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

IB Physics Capacitance

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

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

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?

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?

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

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?