IB Physics Why does a Satellite not Fall to the Earth?

A tutorial sheet on satellite orbits is given below.

1. A satellite orbits the Earth in a circular path. Is the satellite "falling" towards the Earth?
2. As a satellite orbits the Earth in a circular path does the Earth "fall" away from the satellite?
3. Determine the orbital speed of a geostationary satellite.
4. How far does a geostationary satellite "fall" towards the Earth in one second? How far does the Earth "fall" away from the satellite orbit in one second?

IB Physics Double Slit Interference

A tutorial sheet on Young’s double slit experiment follows.

1. A Young's double slit experiment is carried out with the wavelength much greater than the slit separation. Describe the intensity pattern on a distant screen.
2. In a Young's double slit experiment the wavelength is much less thn the slit separation. Describe the intensity pattern on a distant screen.
3. In a double slit experiment with slits of width b separated by a distance d are all of the maxima on a distant screen of the same intensity?
4. A double slit experiment is carried out with b much less than d. Describe the intensity variation on a distant screen.

IB Physics Energy of Capacitors

A tutorial sheet of problems on the HL topic energy of capacitors is given below.

1. A capacitor gains a charge Q when it is connected by wires to a battery of emf V and zero internal resistance. Is the work done by the battery equal to the energy stored in the capacitor?
2. A charged capacitor of capacitance C is connected by wires to an uncharged capacitor of equal capacitance. Show that one half of the original energy is lost. Where does it go?
3. A capacitance C holds a charge Q and is connected in series with a resistance R. What is the heat energy released in R as the capacitor discharges?
4. A dielectric slab is placed between the plates of a parallel plate capacitor. Explain the change in energy of the capacitor if the slab is inserted keeping (i) the potential difference between the plates constant, (ii) the charge on the plates constant.
5. See Physics Education, vol 5, p 33, Sep 1998

IB Physics Half-life

A tutorial sheet on the terms decay constant, mean lifetime and half-life is given below.

1. Is the mean lifetime of a particle the same as the half-life of a sample? [No]
2. Show that mean lifetime of a nucleus = 1/λ, where λ is the decay constant.
3. Show that half-life of a sample = ln2/λ.
4. What is the definition of half-life of a sample?
5. Is the decay constant equal to the probability of a nucleus decaying?
6. The mean lifetime of a muon is 2.2 μs. Show that the half-life of a sample of muons is 1.52 μs.
7. A large number of dice are thrown and the die showing a 6 are removed on each throw. A graph is drawn showing the number of remaining dice versus throw number. Show that the decay constant is 1/6 and the half-life is 6ln2 throws.
8. Radioactive decay is a spontaneous, random process. Define each term.
9. Two samples of the same element have a different mass. How do the half-lifes of the samples compare?
10. Why is the half-life constant as a material decays?
11. A sample of half-life T1 decays into a material of half-life T2. How many daughter nuclei are present when N parent nuclei have decayed?
12. When a nucleus undergoes beta decay the daughter nucleus has the same number of nucleons as the parent nucleus but the atomic number increases or decreases by 1. True or false?
13. In the alpha decay of a nucleus the change in binding energy appears as the kinetic energy of the alpha particle and the daughter nucleus. Since the products have equal but opposite momenta the alpha particle has a much greater kinetic energy than the daughter nucleus. True or false?
14. Gamma decay occurs very often after alpha or beta decay which leaves the daughter nucleus in an excited state. The excess energy is released as a photon from the nucleus. The mass of the excited nucleus is greater than that of the ground state nucleus.True or false?
15. See P.Dunne et.al, Physics Education, Measurement of the mean lifetime of cosmic ray muons in the A level laboratory, 33, Number 5, 1998.

IB Physics Centrifugal Force?

A tutorial sheet on rotating reference frames is given below.

1. "For matter in a circular orbit at radius r around a mass M the centrifugal force and the gravitational attraction balance". Is this statement correct?
2. A tube containing liquid is spun about a vertical axis through one end. Where in the tube is the pressure greatest? Show that the pressure difference between the end of a straight tube of length L and its axis is ⍴⍵²L²/2, where ⍴ is the density of the fluid in the tube and ⍵ is the angular speed of the tube. The tube rotates about an axis through one end perpendicular to the tube.
3. A bucket of water spins at a constant rate about an axis through its centre. Why does the water build up at the edge of the bucket? (the fluid at the edge has greatest speed, creating a pressure gradient in the fluid between the centre and the edge pushing the fluid highest at the edges, there is no centrifugal force in an inertial reference frame)
4. Why does the acceleration due to gravity on the surface a planet decrease if the planet spins faster?
5. A space station has a large toroidal (doughnut) shape. When it spins are objects inside the space station weightless?
6. A bead is placed half-way along a smooth horizontal wire. The wire now spins about a vertical axis through one end. Why does the bead move outwards along the wire?
7. In question 3 there are now two fluids in the bucket, each of different density ⍴₁ and ⍴₂. What is the shape of the common surface when the bucket is spun at a constant angular speed ⍵?

IB Physics Atomic Mass

A tutorial sheet on atomic mass follows.

1. Define the term atomic mass.
2. What is the atomic mass of the C-12 atom?
3. The atomic mass of carbon is 12.011 u. Why is this not exactly 12 u?
4. Is 1 u the mass of one proton?
5. Is the mass of a nucleus equal to A u where A is the mass number of the nucleus?
6. Give two reasons why the mass in u of a nucleus is not equal to the mass number of the nucleus. (protons and neutrons have a slightly different mass, the nuclear binding energy varies between nuclei; for two nuclei having the same mass number the one with greater binding energy will have a smaller mass).

IB Physics Static Electricity

A tutorial sheet on electroscope questions is given below

1. A radioactive sample is placed inside a charged electroscope. Describe what happens to the leaves of the electroscope.(radiation ionises the air inside the electroscope creating ions which are attracted to the leaves reducing their net charge causing them to collapse gradually).
2. A rod is brought near the cap of a positively charged electroscope. The leaves of the electroscope collapse and then diverge as the rod comes closer to the cap. Must the rod have a net negative charge? (yes, in this case the size of the charge on the rod is much greater than the size of the charge on the electroscope).
3. An electroscope has a net positive charge. A rod is brought near the cap of the electroscope and the leaves continually diverge as the rod approaches. Must the rod have a net positive charge? (yes).
4. A rod is brought near the cap of a positively charged electroscope. The leaves of the electroscope diverge when the rod is near the cap. Must the rod have a net positive charge? (no).
5. What is the test for determining the relative sign of the charge on a charged electroscope and a rod? (observe the initial effect; if the leaves collapse they are oposite in sign,if they diverge they have the same sign).
6. A charged body at first attracts an uncharged object. True or false? (True. When a charged ebonite rod is brought near small pieces of paper a charge of unlike sign is induced on the near side of the paper attracting them to the rod. When contact is made with the rod charge of like sign is transferred to the paper repelling it from the rod).
7. An uncharged metal disc has a radius a. A point charge q is placed on the axis of the disk at a distance d from its centre. What is the magnitude of the electric force acting on the charge q?
8. A metal disc of radius a has a charge Q. What work was done in charging this disc?

IB Physics Harder Questions

1. Two parallel wires each of length 2.00 m and mass 50.0 g are supported from the same point by light insulating strings of length 1.00 m and carry equal currents of 100.0 A in opposite directions. Determine the angle between the strings. (5.18°)
2. Two point charges of +6.00 μC and mass 50.0 g are suspended from a point by two light insulating threads of length 37.0 cm. Find the angle made by each string with the vertical when the charges are in equilibrium. (58.8°)
3. A 1200 kg car rounds a curve of radius 70 m banked at an angle of 12°. If the car is travelling at a constant speed of 90kmh ^-1 , determine the magnitude of the friction force between the tyres and the road. (8035N)
4. A bicycle and rider of total mass 75.0 kg can coast down a 4.00° hill at a constant speed of 10.0 kmh^-1. At maximum exertion the cyclist can descend the hill at a speed of 30.0 kmh^-1. Using the same power, at what speed can the cyclist climb this hill? Assume that the drag force on the cyclist is proportional to the square of the speed of the cyclist. (27.7 kmh^-1)
5. A ball is tied to a string of length L the other end of the string being fixed. The string is held horizontal and the ball is released from rest. A peg is located a distance 0.8L directly below the point of attachment of the string. Find the speed of the ball when it reaches the top of its circular path about the peg.
6. Tarzan's problem. A rope of length 4.00 m hangs from a tree branch at the edge of a cliff. Tarzan runs at 10.0 ms^-1 and grabs the rope at a height of 2.00 m. What is the maximum width of the valley that he can jump across? (13.6m, lets go of rope at 37.76° to the vertical). See The Physics Teacher, Jan 2014, page 6 for references.
7. Tarzan tries again. Tarzan needs to jump across a valley of width 15.0 m. If the rope length and grab height are the same as in the previous problem, what is the least speed at which he must run if he is to reach the other side? (10.6 ms^-1, lets go at 38.46° to the vertical)

Mathematical Tripos Dynamics and Relativity 2020

Below are my answers to the 2020 MT Part 1A Dynamics and Relativity questions.

1. 4C (i) 2b²/(p(b² - p²)) (ii) A = (L²/b² - 2k/R), B = 2k, C = - L²
2. 11C, ⍵ = aq(1-e^{-λt/(a2(1+q))})/λ , q = 93/70
3. 12C (a) sin(𝜽/2) = E/√( 4E² - M²c⁴ ) (b) f(r) = √( (1 - r²)/(1 + 3r²) ), ct = c𝛕/2√( 3 + 1/r² ), x = c𝛕/2√( 1/r² - 1 )

IB Physics Why do Tyres of a Moving Car Heat Up?

As a car moves along a road its tyres heat up. This is due to friction between the tyres and the road. True or false? False. The work done by the friction force on a rolling object is zero. Where does the “heat” come from? If the tyres were solid would they heat up? From Physics Education.

IB Physics Binding Energy per Nucleon

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 Viscosity

Why is it that some liquids flow easily but some do not?

A reference is Physics Education Vol 34 Number 3 May 1999 page 149

IB Physics River Crossing Problems

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 Is Mass Converted into Energy?

A constant source of confusion in Physics is the "conversion"of mass into energy. Does it happen? NO it is already there.

1. Can matter be converted into energy?
2. Can mass be converted into energy?
3. Can energy be converted into mass?
4. Are energy and mass equivalent?
5. When does the equation E=mc² apply? {E is the rest energy of a mass m}

I

IB Physics Gravity in a Vertical Mineshaft

Does the acceleration due to gravity in a vertical mineshaft increase , stay the same or decrease with depth from the surface of the Earth? [increases, The Observatory, p340, Vol 121, No 1164, 2001 October, J W Warren in response to J B Tatum]

HSC Physics Beckham's Free Kick

Why does a football curve so much after it is kicked?

See Physics Education vol 36 number 1 January 2001 page 10.

HSC Physics Area Under Momentum-Velocity Graph

The ‘area” under a momentum-velocity graph has the dimensions of energy. What is the significance of this area?

See Physics Education vol 36 Number 1 Jan 2001 page 61 Richard Newburgh Harvard Extension School

IB Physics Melting Icebergs

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

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

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