSC Physics Fundamental Particles

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  1. What is meant by the term fundamental particle?
  2. Is a neutron a fundamental particle?
  3. List three fundamental particles.
  4. Is a photon a fundamental particle?
  5. Is a positron a fundamental particle?
  6. Do an electron and a positron have opposite spins?
  7. In beta minus decay a neutron "converts" into a proton. How can a neutron convert into a proton?
  8. Radioactive materials emit gamma rays. Where does the energy of a gamma ray come from?
  9. Does a positron have a negative energy? [No, Dirac said that this would make the "dynamical relations all wrong", see Physics Today, June 2001, p63]
  10. Does a fundamental particle have a radius? [no]
  11. This year the radius of a proton was measured as 0.831±0.014 fm. This is given in Nature , 575, 61-62, 2019